Second law of thermodynamics

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close to the initial one. The Poincaré recurrence time is the length of time elapsed until the return. It is exceedingly long, likely longer than the life of the universe, and depends sensitively on the geometry of the wall that was removed by the thermodynamic operation. The recurrence theorem may be perceived as apparently contradicting the second law of thermodynamics. More obviously, however, it is simply a microscopic model of thermodynamic equilibrium in an isolated system formed by removal of a wall between two systems. For a typical thermodynamical system, the recurrence time is so large (many many times longer than the lifetime of the universe) that, for all practical purposes, one cannot observe the recurrence. One might wish, nevertheless, to imagine that one could wait for the Poincaré recurrence, and then re-insert the wall that was removed by the thermodynamic operation. It is then evident that the appearance of irreversibility is due to the utter unpredictability of the Poincaré recurrence given only that the initial state was one of thermodynamic equilibrium, as is the case in macroscopic thermodynamics. Even if one could wait for it, one has no practical possibility of picking the right instant at which to re-insert the wall. The Poincaré recurrence theorem provides a solution to Loschmidt's paradox. If an isolated thermodynamic system could be monitored over increasingly many multiples of the average Poincaré recurrence time, the thermodynamic behavior of the system would become invariant under time reversal.

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to the raw materials they were made from. Thus, system entropy or disorder decreases while the tendency towards uniformity between the system and its environment is counteracted. In this example, the instructions, as well as the source of work may be internal or external to the system, and they may or may not cross the system boundary. To illustrate, the instructions may be pre-coded and the electrical work may be stored in an energy storage system on-site. Alternatively, the control of the machinery may be by remote operation over a communications network, while the electric work is supplied to the factory from the local electric grid. In addition, humans may directly play, in whole or in part, the role that the robotic machinery plays in manufacturing. In this case, instructions may be involved, but intelligence is either directly responsible, or indirectly responsible, for the direction or application of work in such a way as to counteract the tendency towards disorder and uniformity.

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uniformity in intensive properties of the system with its surroundings. This occurs spontaneously because the energy or mass transferred from the system to its surroundings results in a higher entropy in the surroundings, that is, it results in higher overall entropy of the system plus its surroundings. Note that this transfer of entropy requires dis-equilibrium in properties, such as a temperature difference. One example of this is the cooling crystallization of water that can occur when the system's surroundings are below freezing temperatures. Unconstrained heat transfer can spontaneously occur, leading to water molecules freezing into a crystallized structure of reduced disorder (sticking together in a certain order due to molecular attraction). The entropy of the system decreases, but the system approaches uniformity with its surroundings (category III).

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system but at least of two, which you may for the moment consider isolated from the rest of the world, but not always from each other." The two systems are isolated from each other by the wall, until it is removed by the thermodynamic operation, as envisaged by the law. The thermodynamic operation is externally imposed, not subject to the reversible microscopic dynamical laws that govern the constituents of the systems. It is the cause of the irreversibility. The statement of the law in this present article complies with Schrödinger's advice. The cause–effect relation is logically prior to the second law, not derived from it.

9408:, also known as the equal prior probability postulate, so long as one is clear that simple probability arguments are applied only to the future, while for the past there are auxiliary sources of information which tell us that it was low entropy. The first part of the second law, which states that the entropy of a thermally isolated system can only increase, is a trivial consequence of the equal prior probability postulate, if we restrict the notion of the entropy to systems in thermal equilibrium. The entropy of an isolated system in thermal equilibrium containing an amount of energy of 5096: 3961:

while idealized reversible processes produce no entropy and no process is known to exist that destroys entropy. The tendency of a system to approach uniformity may be counteracted, and the system may become more ordered or complex, by the combination of two things, a work or exergy source and some form of instruction or intelligence. Where ‘exergy’ is the thermal, mechanical, electric or chemical work potential of an energy source or flow, and ‘instruction or intelligence’, although subjective, is in the context of the set of category IV processes.

12496:, so that when gravity is important, uniform conditions (e.g. gas of uniform density) in fact have lower entropy compared to non-uniform ones (e.g. black holes in empty space). Yet another approach is that the universe had high (or even maximal) entropy given its size, but as the universe grew it rapidly came out of thermodynamic equilibrium, its entropy only slightly increased compared to the increase in maximal possible entropy, and thus it has arrived at a very low entropy when compared to the much larger possible maximum given its later size. 5983:{\displaystyle {\begin{aligned}&{{\eta }_{2}}=1-{\frac {|{{q}_{2}}|}{|{{q}_{1}}|}}\to |{{w}_{2}}|=|{{q}_{1}}|-|{{q}_{2}}|,\\&{{\eta }_{3}}=1-{\frac {|{{q}_{3}}|}{|{{q}_{2}}^{*}|}}\to |{{w}_{3}}|=|{{q}_{2}}^{*}|-|{{q}_{3}}|,\\&|{{w}_{2}}|+|{{w}_{3}}|=(|{{q}_{1}}|-|{{q}_{2}}|)+(|{{q}_{2}}^{*}|-|{{q}_{3}}|),\\&{{\eta }_{1}}=1-{\frac {|{{q}_{3}}|}{|{{q}_{1}}|}}={\frac {(|{{w}_{2}}|+|{{w}_{3}}|)}{|{{q}_{1}}|}}={\frac {(|{{q}_{1}}|-|{{q}_{2}}|)+(|{{q}_{2}}^{*}|-|{{q}_{3}}|)}{|{{q}_{1}}|}}.\\\end{aligned}}} 12613:. Such an assumption may rely on trial and error for its justification. If the assumption is justified, it can often be very valuable and useful because it makes available the theory of thermodynamics. Elements of the equilibrium assumption are that a system is observed to be unchanging over an indefinitely long time, and that there are so many particles in a system, that its particulate nature can be entirely ignored. Under such an equilibrium assumption, in general, there are no macroscopically detectable 1837:. A heat pump can reverse this heat flow, but the reversal process and the original process, both cause entropy production, thereby increasing the entropy of the system's surroundings. If an isolated system containing distinct subsystems is held initially in internal thermodynamic equilibrium by internal partitioning by impermeable walls between the subsystems, and then some operation makes the walls more permeable, then the system spontaneously evolves to reach a final new internal 3949:

optimization. As a result, a conceptual statement of the principle is very useful in engineering analysis. Thermodynamic systems can be categorized by the four combinations of either entropy (S) up or down, and uniformity (Y) - between system and its environment - up or down. This ‘special' category of processes, category IV, is characterized by movement in the direction of low disorder and low uniformity, counteracting the second law tendency towards uniformity and disorder.

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convection, and the case of ideal infinitesimal blackbody radiation (BR) transfer, but does not apply to most radiative transfer scenarios and in some cases has no physical meaning whatsoever. Consequently, the Clausius inequality was re-stated so that it is applicable to cycles with processes involving any form of heat transfer. The entropy transfer with radiative fluxes (

2436: 12814:. Szilárd pointed out that a real-life Maxwell's demon would need to have some means of measuring molecular speed, and that the act of acquiring information would require an expenditure of energy. Likewise, Brillouin demonstrated that the decrease in entropy caused by the demon would be less than the entropy produced by choosing molecules based on their speed. 11455: 3856: 1700:. For example, the first law allows the process of a cup falling off a table and breaking on the floor, as well as allowing the reverse process of the cup fragments coming back together and 'jumping' back onto the table, while the second law allows the former and denies the latter. The second law may be formulated by the observation that the entropy of 2280: 12464: 8436:) is a necessary condition for a process to be spontaneous. This is the most useful form of the second law of thermodynamics in chemistry, where free-energy changes can be calculated from tabulated enthalpies of formation and standard molar entropies of reactants and products. The chemical equilibrium condition at constant 2184: 11917: 12850:– then so much the worse for Maxwell's equations. If it is found to be contradicted by observation – well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation. 8629:, as well as lack of specific conditions, e.g. open, closed, or isolated, many people take this simple statement to mean that the second law of thermodynamics applies virtually to every subject imaginable. This is not true; this statement is only a simplified version of a more extended and precise description. 12706:

In the opinion of Schrödinger, "It is now quite obvious in what manner you have to reformulate the law of entropy – or for that matter, all other irreversible statements – so that they be capable of being derived from reversible models. You must not speak of one isolated

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is a consequence of the asymmetric character of thermodynamic operations, and not of any internally irreversible microscopic properties of the bodies. Thermodynamic operations are macroscopic external interventions imposed on the participating bodies, not derived from their internal properties. There

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For non-equilibrium situations in general, it may be useful to consider statistical mechanical definitions of other quantities that may be conveniently called 'entropy', but they should not be confused or conflated with thermodynamic entropy properly defined for the second law. These other quantities

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There are two principal ways of formulating thermodynamics, (a) through passages from one state of thermodynamic equilibrium to another, and (b) through cyclic processes, by which the system is left unchanged, while the total entropy of the surroundings is increased. These two ways help to understand

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of the system and because of the constant motion, the system is constantly changing its microstate. Statistical mechanics postulates that, in equilibrium, each microstate that the system might be in is equally likely to occur, and when this assumption is made, it leads directly to the conclusion that

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However, for some non-isolated systems which can exchange energy with their surroundings, the surroundings exchange enough heat with the system, or do sufficient work on the system, so that the processes occur in the opposite direction. This is possible provided the total entropy change of the system

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There are also situations where the entropy spontaneously decreases by means of energy and entropy transfer. When thermodynamic constraints are not present, spontaneously energy or mass, as well as accompanying entropy, may be transferred out of a system in a progress to reach external equilibrium or

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are the energy and entropy fluxes per unit frequency, area, and solid angle. In deriving this blackbody spectral entropy radiance, with the goal of deriving the blackbody energy formula, Planck postulated that the energy of a photon was quantized (partly to simplify the mathematics), thereby starting

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Living organisms may be considered as open systems, because matter passes into and out from them. Thermodynamics of open systems is currently often considered in terms of passages from one state of thermodynamic equilibrium to another, or in terms of flows in the approximation of local thermodynamic

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An important and revealing idealized special case is to consider applying the second law to the scenario of an isolated system (called the total system or universe), made up of two parts: a sub-system of interest, and the sub-system's surroundings. These surroundings are imagined to be so large that

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Consider a category IV example of robotic manufacturing and assembly of vehicles in a factory. The robotic machinery requires electrical work input and instructions, but when completed, the manufactured products have less uniformity with their surroundings, or more complexity (higher order) relative

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result, than that for BR emission. This observation is consistent with Max Planck's blackbody radiation energy and entropy formulas and is consistent with the fact that blackbody radiation emission represents the maximum emission of entropy for all materials with the same temperature, as well as the

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Though it is almost customary in textbooks to say that Carathéodory's principle expresses the second law and to treat it as equivalent to the Clausius or to the Kelvin-Planck statements, such is not the case. To get all the content of the second law, Carathéodory's principle needs to be supplemented

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in its usual short statement allows recognition that two bodies in a relation of thermal equilibrium have the same temperature, especially that a test body has the same temperature as a reference thermometric body. For a body in thermal equilibrium with another, there are indefinitely many empirical

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It can easily happen that a physical system exhibits internal macroscopic changes that are fast enough to invalidate the assumption of the constancy of the entropy. Or that a physical system has so few particles that the particulate nature is manifest in observable fluctuations. Then the assumption

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Furthermore, the ability of living organisms to grow and increase in complexity, as well as to form correlations with their environment in the form of adaption and memory, is not opposed to the second law – rather, it is akin to general results following from it: Under some definitions, an increase

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approach. It says that, over long periods of time, the time spent in some region of the phase space of microstates with the same energy is proportional to the volume of this region, i.e. that all accessible microstates are equally probable over a long period of time. Equivalently, it says that time

8216:). Those changes have already been considered by the assumption that the system under consideration can reach equilibrium with the reference state without altering the reference state. An efficiency for a process or collection of processes that compares it to the reversible ideal may also be found ( 3096:, the entropy is a monotonic function of the internal energy. Nevertheless, this principle of Planck is not actually Planck's preferred statement of the second law, which is quoted above, in a previous sub-section of the present section of this present article, and relies on the concept of entropy. 3087:

This formulation does not mention heat and does not mention temperature, nor even entropy, and does not necessarily implicitly rely on those concepts, but it implies the content of the second law. A closely related statement is that "Frictional pressure never does positive work." Planck wrote: "The

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The second law is concerned with the direction of natural processes. It asserts that a natural process runs only in one sense, and is not reversible. That is, the state of a natural system itself can be reversed, but not without increasing the entropy of the system's surroundings, that is, both the

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from the sun, which may be regarded as heat, and carbon dioxide and water. They give out oxygen. In this way they grow. Eventually they die, and their remains rot away, turning mostly back into carbon dioxide and water. This can be regarded as a cyclic process. Overall, the sunlight is from a high

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is the "equivalence-value" of all uncompensated transformations involved in a cyclical process. Later, in 1865, Clausius would come to define "equivalence-value" as entropy. On the heels of this definition, that same year, the most famous version of the second law was read in a presentation at the

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On the other hand, consider the refrigeration of water in a warm environment. Due to refrigeration, as heat is extracted from the water, the temperature and entropy of the water decreases, as the system moves further away from uniformity with its warm surroundings or environment (category IV). The

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Due to the inherent emission of radiation from all matter, most entropy flux calculations involve incident, reflected and emitted radiative fluxes. The energy and entropy of unpolarized blackbody thermal radiation, is calculated using the spectral energy and entropy radiance expressions derived by

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Clausius is the author of the sibyllic utterance, "The energy of the universe is constant; the entropy of the universe tends to a maximum." The objectives of continuum thermomechanics stop far short of explaining the "universe", but within that theory we may easily derive an explicit statement in

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considers a theoretical microscopic description of an isolated physical system. This may be considered as a model of a thermodynamic system after a thermodynamic operation has removed an internal wall. The system will, after a sufficiently long time, return to a microscopically defined state very

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of the engine when the engine operation is not reversed. Thus a violation of the Kelvin statement implies a violation of the Clausius statement, i.e. the Clausius statement implies the Kelvin statement. We can prove in a similar manner that the Kelvin statement implies the Clausius statement, and

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This is because a general process for this case (no mass exchange between the system and its surroundings) may include work being done on the system by its surroundings, which can have frictional or viscous effects inside the system, because a chemical reaction may be in progress, or because heat

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is maximized, implies that the entropy will have increased or it will have stayed the same (if the value at which the variable was fixed happened to be the equilibrium value). Suppose we start from an equilibrium situation and we suddenly remove a constraint on a variable. Then right after we do

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The equality sign holds in the case that only reversible processes take place inside the system. If irreversible processes take place (which is the case in real systems in operation) the >-sign holds. If heat is supplied to the system at several places we have to take the algebraic sum of the

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The second law can be conceptually stated as follows: Matter and energy have the tendency to reach a state of uniformity or internal and external equilibrium, a state of maximum disorder (entropy). Real non-equilibrium processes always produce entropy, causing increased disorder in the universe,

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is idealized. A main postulate or assumption, often not even explicitly stated, is the existence of systems in their own internal states of thermodynamic equilibrium. In general, a region of space containing a physical system at a given time, that may be found in nature, is not in thermodynamic

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Second law analysis is valuable in scientific and engineering analysis in that it provides a number of benefits over energy analysis alone, including the basis for determining energy quality (exergy content), understanding fundamental physical phenomena, and improving performance evaluation and

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The second term represents work of internal variables that can be perturbed by external influences, but the system cannot perform any positive work via internal variables. This statement introduces the impossibility of the reversion of evolution of the thermodynamic system in time and can be

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is the number of particles in the system. For everyday (macroscopic) situations, the probability that the second law will be violated is practically zero. However, for systems with a small number of particles, thermodynamic parameters, including the entropy, may show significant statistical

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The Clausius inequality, as well as some other statements of the second law, must be re-stated to have general applicability for all forms of heat transfer, i.e. scenarios involving radiative fluxes. For example, the integrand (đQ/T) of the Clausius expression applies to heat conduction and

11599: 12567:, meaning that their temperature rises with their internal energy. Therefore, when energy flows from a high-temperature object to a low-temperature object, the source temperature decreases while the sink temperature is increased; hence temperature differences tend to diminish over time. 8853:

by all processes inside the system. The advantage of this formulation is that it shows the effect of the entropy production. The rate of entropy production is a very important concept since it determines (limits) the efficiency of thermal machines. Multiplied with ambient temperature

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temperature source, the sun, and its energy is passed to a lower temperature sink, i.e. radiated into space. This is an increase of entropy of the surroundings of the plant. Thus animals and plants obey the second law of thermodynamics, considered in terms of cyclic processes.

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is the flow of entropy into the system associated with the flow of matter entering the system. It should not be confused with the time derivative of the entropy. If matter is supplied at several places we have to take the algebraic sum of these contributions.

4589:, then the efficiency of this engine must be same to the other engine at the same reservoirs. If we choose engines such that work done by the one cycle engine and the two cycle engine are same, then the efficiency of each heat engine is written as the below. 16224: 7686:

where we have first used the definition of entropy in classical thermodynamics (alternatively, in statistical thermodynamics, the relation between entropy change, temperature and absorbed heat can be derived); and then the second law inequality from above.

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This is not always the case for systems in which the gravitational force is important: systems that are bound by their own gravity, such as stars, can have negative heat capacities. As they contract, both their total energy and their entropy decrease but

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will depend on the values of these variables. If a variable is not fixed, (e.g. we do not clamp a piston in a certain position), then because all the accessible states are equally likely in equilibrium, the free variable in equilibrium will be such that

12253: 2111: 11755: 2514:, and before the mathematical expression of the concept of entropy. Interpreted in the light of the first law, Carnot's analysis is physically equivalent to the second law of thermodynamics, and remains valid today. Some samples from his book are: 4294: 3562: 7179: 2648:

Suppose there is an engine violating the Kelvin statement: i.e., one that drains heat and converts it completely into work (the drained heat is fully converted to work) in a cyclic fashion without any other result. Now pair it with a reversed

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In a nutshell, the Clausius inequality is saying that when a cycle is completed, the change in the state property S will be zero, so the entropy that was produced during the cycle must have transferred out of the system by heat transfer. The

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of quantum mechanics, in the limit of an infinitely slow change of the system's Hamiltonian, the system will stay in the same energy eigenstate and thus change its energy according to the change in energy of the energy eigenstate it is in.

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To a fair approximation, living organisms may be considered as examples of (b). Approximately, an animal's physical state cycles by the day, leaving the animal nearly unchanged. Animals take in food, water, and oxygen, and, as a result of

10499: 9928: 12025: 12665:) since the second law applies statistically on time-asymmetric boundary conditions. The second law has been related to the difference between moving forwards and backwards in time, or to the principle that cause precedes effect ( 3973:

main point, take-away, is that refrigeration not only requires a source of work, it requires designed equipment, as well as pre-coded or direct operational intelligence or instructions to achieve the desired refrigeration effect.

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equilibrium. The problem for living organisms may be further simplified by the approximation of assuming a steady state with unchanging flows. General principles of entropy production for such approximations are a subject of

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gives an explanation for the second law by postulating that a material is composed of atoms and molecules which are in constant motion. A particular set of positions and velocities for each particle in the system is called a

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For any irreversible process, since entropy is a state function, we can always connect the initial and terminal states with an imaginary reversible process and integrating on that path to calculate the difference in entropy.

2431:{\displaystyle \mathrm {d} S={\frac {\delta Q}{T}}-{\frac {1}{T}}\sum _{j}\,\Xi _{j}\,\delta \xi _{j}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{(closed system; actually possible quasistatic irreversible process).}}} 3996:

by extracting the massive internal energy of the environment as the power of the machine. Such a machine is called a "perpetual motion machine of the second kind". The second law declared the impossibility of such machines.

1669:. A simple statement of the law is that heat always flows spontaneously from hotter to colder regions of matter (or 'downhill' in terms of the temperature gradient). Another statement is: "Not all heat can be converted into 12703:, also known as the reversibility paradox, is the objection that it should not be possible to deduce an irreversible process from the time-symmetric dynamics that describe the microscopic evolution of a macroscopic system. 9236: 2973:

Every process occurring in nature proceeds in the sense in which the sum of the entropies of all bodies taking part in the process is increased. In the limit, i.e. for reversible processes, the sum of the entropies remains

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in entropy also results in an increase in complexity, and for a finite system interacting with finite reservoirs, an increase in entropy is equivalent to an increase in correlations between the system and the reservoirs.

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The statement by Clausius uses the concept of 'passage of heat'. As is usual in thermodynamic discussions, this means 'net transfer of energy as heat', and does not refer to contributory transfers one way and the other.

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Planck offered the following proposition as derived directly from experience. This is sometimes regarded as his statement of the second law, but he regarded it as a starting point for the derivation of the second law.

10409: 2506:. It represents the theoretical maximum efficiency of a heat engine operating between any two given thermal or heat reservoirs at different temperatures. Carnot's principle was recognized by Carnot at a time when the 12215: 12491:

This may seem somewhat paradoxical, since in many physical systems uniform conditions (e.g. mixed rather than separated gases) have high entropy. The paradox is solved once realizing that gravitational systems have

1759:, who in 1824 showed that the efficiency of conversion of heat to work in a heat engine has an upper limit. The first rigorous definition of the second law based on the concept of entropy came from German scientist 12121: 11450:{\displaystyle \left({\frac {\partial \Omega }{\partial x}}\right)_{E}=-\sum _{Y}Y\left({\frac {\partial \Omega _{Y}}{\partial E}}\right)_{x}=\left({\frac {\partial \left(\Omega X\right)}{\partial E}}\right)_{x}\,} 9651:

Suppose we have an isolated system whose macroscopic state is specified by a number of variables. These macroscopic variables can, e.g., refer to the total volume, the positions of pistons in the system, etc. Then

4969: 4842: 4715: 7582: 3851:{\displaystyle L_{\nu }={\frac {2k\nu ^{2}}{c^{2}}}((1+{\frac {c^{2}K_{\nu }}{2h\nu ^{3}}})\ln(1+{\frac {c^{2}K_{\nu }}{2h\nu ^{3}}})-({\frac {c^{2}K_{\nu }}{2h\nu ^{3}}})\ln({\frac {c^{2}K_{\nu }}{2h\nu ^{3}}}))} 2582:

laid the foundation for the second law of thermodynamics in 1850 by examining the relation between heat transfer and work. His formulation of the second law, which was published in German in 1854, is known as the

9032: 4008:(1824) is a principle that limits the maximum efficiency for any possible engine. The efficiency solely depends on the temperature difference between the hot and cold thermal reservoirs. Carnot's theorem states: 3270: 10175: 1818:. Conceptually, the first law describes the fundamental principle that systems do not consume or 'use up' energy, that energy is neither created nor destroyed, but is simply converted from one form to another. 11106: 2994:... in an irreversible or spontaneous change from one equilibrium state to another (as for example the equalization of temperature of two bodies A and B, when brought in contact) the entropy always increases. 4103: 2566:

depends only on the temperatures of the two heat reservoirs, and is the same, whatever the working substance. A Carnot engine operated in this way is the most efficient possible heat engine using those two

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The second law of thermodynamics is a physical law that is not symmetric to reversal of the time direction. This does not conflict with symmetries observed in the fundamental laws of physics (particularly

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The first term is intensive, i.e. it does not scale with system size. In contrast, the last term scales as the inverse system size and will thus vanish in the thermodynamic limit. We have thus found that:

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Roberts, J.K., Miller, A.R. (1928/1960), p. 382. This source is partly verbatim from Planck's statement, but does not cite Planck. This source calls the statement the principle of the increase of entropy.

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expression (noting that emitted and reflected entropy fluxes are, in general, not independent). For the emission of NBR, including graybody radiation (GR), the resultant emitted entropy flux, or radiance

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Not mentioning entropy, this principle of Planck is stated in physical terms. It is very closely related to the Kelvin statement given just above. It is relevant that for a system at constant volume and

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Axiom II: In jeder beliebigen Umgebung eines willkürlich vorgeschriebenen Anfangszustandes gibt es Zustände, die durch adiabatische Zustandsänderungen nicht beliebig approximiert werden können. (p.363)

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The motive power of heat is independent of the agents employed to realize it; its quantity is fixed solely by the temperatures of the bodies between which is effected, finally, the transfer of caloric.

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temperature scales, in general respectively depending on the properties of a particular reference thermometric body. The second law allows a distinguished temperature scale, which defines an absolute,

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There are intermediate cases, in which the assumption of local thermodynamic equilibrium is a very good approximation, but strictly speaking it is still an approximation, not theoretically ideal.

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The second law therefore implies that for any process which can be considered as divided simply into a subsystem, and an unlimited temperature and pressure reservoir with which it is in contact,

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A non-equilibrium statistical mechanics approach has also been used to obtain the same result as Planck, indicating it has wider significance and represents a non-equilibrium entropy. A plot of

12038:. We now consider an infinitesimal reversible change in the temperature and in the external parameters on which the energy levels depend. It follows from the general formula for the entropy: 8766: 3456: 2629:

It is impossible, by means of inanimate material agency, to derive mechanical effect from any portion of matter by cooling it below the temperature of the coldest of the surrounding objects.

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fictively operated in the limiting mode of extreme slowness known as quasi-static, so that the heat and work transfers are between subsystems that are always in their own internal states of

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which is the basis of the accurate determination of the absolute entropy of pure substances from measured heat capacity curves and entropy changes at phase transitions, i.e. by calorimetry.

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of accessible microstates, but equilibrium has not yet been reached, so the actual probabilities of the system being in some accessible state are not yet equal to the prior probability of

8599: 6945: 11276: 11029: 8947: 9494: 3339:), where the temperature is evaluated at the system boundary where the heat transfer occurs. The modified Clausius inequality, for all heat transfer scenarios, can then be expressed as, 2275:{\displaystyle \mathrm {d} S={\frac {\delta Q}{T}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{(actually possible quasistatic irreversible process without composition change).}}} 3344: 10340: 3008:

formulated thermodynamics on a purely mathematical axiomatic foundation. His statement of the second law is known as the Principle of Carathéodory, which may be formulated as follows:

2482:(1909). These statements cast the law in general physical terms citing the impossibility of certain processes. The Clausius and the Kelvin statements have been shown to be equivalent. 12459:{\displaystyle dS={\frac {1}{T}}\sum _{j}E_{j}dP_{j}={\frac {1}{T}}\sum _{j}d\left(E_{j}P_{j}\right)-{\frac {1}{T}}\sum _{j}P_{j}dE_{j}={\frac {dE+\delta W}{T}}={\frac {\delta Q}{T}}} 9825: 7037: 15145: 10084: 15329: 8680: 10553: 10209: 9528: 8196: 8084: 2179:{\displaystyle \mathrm {d} S>{\frac {\delta Q}{T_{\text{surr}}}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{(closed system; actually possible, irreversible process).}}} 13112: 11912:{\displaystyle dS=\left({\frac {\partial S}{\partial E}}\right)_{x}dE+\left({\frac {\partial S}{\partial x}}\right)_{E}dx={\frac {dE}{T}}+{\frac {X}{T}}dx={\frac {\delta Q}{T}}\,} 10253: 9278: 9074: 8808: 11227: 3099:

A statement that in a sense is complementary to Planck's principle is made by Claus Borgnakke and Richard E. Sonntag. They do not offer it as a full statement of the second law:

12484:. From a statistical point of view, these were very special conditions. On the other hand, they were quite simple, as the universe - or at least the part thereof from which the 2890: 10650: 10853: 1876:

thermodynamic system of interest, (which allows the entry or exit of energy – but not transfer of matter), from an auxiliary thermodynamic system, an infinitesimal increment (

9625:. However, in the thermodynamic limit (i.e. in the limit of infinitely large system size), the specific entropy (entropy per unit volume or per unit mass) does not depend on 4141: 8847: 8151: 7310: 3901:

gives a family of blackbody radiation energy spectra, and likewise for the entropy spectra. For non-blackbody radiation (NBR) emission fluxes, the spectral entropy radiance

2093: 9765:. We have already seen that in the final equilibrium state, the entropy will have increased or have stayed the same relative to the previous equilibrium state. Boltzmann's 8426: 8386: 6387: 1899: 1763:

in the 1850s and included his statement that heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time.

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In all cases, the assumption of thermodynamic equilibrium, once made, implies as a consequence that no putative candidate "fluctuation" alters the entropy of the system.

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For an actually possible infinitesimal process without exchange of mass with the surroundings, the second law requires that the increment in system entropy fulfills the

852: 805: 720: 673: 585: 538: 9763: 6050: 2065: 11156: 10110: 9646: 9623: 9600: 8477:

in 1824. He was the first to realize correctly that the efficiency of this conversion depends on the difference of temperature between an engine and its surroundings.

3306: 1926: 756: 624: 11478: 11129: 10922: 9735: 9714: 9691: 9670: 3067:

by Planck's principle, that isochoric work always increases the internal energy of a closed system that was initially in its own internal thermodynamic equilibrium.

4374:

states that all reversible engines operating between the same heat reservoirs are equally efficient. Thus, any reversible heat engine operating between temperatures

990: 12245: 10028: 9696:

If the variable was initially fixed to some value then upon release and when the new equilibrium has been reached, the fact the variable will adjust itself so that

8879: 6347: 6018: 5088: 5061: 5034: 5007: 3111:

Differing from Planck's just foregoing principle, this one is explicitly in terms of entropy change. Removal of matter from a system can also decrease its entropy.

2306: 9985: 8496:

of heat popular at the time, which considered heat as a fluid. From there he was able to infer the principle of Sadi Carnot and the definition of entropy (1865).

2599:

Heat cannot spontaneously flow from cold regions to hot regions without external work being performed on the system, which is evident from ordinary experience of

1955: 2912:

It is impossible to construct an engine which will work in a complete cycle, and produce no effect except the production of work and cooling of a heat reservoir.

489: 10873: 10670: 10577: 10420: 10273: 9836: 9548: 9426: 9131: 7813:

done merely by the sub-system expanding against the surrounding external pressure, giving the following relation for the useful work (exergy) that can be done:

3992:

Before the establishment of the second law, many people who were interested in inventing a perpetual motion machine had tried to circumvent the restrictions of

1859: 828: 781: 696: 649: 561: 514: 16319: 6623:{\displaystyle f(T_{2},T_{3})={\frac {f(T_{1},T_{3})}{f(T_{1},T_{2})}}={\frac {273.16{\text{ K}}\cdot f(T_{1},T_{3})}{273.16{\text{ K}}\cdot f(T_{1},T_{2})}}.} 2308:

to describe the deviation of a thermodynamic system from a chemical equilibrium state in physical equilibrium (with the required well-defined uniform pressure

11941: 12606:

equilibrium, read in the most stringent terms. In looser terms, nothing in the entire universe is or has ever been truly in exact thermodynamic equilibrium.

10734: 3337: 6719: 12587:

emitted by the bodies is included, however, the total entropy of the system can be shown to increase even as the entropy of the planet or star decreases.

7819: 3081:

The internal energy of a closed system is increased by an adiabatic process, throughout the duration of which, the volume of the system remains constant.

2727: 2027:{\displaystyle \mathrm {d} S={\frac {\delta Q}{T}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{(closed system; idealized, reversible process)}}.} 11683: 11611: 15950:"On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam" 15934:"On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam" 9393:, and thus the second law is ultimately a consequence of the initial conditions somewhere in the past, probably at the beginning of the universe (the 9147: 4027:. Carnot, however, further postulated that some caloric is lost, not being converted to mechanical work. Hence, no real heat engine could realize the 4023:

In his ideal model, the heat of caloric converted into work could be reinstated by reversing the motion of the cycle, a concept subsequently known as

3445: 11594:{\displaystyle \left({\frac {\partial \ln \left(\Omega \right)}{\partial x}}\right)_{E}=\beta X+\left({\frac {\partial X}{\partial E}}\right)_{x}\,} 1630: 4575:. This is because, if a part of the two cycle engine is hidden such that it is recognized as an engine between the reservoirs at the temperatures 10348: 12132: 1331: 14532: 14313:

Gyenis, Balazs (2017). "Maxwell and the normal distribution: A colored story of probability, independence, and tendency towards equilibrium".

9330:

the second law must hold in a statistical sense. That is, the second law will hold on average, with a statistical variation on the order of 1/

7345: – so that no matter how much heat is transferred to (or from) the sub-system, the temperature of the surroundings will remain 15502: 12044: 4849: 4722: 4595: 2603:, for example. In a refrigerator, heat is transferred from cold to hot, but only when forced by an external agent, the refrigeration system. 1219: 7504: 6878:) = 273.16 K. (Any reference temperature and any positive numerical value could be used – the choice here corresponds to the 2620:

It is impossible for a self-acting machine, unaided by any external agency, to convey heat from one body to another at a higher temperature.

15173: 13100:{David Sanborn Scott, The arrow of time, International Journal of Hydrogen Energy, Volume 28, Issue 2, 2003, Pages 147-149, ISSN 0360-3199} 8958: 4975:

Here, the engine 1 is the one cycle engine, and the engines 2 and 3 make the two cycle engine where there is the intermediate reservoir at

3211: 1708:

where the entropy is highest at the given internal energy. An increase in the combined entropy of system and surroundings accounts for the

15356: 10118: 1747:. The second law has been expressed in many ways. Its first formulation, which preceded the proper definition of entropy and was based on 16163:

Revisiting The Second Law of Energy Degradation and Entropy Generation: From Sadi Carnot's Ingenious Reasoning to Holistic Generalization

4019:

All reversible heat engines between two heat reservoirs are equally efficient with a Carnot engine operating between the same reservoirs.

453: 11037: 2466:

The second law of thermodynamics may be expressed in many specific ways, the most prominent classical statements being the statement by

1822:

state of the system plus the state of its surroundings cannot be together, fully reversed, without implying the destruction of entropy.

12480:

As elaborated above, it is thought that the second law of thermodynamics is a result of the very low-entropy initial conditions at the

12035: 8952:

The expression of the second law for closed systems (so, allowing heat exchange and moving boundaries, but not exchange of matter) is:

15235:

The Mathematical Theory of Non-uniform gases. An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases

13079: 9602:

is a macroscopically small energy interval that is kept fixed. Strictly speaking this means that the entropy depends on the choice of

4060: 1309: 14533:

Physicists Debate Hawking's Idea That the Universe Had No Beginning. Wolchover, N. Quantmagazine, June 6, 2019. Retrieved 2020-11-28

7190: 2865:, where (1) the sign convention of heat is used in which heat entering into (leaving from) an engine is positive (negative) and (2) 12632:

of thermodynamic equilibrium is to be abandoned. There is no unqualified general definition of entropy for non-equilibrium states.

7700: 7042:

With this we can only obtain the difference of entropy by integrating the above formula. To obtain the absolute value, we need the

9344:

deviations from that predicted by the second law. Classical thermodynamic theory does not deal with these statistical variations.

8526:

There is a traditional doctrine, starting with Clausius, that entropy can be understood in terms of molecular 'disorder' within a

16314: 16135: 12972: 1342: 6312:{\displaystyle f(T_{1},T_{3})={\frac {|q_{3}|}{|q_{1}|}}={\frac {|q_{2}||q_{3}|}{|q_{1}||q_{2}|}}=f(T_{1},T_{2})f(T_{2},T_{3}).} 4396: 8093:

the subsystem (or, the change in the subsystem's exergy less any work, additional to that done by the pressure reservoir, done

16274: 15189: 12795:

they will have slowed down on average. Since average molecular speed corresponds to temperature, the temperature decreases in

2591:

Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time.

16196: 16106: 16091: 16073: 15884: 15699: 15625: 15512: 15099: 14996: 14981: 14838: 14555: 14429: 14273: 13881: 13742: 13409: 13284: 13257: 13148: 13121: 13087: 13048: 8250:, no energy is provided by the surroundings and the second law requires that the entropy of the system alone must increase: Δ 6643: 2668: 912: 8706:

The equality sign applies after equilibration. An alternative way of formulating of the second law for isolated systems is:

8313:

3) A solute can move from a region of lower concentration to a region of higher concentration in the biochemical process of

7951: 7352:; and no matter how much the volume of the sub-system expands (or contracts), the pressure of the surroundings will remain 4005: 3105:... there is only one way in which the entropy of a system can be decreased, and that is to transfer heat from the system. 1752: 1623: 1210: 879: 446: 324: 15193: 9783:

The second part of the second law states that the entropy change of a system undergoing a reversible process is given by:

2809: 16236: 7609: 7386: 1865: 262: 9404:

Given these assumptions, in statistical mechanics, the second law is not a postulate, rather it is a consequence of the

2923:

It is almost customary in textbooks to speak of the "Kelvin–Planck statement" of the law, as for example in the text by

16068:. Harvard Univ. Press. Chpts. 4–9 contain an introduction to the second law, one a bit less technical than this entry. 13338: 9375: 9326: 8246:

The second law determines whether a proposed physical or chemical process is forbidden or may occur spontaneously. For

6995:

So we can define a state function S called entropy, which for a reversible process or for pure heat transfer satisfies

6891: 3024:. It follows from Carathéodory's principle that quantity of energy quasi-statically transferred as heat is a holonomic 1394: 1368: 889: 343: 2494:'s theoretical analysis of the flow of heat in steam engines (1824). The centerpiece of that analysis, now known as a 16154: 16030: 16004: 15972: 15929: 15866: 15777: 15752: 15610: 15591: 15538: 15494: 15479: 15446: 15431: 15217: 15134: 15063: 15026: 15011: 14952: 14252: 13908: 13817: 13020: 12902: 9362:

that molecular collisions entail an equalization of temperatures and hence a tendency towards equilibrium was due to

8712: 4115:

as the temperature of the heat bath (surroundings) here. The reversible case is used to introduce the state function

2611: 2471: 295: 8268:

3) A solute can move from a region of higher concentration to a region of lower concentration (but not the reverse).

6953: 3931:), than that of BR. That is, the entropy flux of NBR emission is farther removed from the conduction and convection 15246:"Ueber Die Bewegende Kraft Der Wärme Und Die Gesetze, Welche Sich Daraus Für Die Wärmelehre Selbst Ableiten Lassen" 9405: 8560: 8104:

reference state is chosen as the system surroundings in the real world, then the second law predicts a decrease in

6909: 1447: 918: 317: 11232: 10985: 9389:

at some time in the past; this allows for simple probabilistic treatment. This assumption is usually thought as a

8884: 8209:) to utilize the second law without directly measuring or considering entropy change in a total isolated system. ( 16309: 15758: 15740: 14797: 14785: 12618: 9434: 4371: 2720:

from the cooler reservoir to the hotter one, which violates the Clausius statement. This is a consequence of the

1616: 14446: 13872:

Grubbström, Robert W. (1985). "Towards a Generalized Exergy Concept". In Van Gool, W.; Bruggink, J.J.C. (eds.).

12829:

on a microscopic scale, not just observing ordinary spontaneous or natural macroscopic thermodynamic processes.

7932:

It is convenient to define the right-hand-side as the exact derivative of a thermodynamic potential, called the

15226: 12962: 12596: 12552: 10307: 9693:

is maximized at the given energy of the isolated system as that is the most probable situation in equilibrium.

1547: 79: 15467:, edited by W.R. Longley, R.G. Van Name, Longmans, Green & Co., New York, 1928, volume 1, pp. 55–353. 15404:

The Mechanical Theory of Heat – with its Applications to the Steam Engine and to Physical Properties of Bodies

15203: 13493: 12722: 12716: 9789: 8474: 7001: 3012:

In every neighborhood of any state S of an adiabatically enclosed system there are states inaccessible from S.

2491: 1756: 1442: 16304: 15827:

Pokrovskii V.N. (2005) Extended thermodynamics in a discrete-system approach, Eur. J. Phys. vol. 26, 769–781.

15295:"On the Moving Force of Heat, and the Laws regarding the Nature of Heat itself which are deducible therefrom" 13810:

Fundamentals of Maxwell's Kinetic Theory of a Simple Monatomic Gas, Treated as a Branch of Rational Mechanics

13349:

Pokrovskii V.N. (2005) Extended thermodynamics in a discrete-system approach, Eur. J. Phys. vol. 26, 769–781.

12932: 12895:

Fundamentals of Maxwell's Kinetic Theory of a Simple Monatomic Gas, Treated as a Branch of Rational Mechanics

12516:

the processes of life. The thermodynamics of living organisms has been considered by many authors, including

10036: 1522: 1295: 272: 8642: 8625:

This statement is the best-known phrasing of the second law. Because of the looseness of its language, e.g.

3020:

for the first time and provided the foundation for a new subfield of classical thermodynamics, often called

2446:– the formulation, which is, of course, equivalent to the formulation of the principle in terms of entropy. 2208:

The equality still applies for pure heat flow (only heat flow, no change in chemical composition and mass),

12977: 12917: 10527: 10183: 9502: 8617:

Philosophical Society of Zurich on April 24, in which, in the end of his presentation, Clausius concludes:

8511:

and produce a net amount of work." This statement was shown to be equivalent to the statement of Clausius.

8156: 8044: 2450: 1771: 907: 100: 16246: 15797: 13449: 12885:

some ways reminiscent of Clausius, but referring only to a modest object: an isolated body of finite size.

10214: 9241: 9037: 8771: 4119:. This is because in cyclic processes the variation of a state function is zero from state functionality. 2190:

transfer actually occurs only irreversibly, driven by a finite difference between the system temperature (

16252: 15678:

Lieb, E.H., Yngvason, J. (2003). The Entropy of Classical Thermodynamics, pp. 147–195, Chapter 8 of

15221: 12927: 12922: 11194: 9385:, derivations of the second law have to make an assumption regarding the past, namely that the system is 7456: 7043: 4108:

The equality holds in the reversible case and the strict inequality holds in the irreversible case, with

4024: 3993: 3075:

In 1926, Max Planck wrote an important paper on the basics of thermodynamics. He indicated the principle

2721: 2511: 1791: 1693: 115: 105: 4289:{\displaystyle \eta ={\frac {|W_{n}|}{q_{H}}}={\frac {q_{H}+q_{C}}{q_{H}}}=1-{\frac {|q_{C}|}{|q_{H}|}}} 3557:{\displaystyle K_{\nu }={\frac {2h}{c^{2}}}{\frac {\nu ^{3}}{\exp \left({\frac {h\nu }{kT}}\right)-1}},} 2868: 15814:, a translation by Masius, M. of the second German edition, P. Blakiston's Son & Co., Philadelphia. 14505:

Carroll, S. (2017). The big picture: on the origins of life, meaning, and the universe itself. Penguin.

12942: 12572: 9386: 1399: 1363: 141: 75: 15439:

Generalized Thermodynamics. The Thermodynamics of Irreversible Processes and Generalized Hydrodynamics

15141: 14171:"A generalized and explicit conceptual statement of the principle of the second law of thermodynamics" 13711: 10823: 10611: 3005: 2479: 1437: 15949: 15632:

Lieb, E. H.; Yngvason, J. (1999). "The Physics and Mathematics of the Second Law of Thermodynamics".

12987: 12947: 12610: 12602: 8551: 4128: 3274: 2503: 2455: 1929: 1838: 1767: 1705: 1192: 940: 386: 199: 189: 16218: 16179: 15933: 15294: 14811: 12639:

indeed belong to statistical mechanics, not to thermodynamics, the primary realm of the second law.

12493: 8816: 8114: 7286: 7174:{\displaystyle -\Delta S+\int {\frac {\delta Q}{T_{surr}}}=\oint {\frac {\delta Q}{T_{surr}}}\leq 0} 3132:

of the other extensive properties of the system. That is, when a system is described by stating its

2640: 2070: 15375: 12869:

There have been nearly as many formulations of the second law as there have been discussions of it.

12856: 12504: 10112:, we define the generalized force for the system as the expectation value of the above expression: 8402: 8362: 8322: 8231: 7061:

Now reverse the reversible process and combine it with the said irreversible process. Applying the

6356: 4388:

must have the same efficiency, that is to say, the efficiency is a function of temperatures only:

3421:{\displaystyle \int _{\text{cycle}}({\frac {\delta Q_{CC}}{T_{b}}}+\delta S_{\text{NetRad}})<=0} 1879: 1736: 15055: 12666: 3031: 15112: 15047: 12875: 12826: 12655: 12034:

is a factor that normalizes the sum of all the probabilities to 1, this function is known as the

9934: 9359: 8500: 3017: 2945:

operating device, the sole effect of which is to absorb energy in the form of heat from a single

1652: 1604: 1432: 1229: 1110: 1055: 1000: 932: 871: 407: 396: 62: 16275:

Caratheodory, C., "Examination of the foundations of thermodynamics," trans. by D. H. Delphenich

15822:

Sitzungsberichte der Preussischen Akademie der Wissenschaften: Physikalisch-mathematische Klasse

11931:

then, in equilibrium, the probability distribution over the energy eigenvalues are given by the

11165: 10956: 10927: 10878: 10675: 10582: 10278: 9937:

for the justification for this definition. Suppose that the system has some external parameter,

9775:

increases monotonically as a function of time during the intermediate out of equilibrium state.

9553: 9286: 9085: 7257: 834: 787: 702: 655: 567: 520: 16174: 16025:, Greven, A., Keller, G., Warnecke (editors) (2003), Princeton University Press, Princeton NJ, 15424:

The Principles of Chemical Equilibrium. With Applications in Chemistry and Chemical Engineering

14578:

Ladyman, James; Lambert, James; Wiesner, Karoline (19 June 2012). "What is a complex system?".

14523:

Davies, P. C. (1983). Inflation and time asymmetry in the universe. Nature, 301(5899), 398-400.

14207: 12967: 12957: 12847: 12700: 12695: 12500: 9740: 9382: 8318: 8254:> 0. Examples of spontaneous physical processes in isolated systems include the following: 6023: 2044: 1815: 1689: 1537: 1254: 338: 92: 67: 15874: 14421: 13401: 12625:. For laboratory studies of critical states, exceptionally long observation times are needed. 11138: 10092: 9628: 9605: 9582: 8467: 7380:

of the isolated total system must not decrease according to the second law of thermodynamics:

3283: 1908: 1457: 738: 603: 16118: 15230: 12682: 11463: 11114: 10907: 9720: 9699: 9676: 9655: 9321: 8396: 1807: 1732: 1670: 1666: 1472: 1049: 362: 208: 57: 14514:

Greene, B. (2004). The fabric of the cosmos: Space, time, and the texture of reality. Knopf.

13393: 12642:

The physics of macroscopically observable fluctuations is beyond the scope of this article.

2510:

represented the dominant understanding of the nature of heat, before the recognition of the

960: 16289: 16166: 16083: 15651: 15558: 15544: 15452: 15340: 15257: 14910: 14648: 14461: 14375: 14332: 13988: 12622: 12614: 12584: 12223: 10006: 8857: 8481: 8295:

1) Heat can be transferred from a region of lower temperature to a higher temperature in a

6325: 5996: 5066: 5039: 5012: 4985: 1799: 1685: 1552: 1477: 1467: 267: 129: 15900: 15245: 14854: 14022:

Wright (2001). "On the entropy of radiative heat transfer in engineering thermodynamics".

12609:

For purposes of physical analysis, it is often enough convenient to make an assumption of

12517: 10494:{\displaystyle X=-{\frac {1}{\Omega \left(E\right)}}\sum _{Y}Y\Omega _{Y}\left(E\right)\,} 9923:{\displaystyle {\frac {1}{k_{\mathrm {B} }T}}\equiv \beta \equiv {\frac {d\ln \left}{dE}}} 2291: 8: 15809: 15709: 12937: 12748: 12485: 9964: 9363: 8335: 8206: 7062: 2942: 1934: 1869: 1697: 1497: 1259: 281: 247: 242: 155: 16170: 15655: 15402: 15344: 15261: 14914: 14661: 14652: 14626: 14465: 14379: 14336: 14051:"The exergy flux of radiative heat transfer for the special case of blackbody radiation" 13992: 12763:

at equal temperatures and placed next to each other, separated by a wall. Observing the

12020:{\displaystyle P_{j}={\frac {\exp \left(-{\frac {E_{j}}{k_{\mathrm {B} }T}}\right)}{Z}}} 8488:

was the first to formulate the second law during 1850, in this form: heat does not flow

7373:

occur in the entropies of the sub-system and the surroundings individually, the entropy

3188:

of the internal energy with respect to the entropy (essentially equivalent to the first

1829:

is made available, heat always flows spontaneously from a hotter to a colder body. Such

1492: 471: 16290:

The Journal of the International Society for the History of Philosophy of Science, 2012

16240: 16206: 15992: 15729: 15667: 15641: 15376:"On a Modified Form of the Second Fundamental Theorem in the Mechanical Theory of Heat" 15165: 15037: 14638: 14603: 14348: 14322: 13805: 13532: 13065: 12952: 12890: 12743: 11932: 10858: 10655: 10562: 10258: 9941:, that can be changed. In general, the energy eigenstates of the system will depend on 9533: 9411: 9390: 9116: 8850: 8527: 8515: 8457: 7597: 3185: 3021: 1844: 1720: 1586: 1249: 1244: 1197: 813: 766: 681: 634: 546: 499: 429: 413: 300: 252: 237: 227: 36: 30: 16132: 16021:

Uffink, J. (2003). Irreversibility and the Second Law of Thermodynamics, Chapter 7 of

15663: 14989:

Non-equilibrium Thermodynamics and Statistical Mechanics: Foundations and Applications

14105: 14066: 14035: 10810:{\displaystyle N_{Y}\left(E\right)={\frac {\Omega _{Y}\left(E\right)}{\delta E}}Ydx\,} 1901:) in the entropy of the system of interest is defined to result from an infinitesimal 16192: 16150: 16102: 16087: 16069: 16026: 16000: 15982: 15880: 15862: 15773: 15748: 15695: 15671: 15621: 15606: 15587: 15534: 15518: 15508: 15490: 15475: 15442: 15427: 15213: 15169: 15130: 15095: 15069: 15059: 15022: 15007: 14992: 14977: 14958: 14948: 14834: 14666: 14595: 14551: 14425: 14414: 14391: 14269: 14248: 14190: 14148: 14109: 14070: 14004: 14000: 13942: 13904: 13877: 13813: 13738: 13405: 13394: 13334: 13280: 13253: 13144: 13117: 13044: 13016: 12898: 12838:

The law that entropy always increases holds, I think, the supreme position among the

10003:

is the pressure. The generalized force for a system known to be in energy eigenstate

9946: 8354: 8219: 7251: 6843:{\displaystyle f(T_{2},T_{3})=f(T_{2}^{*},T_{3}^{*})={\frac {T_{3}^{*}}{T_{2}^{*}}},} 2096: 1704:

left to spontaneous evolution cannot decrease, as they always tend toward a state of

1581: 1542: 1532: 1104: 902: 730: 232: 222: 164: 16123:

Reflections on the Motive Power of Heat and on Machines Fitted to Develop That Power

15790:, original publication 1957, reprint 1966, Cambridge University Press, Cambridge UK. 15733: 14870: 14607: 14352: 14170: 13922: 12811: 12771:

guards a microscopic trapdoor in the wall. When a faster-than-average molecule from

12527: 4350:

to a cold reservoir from the engine. Thus the efficiency depends only on the ratio |

4012:

All irreversible heat engines between two heat reservoirs are less efficient than a

2893: 2799:{\textstyle {\text{Input}}+{\text{Output}}=0\implies (Q+Q_{c})-{\frac {Q}{\eta }}=0} 2654: 16184: 16036: 15918: 15844: 15721: 15659: 15348: 15306: 15273: 15265: 15157: 15080: 15051: 15033: 14918: 14899:"All Shook Up: Fluctuations, Maxwell's Demon and the Thermodynamics of Computation" 14656: 14622: 14587: 14469: 14383: 14340: 14289: 14213: 14186: 14182: 14140: 14101: 14089: 14062: 14050: 14031: 13996: 13960:

Planck, Max (1914). "Translation by Morton Mausius, The Theory of Heat Radiation".

13938: 13934: 13699: 13654: 13372: 12807: 9367: 8317:, if sufficient work is provided by a concentration gradient of a chemical such as 8314: 8212: 7922:{\displaystyle \delta w_{u}\leq -d\left(U-T_{R}S+p_{R}V-\sum \mu _{iR}N_{i}\right)} 7250:

where the equality holds if the transformation is reversible. If the process is an

6897: 4051: 3987: 3311: 3308:) is taken separately from that due to heat transfer by conduction and convection ( 3025: 2981: 2928: 2103: 1902: 1502: 1487: 1427: 1422: 1239: 1234: 884: 352: 217: 16264: 15618:

Understanding Non-equilibrium Thermodynamics: Foundations, Applications, Frontiers

11739:{\displaystyle \left({\frac {\partial S}{\partial E}}\right)_{x}={\frac {1}{T}}\,} 11667:{\displaystyle \left({\frac {\partial S}{\partial x}}\right)_{E}={\frac {X}{T}}\,} 9374:

of 1872 also argued that due to collisions gases should over time tend toward the

3275:

Second law statements, such as the Clausius inequality, involving radiative fluxes

1688:. It predicts whether processes are forbidden despite obeying the requirement of 16139: 16128: 15691: 15579: 15398: 15330:"Über eine veränderte Form des zweiten Hauptsatzes der mechanischen Wärmetheorie" 15325: 15241: 14545: 13274: 13247: 13165: 13138: 12839: 12475: 9398: 8633: 8547: 8485: 8262:

from a region of higher temperature to a lower temperature (but not the reverse).

8247: 8235: 8202: 3133: 3129: 3120: 2579: 2467: 1795: 1760: 1709: 1701: 1452: 1300: 954: 595: 418: 179: 146: 14344: 13976: 9231:{\displaystyle {\frac {dS}{dt}}={\frac {\dot {Q}}{T}}+{\dot {S}}+{\dot {S}}_{i}} 8632:

In terms of time variation, the mathematical statement of the second law for an

8395:< 0. For a similar process at constant temperature and volume, the change in 6020:

flown from the engine 2 to the intermediate reservoir must be equal to the heat

2522:

wherever there exists a difference of temperature, motive power can be produced.

2269:(actually possible quasistatic irreversible process without composition change). 15598: 15575: 15278: 15122: 13896: 13563: 12775:

flies towards the trapdoor, the demon opens it, and the molecule will fly from

12539: 12522: 8508: 8504: 8493: 4035: 3956:

Four categories of processes given entropy up or down and uniformity up or down

3943: 2950: 2946: 2918: 2507: 2458:, independent of the properties of any particular reference thermometric body. 1748: 1728: 1674: 1507: 1277: 377: 257: 194: 184: 52: 22: 16080:

Maxwell's Demon 2 : Entropy, classical and quantum information, computing

15310: 14715: 14591: 14129:"Exergetic Efficiencies and the Exergy Content of Terrestrial Solar Radiation" 13903:, (first edition 1960), second edition 1985, John Wiley & Sons, New York, 12503:

was enough to wipe off non-smoothness, while another is that the universe was

8492:

from cold to hot bodies. While common knowledge now, this was contrary to the

8265:

2) Mechanical energy can be converted to thermal energy (but not the reverse).

3872:

is Planck's constant or (6.626)10 J s, v is frequency (s), and the quantities

2665:. The net and sole effect of the combined pair of engines is to transfer heat 16298: 16282:, BBC Radio 4 discussion with John Gribbin, Peter Atkins & Monica Grady ( 16046: 15914: 15783: 15522: 15352: 15269: 15073: 14685: 14670: 14599: 14387: 14194: 14152: 14113: 14074: 14008: 13946: 13650: 13427: 13326: 12982: 12651: 12564: 11922: 8259: 7051: 4013: 3434: 2924: 2650: 2600: 2533: 2495: 2038: 1873: 1803: 1713: 1576: 894: 463: 424: 136: 16279: 9778: 15977:

On the universal tendency in nature to the dissipation of mechanical energy

15725: 15380:

London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science

15299:

London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science

14969: 14962: 14409: 14285: 13008: 12662: 12499:

As for the reason why initial conditions were such, one suggestion is that

8466:

Nicolas Léonard Sadi Carnot in the traditional uniform of a student of the

8296: 6350: 4526:

must have the same efficiency as one consisting of two cycles, one between

4028: 3114: 2563: 1648: 1527: 1512: 1462: 945: 15897:, (first edition 1928), fifth edition, Blackie & Son Limited, Glasgow. 15849: 15832: 15472:

Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)

15207: 14395: 13377: 13360: 10404:{\displaystyle \Omega \left(E\right)=\sum _{Y}\Omega _{Y}\left(E\right)\,} 8473:

The first theory of the conversion of heat into mechanical work is due to

3940:

maximum entropy emission for all radiation with the same energy radiance.

16260: 15646: 13923:"The Clausius inequality corrected for heat transfer involving radiation" 13143:. Cambridge UK: Cambridge University Press. p. 150, n259, 772, 743. 12817:

Maxwell's 'demon' repeatedly alters the permeability of the wall between

12210:{\displaystyle dS=-k_{\mathrm {B} }\sum _{j}\ln \left(P_{j}\right)dP_{j}} 8307: 8227: 3093: 2499: 1766:

The second law of thermodynamics allows the definition of the concept of

1658: 1482: 290: 14947:(1st ed. 1968, 3rd ed.). Cambridge UK: Cambridge University Press. 12507:

where the mechanism of creation implies low-entropy initial conditions.

2635: 1782: 16010:

Uffink, J. (2001). Bluff your way in the second law of thermodynamics,

15820:(1926). Über die Begründung des zweiten Hauptsatzes der Thermodynamik, 15817: 15805: 15793: 15570:

Non-equilibrium Thermodynamics. Field Theory and Variational Principles

15161: 14128: 14090:"The exergy flux of radiative heat transfer with an arbitrary spectrum" 13841: 13829: 13775: 13678: 13666: 13629: 13210: 13178: 12729: 12576: 12535: 12116:{\displaystyle S=-k_{\mathrm {B} }\sum _{j}P_{j}\ln \left(P_{j}\right)} 11927:

If a system is in thermal contact with a heat bath at some temperature

10089:

Since the system can be in any energy eigenstate within an interval of

8201:

This expression together with the associated reference state permits a

4964:{\displaystyle \eta _{3}=1-{\frac {|q_{3}|}{|q_{2}|}}=1-f(T_{2},T_{3})} 4837:{\displaystyle \eta _{2}=1-{\frac {|q_{2}|}{|q_{1}|}}=1-f(T_{1},T_{2})} 4710:{\displaystyle \eta _{1}=1-{\frac {|q_{3}|}{|q_{1}|}}=1-f(T_{1},T_{3})} 2964: 1830: 1571: 1517: 16188: 14923: 14898: 14144: 10559:, causing energy eigenstates to move into or out of the range between 7577:{\displaystyle dU=\delta q-\delta w+d\left(\sum \mu _{iR}N_{i}\right)} 15833:"A Derivation of the Main Relations of Nonequilibrium Thermodynamics" 15788:

Elements of Classical Thermodynamics for Advanced Students of Physics

15087:, translated by S.G. Brush, University of California Press, Berkeley. 15041: 14473: 14088:

Wright, S.E.; Rosen, M.A.; Scott, D.S.; Haddow, J.B. (January 2002).

14049:

Wright, S.E.; Rosen, M.A.; Scott, D.S.; Haddow, J.B. (January 2002).

13361:"A Derivation of the Main Relations of Nonequilibrium Thermodynamics" 12670: 12563:

Commonly, systems for which gravity is not important have a positive

9766: 9371: 9353: 9027:{\displaystyle {\frac {dS}{dt}}={\frac {\dot {Q}}{T}}+{\dot {S}}_{i}} 8519: 8300: 4512:

In addition, a reversible heat engine operating between temperatures

3265:{\displaystyle T=\left({\frac {\partial U}{\partial S}}\right)_{V,N}} 2475: 1826: 1655: 169: 10705:, all such energy eigenstates that are in the interval ranging from 10504:

We can relate this to the derivative of the entropy with respect to

10170:{\displaystyle X=-\left\langle {\frac {dE_{r}}{dx}}\right\rangle \,} 8338:

in a closed system at constant temperature and pressure without non-

8108:

for an irreversible process and no change for a reversible process.

8089:

i.e. the change in the subsystem's exergy plus the useful work done

2425:(closed system; actually possible quasistatic irreversible process). 14702:... gravitationally bound ball of gas has a negative specific heat! 14327: 12843: 12764: 12686:

are reputed "paradoxes" that arise from failure to recognize this.

12481: 9394: 8626: 1744: 1285: 1202: 994: 402: 174: 15603:

Modern Thermodynamics: From Heat Engines to Dissipative Structures

14643: 11101:{\displaystyle N_{Y}\left(E\right)-N_{Y}\left(E+\delta E\right)\,} 8273:

plus the surroundings is positive as required by the second law: Δ

7603:

Now the heat leaving the reservoir and entering the sub-system is

2556:

In modern terms, Carnot's principle may be stated more precisely:

1957:

of the system of interest and the auxiliary thermodynamic system:

15761:(2003). Entropy in Nonequilibrium, pp. 79–109, Chapter 5 of 15563:

Thermodynamics. An Advanced Treatment for Chemists and Physicists

14571: 12580: 10211:

energy eigenstates by counting how many of them have a value for

9133:

is the temperature at the point where the heat enters the system.

4328:> 0 is the heat added to the engine from a hot reservoir, and 4116: 4039: 3142: 2490:

The historical origin of the second law of thermodynamics was in

1834: 1681: 391: 16165:. AIP Conference Proceedings. Vol. 1411. pp. 327–350. 14627:"Entropy production as correlation between system and reservoir" 14620: 13113:

From Eternity to Here: The Quest for the Ultimate Theory of Time

11281:

Expressing the above expression as a derivative with respect to

10855:, all these energy eigenstates will move into the range between 8523:

average and average over the statistical ensemble are the same.

7463:

in the internal energy of the sub-system is the sum of the heat

6713:, viewed as a function of thermodynamic temperatures, is simply 5993:

In order to have the consistency in the last equation, the heat

4098:{\displaystyle \oint {\frac {\delta Q}{T_{\text{surr}}}}\leq 0.} 16269:

Maximum-Entropy and Bayesian Methods in Science and Engineering

15572:, translated by E. Gyarmati and W.F. Heinz, Springer, New York. 10414:

The average defining the generalized force can now be written:

8462: 7938: 7321: 6879: 15772:, translated by E.S. Halberstadt, Wiley–Interscience, London, 15487:

Thermodynamic Theory of Structure, Stability, and Fluctuations

7240:{\displaystyle \Delta S\geq \int {\frac {\delta Q}{T_{surr}}}} 1712:

of natural processes, often referred to in the concept of the

15455:(1876/1878). On the equilibrium of heterogeneous substances, 13756: 13754: 12784: 12768: 11278:, therefore the above expression is also valid in that case. 8550:

stated what he called the "second fundamental theorem in the

8538: 7776:{\displaystyle \delta w\leq -dU+T_{R}dS+\sum \mu _{iR}dN_{i}} 3952: 1724: 15426:, fourth edition, Cambridge University Press, Cambridge UK, 14550:. Dover Books on Physics. Dover Publications, Incorporated. 9530:

is the number of quantum states in a small interval between

8329: 8303:. These machines must provide sufficient work to the system. 3944:

Generalized conceptual statement of the second law principle

2919:

Relation between Kelvin's statement and Planck's proposition

1680:

The second law of thermodynamics establishes the concept of

12842:. If someone points out to you that your pet theory of the 8699: 8306:

2) Thermal energy can be converted to mechanical work in a

4347: 1811: 1740: 1662: 367: 13751: 13279:. Dover Books on Physics. Dover Publications. p. 48. 11923:

Derivation for systems described by the canonical ensemble

11158:

there will be the energy eigenstates that move from below

8503:

says, "It is impossible for any device that operates on a

8310:, if sufficient heat is also expelled to the surroundings. 4489:{\displaystyle {\frac {|q_{C}|}{|q_{H}|}}=f(T_{H},T_{C}).} 1735:

provides a microscopic explanation of the law in terms of

15237:, third edition 1970, Cambridge University Press, London. 13681:(1926), p. 463, translation by Uffink, J. (2003), p. 131. 12760: 9779:

Derivation of the entropy change for reversible processes

6349:

is a fixed reference temperature: the temperature of the

4031:'s reversibility and was condemned to be less efficient. 2538:

to its transportation from a warm body to a cold body ...

2173:(closed system; actually possible, irreversible process). 15129:, (1st edition 1960) 2nd edition 1985, Wiley, New York, 13684: 13463: 13080:"5.2 Axiomatic Statements of the Laws of Thermodynamics" 10924:. The number of energy eigenstates that move from below 10608:. Let's focus again on the energy eigenstates for which 9347: 5063:

is not lost during its passage through the reservoir at

4034:

Though formulated in terms of caloric (see the obsolete

3897:

versus frequency (v) for various values of temperature (

3115:

Relating the second law to the definition of temperature

2713:{\textstyle \Delta Q=Q\left({\frac {1}{\eta }}-1\right)} 16147:

The Low-Down on Entropy and Interpretive Thermodynamics

15801:, translated by A. Ogg, Longmans Green, London, p. 100. 13977:"Thermodynamics of the conversion of diluted radiation" 12806:

One response to this question was suggested in 1929 by

10701:. Since these energy eigenstates increase in energy by 8428:. Thus, a negative value of the change in free energy ( 6699:{\displaystyle T^{*}=273.16{\text{ K}}\cdot f(T_{1},T)} 2724:, as for the total system's energy to remain the same; 2661:

and so the efficiency of the reversed heat engine is 1/

1872:, idealized process of transfer of energy as heat to a 15146:"Untersuchungen über die Grundlagen der Thermodynamik" 15127:

Thermodynamics and an Introduction to Thermostatistics

14087: 14048: 13901:

Thermodynamics and an Introduction to Thermostatistics

13599: 10614: 8226:

This approach to the second law is widely utilized in

3981: 3119:

The second law has been shown to be equivalent to the

2812: 2730: 2671: 15504:

Entropy and the time evolution of macroscopic systems

15465:

The Collected Works of J. Willard Gibbs, Ph.D, LL. D.

14586:(1). Springer Science and Business Media LLC: 33–67. 14577: 14266:

Entropy and the Time Evolution of Macroscopic Systems

13874:

Energy and time in the economic and physical sciences

13057: 12469: 12256: 12226: 12135: 12047: 11944: 11758: 11686: 11614: 11493: 11466: 11298: 11235: 11197: 11168: 11141: 11117: 11040: 10988: 10959: 10930: 10910: 10881: 10861: 10826: 10737: 10678: 10658: 10585: 10565: 10555:

will change because the energy eigenstates depend on

10530: 10423: 10351: 10310: 10281: 10261: 10217: 10186: 10121: 10095: 10039: 10009: 9967: 9839: 9792: 9743: 9723: 9702: 9679: 9658: 9631: 9608: 9585: 9556: 9536: 9505: 9437: 9414: 9289: 9244: 9150: 9141:

For open systems (also allowing exchange of matter):

9119: 9088: 9040: 8961: 8887: 8860: 8819: 8774: 8715: 8645: 8563: 8405: 8365: 8241: 8159: 8117: 8047: 8028:{\displaystyle E=U-T_{R}S+p_{R}V-\sum \mu _{iR}N_{i}} 7954: 7822: 7703: 7612: 7507: 7389: 7289: 7260: 7193: 7081: 7004: 6956: 6912: 6722: 6646: 6412: 6359: 6328: 6064: 6026: 5999: 5099: 5069: 5042: 5015: 5009:

passes through the intermediate thermal reservoir at

4988: 4852: 4725: 4598: 4399: 4144: 4063: 3569: 3459: 3347: 3214: 3034: 2871: 2858:{\textstyle Q_{c}=Q\left({\frac {1}{\eta }}-1\right)} 2636:

Equivalence of the Clausius and the Kelvin statements

2325: 2294: 2217: 2114: 2073: 2047: 1966: 1937: 1911: 1882: 1847: 1113: 1058: 1003: 963: 837: 816: 790: 769: 741: 705: 684: 658: 637: 606: 570: 549: 523: 502: 474: 16053:, fifth edition, McGraw-Hill Book Company, New York. 15997:

The Tragicomical History of Thermodynamics 1822–1854

15765:, Greven, A., Keller, G., Warnecke (editors) (2003). 15682:, Greven, A., Keller, G., Warnecke (editors) (2003). 14486: 14294: 13587: 13575:

Lebon, G., Jou, D., Casas-Vázquez, J. (2008), p. 10.

3451:

Max Planck using equilibrium statistical mechanics,

15529:Greven, A., Keller, G., Warnecke (editors) (2003). 14315:

Studies in History and Philosophy of Modern Physics

13611: 12621:, which exhibit to the naked eye the phenomenon of 7676:{\displaystyle \delta q=T_{R}(-dS_{R})\leq T_{R}dS} 7445:{\displaystyle dS_{\mathrm {tot} }=dS+dS_{R}\geq 0} 3016:With this formulation, he described the concept of 1928:) to the system of interest, divided by the common 15565:, fifth revised edition, North Holland, Amsterdam. 14413: 14366:Hawking, SW (1985). "Arrow of time in cosmology". 13475: 12488:developed - seems to have been extremely uniform. 12458: 12239: 12209: 12115: 12019: 11911: 11738: 11666: 11593: 11472: 11449: 11270: 11221: 11183: 11150: 11123: 11100: 11023: 10974: 10945: 10916: 10896: 10867: 10847: 10809: 10693: 10664: 10644: 10600: 10571: 10547: 10493: 10403: 10334: 10296: 10267: 10247: 10203: 10169: 10104: 10078: 10022: 9979: 9922: 9819: 9757: 9729: 9708: 9685: 9664: 9640: 9617: 9594: 9571: 9542: 9522: 9488: 9420: 9304: 9272: 9230: 9125: 9103: 9068: 9026: 8941: 8873: 8841: 8802: 8760: 8674: 8593: 8420: 8380: 8190: 8145: 8078: 8027: 7921: 7775: 7675: 7600:of chemical species in the external surroundings. 7576: 7444: 7304: 7275: 7239: 7173: 7031: 6984: 6939: 6842: 6698: 6622: 6381: 6341: 6311: 6044: 6012: 5982: 5082: 5055: 5028: 5001: 4963: 4836: 4709: 4488: 4288: 4097: 3850: 3556: 3439: 3420: 3331: 3300: 3264: 3055: 2884: 2857: 2798: 2712: 2430: 2300: 2274: 2178: 2087: 2059: 2026: 1949: 1920: 1893: 1853: 1149: 1094: 1039: 984: 846: 822: 799: 775: 750: 714: 690: 667: 643: 618: 579: 555: 532: 508: 483: 16078:Leff, Harvey S., and Rex, Andrew F. (eds.) 2003. 16051:Heat and Thermodynamics. An Intermediate Textbook 14537: 13163: 4133:For an arbitrary heat engine, the efficiency is: 4042:, this was an early insight into the second law. 3088:production of heat by friction is irreversible." 16296: 15200:, Dowden, Hutchinson & Ross, Stroudsburg PA. 15032: 13641:Roberts, J.K., Miller, A.R. (1928/1960), p. 319. 12803:, contrary to the second law of thermodynamics. 11111:is thus the net contribution to the increase in 8097:the system) must be less than or equal to zero. 7483:any net chemical energy entering the sub-system 7315: 2461: 16043:, American Mathematical Society, Providence RI. 15547:(1949). 'Statistical basis of thermodynamics', 15140: 14625:; Van den Broeck, Christian (15 January 2010). 14164: 14162: 13844:(1926), p. 457, Knowledge editor's translation. 13241: 13239: 13237: 12751:imagined one container divided into two parts, 12538:, give out breakdown products and heat. Plants 8761:{\displaystyle {\frac {dS}{dt}}={\dot {S}}_{i}} 8621:The entropy of the universe tends to a maximum. 3447:(or đ) indicates a path dependent integration. 2644:Derive Kelvin Statement from Clausius Statement 2562:The efficiency of a quasi-static or reversible 15938:Transactions of the Royal Society of Edinburgh 15616:Lebon, G., Jou, D., Casas-Vázquez, J. (2008). 15212:, Manchester University Press, Manchester UK, 14127:Wright, Sean E.; Rosen, Marc A. (2004-02-01). 13981:Journal of Physics A: Mathematical and General 13974: 13890: 13771: 13769: 12710: 8353:transforms into a condition for the change in 6992:is path independent for reversible processes. 6985:{\displaystyle \int _{L}{\frac {\delta Q}{T}}} 6052:flown out from the reservoir to the engine 3. 4319:is the net work done by the engine per cycle, 3141:, an extensive variable, as a function of its 2614:expressed the second law in several wordings. 2532:The production of motive power is then due in 2018:(closed system; idealized, reversible process) 1770:, but this has been formally delegated to the 16320:Philosophy of thermal and statistical physics 15586:, second edition, Freeman, San Francisco CA, 13862:Borgnakke, C., Sonntag., R.E. (2009), p. 304. 13391: 13309: 13307: 13305: 8594:{\displaystyle \int {\frac {\delta Q}{T}}=-N} 6940:{\displaystyle \oint {\frac {\delta Q}{T}}=0} 5090:.) This fact can be proved by the following. 2536:not to an actual consumption of caloric, but 1624: 15979:Philosophical Magazine, Ser. 4, p. 304. 15712:(1867). "On the dynamical theory of gases". 15631: 15533:, Princeton University Press, Princeton NJ, 15507:. Oxford New York: Oxford University Press. 15006:, Cambridge University Press, Cambridge UK, 14247:, Cambridge University Press, Cambridge UK, 14175:International Journal of Engineering Science 14159: 13927:International Journal of Engineering Science 13760: 13735:The Differential Equations of Thermodynamics 13469: 13321: 13319: 13234: 11271:{\displaystyle N_{Y}\left(E+\delta E\right)} 11024:{\displaystyle N_{Y}\left(E+\delta E\right)} 8942:{\displaystyle P_{diss}=T_{a}{\dot {S}}_{i}} 8533: 8291:> 0. For the three examples given above: 8205:working at the macroscopic scale (above the 4122: 3000: 16267:," in G. J. Erickson and C. R. Smith (eds.) 15109:, Cambridge University Press, Cambridge UK. 15021:, American Institute of Physics, New York, 14359: 14245:Entropy in Relation to Incomplete Knowledge 14126: 13766: 13222:Bailyn, M. (1994), Section 71, pp. 113–154. 13136: 9489:{\displaystyle S=k_{\mathrm {B} }\ln \left} 8636:undergoing an arbitrary transformation is: 4982:. We also have used the fact that the heat 3927:, has a higher ratio of entropy-to-energy ( 2196:) and the temperature of the surroundings ( 1825:For example, when a path for conduction or 15830: 14976:, eighth edition, W.H. Freeman, New York, 14734: 14580:European Journal for Philosophy of Science 14218: 13871: 13726: 13672: 13660: 13450:"Concept and Statements of the Second Law" 13358: 13302: 12247:for the canonical ensemble in here gives: 10180:To evaluate the average, we partition the 2980:Rather like Planck's statement is that of 2754: 2750: 1631: 1617: 29: 16178: 16096: 15893:Roberts, J.K., Miller, A.R. (1928/1960). 15848: 15645: 15441:, Kluwer Academic Publishers, Dordrecht, 15277: 15119:, Harvard University Press, Cambridge MA. 15056:10.1093/acprof:oso/9780199562091.001.0001 14922: 14828: 14809: 14660: 14642: 14543: 14326: 13376: 13316: 13266: 12590: 11908: 11735: 11663: 11590: 11446: 11097: 10806: 10490: 10400: 10335:{\displaystyle \Omega _{Y}\left(E\right)} 10166: 9957:, corresponding to the external variable 8881:it gives the so-called dissipated energy 8501:Kelvin-Planck statement of the second law 8499:Established during the 19th century, the 8330:The second law in chemical thermodynamics 7805:the sub-system, over and beyond the work 2422: 2421: 2420: 2419: 2418: 2417: 2416: 2415: 2414: 2413: 2412: 2411: 2410: 2409: 2408: 2407: 2406: 2405: 2404: 2403: 2402: 2401: 2400: 2386: 2375: 2266: 2265: 2264: 2263: 2262: 2261: 2260: 2259: 2258: 2257: 2256: 2255: 2254: 2253: 2252: 2251: 2250: 2249: 2248: 2247: 2246: 2245: 2244: 2170: 2169: 2168: 2167: 2166: 2165: 2164: 2163: 2162: 2161: 2160: 2159: 2158: 2157: 2156: 2155: 2154: 2153: 2152: 2151: 2150: 2149: 2148: 2015: 2014: 2013: 2012: 2011: 2010: 2009: 2008: 2007: 2006: 2005: 2004: 2003: 2002: 2001: 2000: 1999: 1998: 1997: 1996: 1995: 1994: 1993: 1786:Heat flowing from hot water to cold water 15925:, Addison-Wesley Publishing, Reading MA. 15397: 15373: 15324: 15292: 15240: 15107:The Concepts of Classical Thermodynamics 14871:"Maxwell's demon | physics | Britannica" 14758:Lieb, E.H., Yngvason, J. (2003), p. 190. 14444: 14438: 14300: 13853:Lieb, E.H., Yngvason, J. (2003), p. 149. 13605: 13593: 13245: 12728: 12558: 9820:{\displaystyle dS={\frac {\delta Q}{T}}} 9316: 8537: 8461: 7072:as the temperature of the surroundings, 7032:{\displaystyle dS={\frac {\delta Q}{T}}} 6633:Therefore, if thermodynamic temperature 3951: 3184:), then the temperature is equal to the 2639: 2288:Introducing a set of internal variables 1781: 15947: 15928: 15708: 15474:, Cambridge University Press, New York 15209:Reflections on the motive power of fire 14365: 14279: 13975:Landsberg, P T; Tonge, G (April 1979). 13617: 13385: 13109: 12973:Reflections on the Motive Power of Fire 12573:their internal temperature may increase 10079:{\displaystyle X=-{\frac {dE_{r}}{dx}}} 9987:is the work performed by the system if 8484:'s work on the conservation of energy, 7690:It therefore follows that any net work 4533:and another (intermediate) temperature 4054:(1854) states that in a cyclic process 3915:spectral energy radiance data into the 3868:is Boltzmann's constant or (1.38)10 J/K 3864:is the speed of light or (2.9979)10 m/s 2949:and to deliver an equivalent amount of 2900: 16297: 16160: 16116: 16064:Goldstein, Martin, and Inge F., 1993. 15500: 15485:Glansdorff, P., Prigogine, I. (1971). 15090:Borgnakke, C., Sonntag., R.E. (2009). 14991:, Oxford University Press, Oxford UK, 14942: 14896: 14892: 14890: 14865: 14863: 14720:UC Riverside Department of Mathematics 14690:UC Riverside Department of Mathematics 14447:"Boltzmann's Entropy and Time's Arrow" 14408: 14312: 14224: 14168: 14021: 13959: 13920: 13732: 13013:A Modern Course in Statistical Physics 13007: 12759:. Both parts are filled with the same 12689: 8675:{\displaystyle {\frac {dS}{dt}}\geq 0} 4045: 4016:operating between the same reservoirs. 2444:the second principle of thermodynamics 16254:Unified Thermodynamics and Propulsion 15685: 15605:, John Wiley & Sons, Chichester, 14829:Halliwell, J.J.; et al. (1994). 14776:Glansdorff, P., Prigogine, I. (1971). 14492:Young, H. D; Freedman, R. A. (2004). 14243:Denbigh, K.G., Denbigh, J.S. (1985). 13416:This law is the basis of temperature. 13272: 13199: 13088:Massachusetts Institute of Technology 13063:Young, H. D; Freedman, R. A. (2004). 13034: 13032: 12617:. There is an exception, the case of 10548:{\displaystyle \Omega \left(E\right)} 10204:{\displaystyle \Omega \left(E\right)} 9830:where the temperature is defined as: 9523:{\displaystyle \Omega \left(E\right)} 9358:The first mechanical argument of the 9348:Derivation from statistical mechanics 8191:{\displaystyle dE+\delta w_{u}\leq 0} 8079:{\displaystyle dE+\delta w_{u}\leq 0} 3070: 2959: 2573: 2485: 1755:, formulated by the French scientist 1739:of the states of large assemblies of 15489:, Wiley-Interscience, London, 1971, 14722:. University of California Riverside 14713: 14692:. University of California Riverside 14683: 14445:Lebowitz, Joel L. (September 1993). 13544:Adkins, C.J. (1968/1983), pp. 56–58. 10248:{\displaystyle {\frac {dE_{r}}{dx}}} 9769:, however, proves that the quantity 9273:{\displaystyle {\dot {S}}_{i}\geq 0} 9069:{\displaystyle {\dot {S}}_{i}\geq 0} 8803:{\displaystyle {\dot {S}}_{i}\geq 0} 4390: 4135: 2606: 2067:and infinitesimal change of entropy 2037:Different notations are used for an 1719:Historically, the second law was an 1696:and provides necessary criteria for 16265:The evolution of Carnot's principle 16241:Philosophy of Statistical Mechanics 16237:Stanford Encyclopedia of Philosophy 15879:. Universities Press. p. 213. 15872: 14887: 14860: 14816:Stanford Encyclopedia of Philosophy 14767:Gyarmati, I. (1967/1970), pp. 4-14. 14268:, Oxford University Press, Oxford, 14229:. Dover Publications. p. §90. 14133:Journal of Solar Energy Engineering 13481: 13442: 13043:. Universities Press. p. 158. 13041:Chemical Engineering Thermodynamics 13038: 12579:and even gas giant planets such as 12510: 11222:{\displaystyle N_{Y}\left(E\right)} 4000: 3982:Perpetual motion of the second kind 13: 16099:Physical Origins of Time Asymmetry 16058: 14831:Physical Origins of Time Asymmetry 13293: 13190:Munster A. (1970), pp. 8–9, 50–51. 13029: 12737: 12676: 12470:Initial conditions at the Big Bang 12154: 12063: 11994: 11828: 11820: 11784: 11776: 11703: 11695: 11631: 11623: 11571: 11563: 11524: 11515: 11502: 11467: 11427: 11414: 11406: 11376: 11365: 11361: 11315: 11310: 11307: 11118: 10911: 10766: 10531: 10470: 10439: 10380: 10352: 10312: 10187: 9890: 9852: 9752: 9724: 9703: 9680: 9659: 9506: 9467: 9450: 8406: 8366: 8242:Direction of spontaneous processes 7786:It is useful to separate the work 7405: 7402: 7399: 7290: 7194: 7085: 6892:Entropy (classical thermodynamics) 5036:without losing its energy. (I.e., 3237: 3229: 2967:stated the second law as follows. 2931:. This version, also known as the 2885:{\displaystyle {\frac {Q}{\eta }}} 2672: 2653:as shown by the right figure. The 2377: 2327: 2219: 2116: 2078: 1968: 1884: 838: 791: 706: 659: 571: 524: 344:Intensive and extensive properties 14: 16331: 16230: 16149:, La Cañada, CA: DCW Industries. 16066:The Refrigerator and the Universe 16041:Lectures in Statistical Mechanics 15876:An Introduction to thermodynamics 15463:: 108–248, 343–524, reprinted in 14812:"Thermodynamic Asymmetry in Time" 14810:Callender, Craig (29 July 2011). 14740:Grandy, W.T. (Jr) (2008), p. 151. 13876:. North-Holland. pp. 41–56. 13252:. Elsevier Science. p. 120. 10904:and contribute to an increase in 10645:{\textstyle {\frac {dE_{r}}{dx}}} 7694:done by the sub-system must obey 2935:, of the second law states that 2099:, while heat, like work, is not. 1814:. It can be linked to the law of 1802:, and expresses its change for a 16:Physical law for entropy and heat 16280:The second law of Thermodynamics 16125:. New York: J. Wiley & Sons. 15831:Pokrovskii, Vladimir N. (2013). 15198:The Second Law of Thermodynamics 14749:Callen, H.B. (1960/1985), p. 15. 14496:, 11th edition. Pearson. p. 731. 13400:. Taylor & Francis. p. 13396:Entropy and its Physical Meaning 13359:Pokrovskii, Vladimir N. (2013). 13299:Adkins, C.J. (1968/1983), p. 75. 13164:David L. Chandler (2011-05-19). 13137:Jaffe, R.L.; Taylor, W. (2018). 13069:, 11th edition. Pearson. p. 764. 12861:The Nature of the Physical World 12645: 10848:{\displaystyle Ydx\leq \delta E} 9111:is the heat flow into the system 8692:is the entropy of the system and 8530:. This doctrine is obsolescent. 8480:Recognizing the significance of 1600: 1599: 919:Table of thermodynamic equations 16082:. Bristol UK; Philadelphia PA: 14848: 14822: 14803: 14791: 14779: 14770: 14761: 14752: 14743: 14716:"Can Gravity Decrease Entropy?" 14707: 14686:"Can Gravity Decrease Entropy?" 14677: 14614: 14526: 14517: 14508: 14499: 14402: 14306: 14258: 14237: 14201: 14120: 14081: 14042: 14015: 13968: 13953: 13914: 13865: 13856: 13847: 13835: 13823: 13799: 13796:Uffink, J. (2003), pp. 129–132. 13790: 13781: 13717: 13705: 13693: 13644: 13635: 13623: 13578: 13569: 13556: 13547: 13538: 13526: 13517: 13508: 13499: 13487: 13433: 13421: 13352: 13343: 13225: 13216: 13204: 13193: 13184: 8342:work, the Clausius inequality Δ 7790:done by the subsystem into the 2442:considered as a formulation of 2316:), one can record the equality 1794:provides the definition of the 1777: 1395:Maxwell's thermodynamic surface 16315:Non-equilibrium thermodynamics 15092:Fundamentals of Thermodynamics 14547:Science and Information Theory 14187:10.1016/j.ijengsci.2016.11.002 14169:Wright, S.E. (February 2017). 13939:10.1016/j.ijengsci.2007.08.005 13921:Wright, S.E. (December 2007). 13523:Carnot, S. (1824/1986), p. 68. 13514:Carnot, S. (1824/1986), p. 46. 13505:Carnot, S. (1824/1986), p. 51. 13331:Principles of Modern Chemistry 13172: 13157: 13130: 13103: 13094: 13072: 13001: 12963:Maximum entropy thermodynamics 12597:Non-equilibrium thermodynamics 12575:. This can be significant for 11460:The logarithmic derivative of 10652:lies within the range between 10512:as follows. Suppose we change 9376:Maxwell–Boltzmann distribution 8842:{\displaystyle {\dot {S}}_{i}} 8546:In 1865, the German physicist 8507:to receive heat from a single 8146:{\displaystyle dS_{tot}\geq 0} 7651: 7632: 7331:heat reservoir at temperature 7305:{\displaystyle \Delta S\geq 0} 6853:and the reference temperature 6797: 6761: 6752: 6726: 6693: 6674: 6611: 6585: 6566: 6540: 6514: 6488: 6480: 6454: 6442: 6416: 6303: 6277: 6271: 6245: 6232: 6217: 6212: 6197: 6190: 6175: 6170: 6155: 6141: 6126: 6119: 6104: 6094: 6068: 5966: 5947: 5941: 5937: 5918: 5910: 5884: 5880: 5874: 5870: 5851: 5843: 5824: 5820: 5807: 5788: 5782: 5778: 5759: 5751: 5732: 5728: 5715: 5696: 5689: 5670: 5632: 5628: 5609: 5601: 5575: 5571: 5565: 5561: 5542: 5534: 5515: 5511: 5504: 5485: 5477: 5458: 5443: 5424: 5416: 5390: 5382: 5363: 5359: 5352: 5326: 5319: 5300: 5261: 5242: 5234: 5215: 5207: 5188: 5184: 5177: 5158: 5151: 5132: 4958: 4932: 4913: 4898: 4891: 4876: 4831: 4805: 4786: 4771: 4764: 4749: 4704: 4678: 4659: 4644: 4637: 4622: 4480: 4454: 4441: 4426: 4419: 4404: 4279: 4264: 4257: 4242: 4170: 4155: 3976: 3845: 3842: 3795: 3786: 3739: 3733: 3680: 3671: 3618: 3615: 3409: 3358: 2897:hence the two are equivalent. 2774: 2755: 2751: 2088:{\displaystyle (\mathrm {d} )} 2082: 2074: 2054: 2048: 1944: 1938: 1833:are accounted for in terms of 1129: 1117: 1074: 1062: 1019: 1007: 979: 967: 1: 15948:Thomson, W. (December 1852). 15664:10.1016/S0370-1573(98)00082-9 15188:. A translation may be found 14662:10.1088/1367-2630/12/1/013013 14106:10.1016/s1164-0235(01)00041-3 14067:10.1016/s1164-0235(01)00040-1 14036:10.1016/S0020-7225(01)00024-6 13787:Buchdahl, H.A. (1966), p. 69. 13723:Buchdahl, H.A. (1966), p. 68. 13166:"Explained: The Carnot Limit" 12994: 12832: 12825:. It is therefore performing 12791:will have increased while in 8421:{\displaystyle \Delta A<0} 8381:{\displaystyle \Delta G<0} 7327:they can be considered as an 7316:Energy, available useful work 6950:That means the line integral 6382:{\displaystyle T_{1}=273.16K} 2941:It is impossible to devise a 2474:(1851), and the statement in 2462:Various statements of the law 1894:{\displaystyle \mathrm {d} S} 1296:Mechanical equivalent of heat 16248:Second law of thermodynamics 16012:Stud. Hist. Phil. Mod. Phys. 15989:, M.I.T Press, Cambridge MA. 15944:(part II): 261–268, 289–298. 15811:The Theory of Heat Radiation 15117:The Nature of Thermodynamics 14897:Norton, John (3 July 2013). 14714:Baez, John (7 August 2000). 14684:Baez, John (7 August 2000). 13812:, Academic Press, New York, 13325:Oxtoby, D. W; Gillis, H.P., 13015:. Edward Arnold. p. 9. 12978:Relativistic heat conduction 12918:Zeroth law of thermodynamics 12897:, Academic Press, New York, 12767:on both sides, an imaginary 10820:such energy eigenstates. If 8444:without electrical work is d 8336:spontaneous chemical process 6322:Now consider the case where 3056:{\displaystyle \delta Q=TdS} 2894:the definition of efficiency 2451:zeroth law of thermodynamics 1772:zeroth law of thermodynamics 1684:as a physical property of a 1645:second law of thermodynamics 908:Onsager reciprocal relations 7: 16257:from Prof. Z. S. Spakovszky 15620:, Springer-Verlag, Berlin, 15043:Concepts in thermal physics 14420:. Alfred A. Knopf. p. 14345:10.1016/j.shpsb.2017.01.001 13702:, Ford, G.W. (1963), p. 16. 13584:Eu, B.C. (2002), pp. 32–35. 12928:Third law of thermodynamics 12923:First law of thermodynamics 12910: 12893:, Muncaster, R. G. (1980). 12723:Poincaré recurrence theorem 12717:Poincaré recurrence theorem 12711:Poincaré recurrence theorem 12601:The theory of classical or 11191:. They are counted in both 8475:Nicolas Léonard Sadi Carnot 7457:first law of thermodynamics 7044:third law of thermodynamics 6353:of water as 273.16 Kelvin; 4502: 4302: 4025:thermodynamic reversibility 3994:first law of thermodynamics 2722:first law of thermodynamics 2657:of a normal heat engine is 2512:first law of thermodynamics 1792:first law of thermodynamics 1694:first law of thermodynamics 1400:Entropy as energy dispersal 1211:"Perpetual motion" machines 1150:{\displaystyle G(T,p)=H-TS} 1095:{\displaystyle A(T,V)=U-TS} 1040:{\displaystyle H(S,p)=U+pV} 10: 16336: 16145:Stephen Jay Kline (1999). 15987:Generalized Thermodynamics 15923:Elements of Thermodynamics 15861:, Academic Press, London, 15799:Treatise on Thermodynamics 15501:Grandy, Walter T. (2008). 15374:Clausius, R. (July 1856). 15293:Clausius, R. (July 1851). 15194:translation is to be found 15094:, seventh edition, Wiley, 15019:A Survey of Thermodynamics 14974:Atkins' Physical Chemistry 14945:Equilibrium thermodynamics 14935: 14227:Treatise on Thermodynamics 14001:10.1088/0305-4470/12/4/015 13808:, Muncaster, R.G. (1980). 13761:Lieb & Yngvason (1999) 13553:Münster, A. (1970), p. 11. 13470:Lieb & Yngvason (1999) 13313:Münster, A. (1970), p. 45. 13231:Bailyn, M. (1994), p. 120. 12943:Heat death of the universe 12741: 12714: 12693: 12649: 12603:equilibrium thermodynamics 12594: 12583:. When the entropy of the 12473: 12220:Inserting the formula for 11184:{\displaystyle E+\delta E} 10975:{\displaystyle E+\delta E} 10946:{\displaystyle E+\delta E} 10897:{\displaystyle E+\delta E} 10694:{\displaystyle Y+\delta Y} 10601:{\displaystyle E+\delta E} 10297:{\displaystyle Y+\delta Y} 9991:is increased by an amount 9572:{\displaystyle E+\delta E} 9401:have also been suggested. 9351: 9305:{\displaystyle {\dot {S}}} 9104:{\displaystyle {\dot {Q}}} 8518:is also important for the 8455: 8451: 7319: 7276:{\displaystyle \delta Q=0} 6889: 6885: 4126: 3985: 3022:geometrical thermodynamics 847:{\displaystyle \partial T} 800:{\displaystyle \partial V} 715:{\displaystyle \partial p} 668:{\displaystyle \partial V} 580:{\displaystyle \partial T} 533:{\displaystyle \partial S} 15903:(1950). Irreversibility, 15714:Phil. Trans. R. Soc. Lond 15568:Gyarmati, I. (1967/1970) 15422:Denbigh, K. (1954/1981). 15407:. London: John van Voorst 15372:Translated into English: 15311:10.1080/14786445108646819 15291:Translated into English: 15192:. Also a mostly reliable 14592:10.1007/s13194-012-0056-8 14264:Grandy, W.T., Jr (2008). 13439:Quinn, T.J. (1983), p. 8. 12988:Thermodynamic equilibrium 12948:History of thermodynamics 12933:Clausius–Duhem inequality 12611:thermodynamic equilibrium 9758:{\displaystyle 1/\Omega } 9717:this, there are a number 8554:" in the following form: 8552:mechanical theory of heat 8534:Account given by Clausius 8238:, and other disciplines. 7467:added to the sub-system, 6045:{\displaystyle q_{2}^{*}} 4540:, and the second between 4129:Thermodynamic temperature 4123:Thermodynamic temperature 3908:is found by substituting 3001:Principle of Carathéodory 2504:thermodynamic equilibrium 2470:(1854), the statement by 2456:thermodynamic temperature 2060:{\displaystyle (\delta )} 1930:thermodynamic temperature 1841:, and its total entropy, 1839:thermodynamic equilibrium 1768:thermodynamic temperature 1737:probability distributions 1706:thermodynamic equilibrium 1321:An Inquiry Concerning the 16097:Halliwell, J.J. (1994). 15770:Classical Thermodynamics 15353:10.1002/andp.18541691202 15270:10.1002/andp.18501550403 15046:(2nd ed.). Oxford: 14621:Esposito, Massimiliano; 14416:The Fabric of the Cosmos 14388:10.1103/PhysRevD.32.2489 13737:. Taylor & Francis. 13213:(1897/1903), pp. 79–107. 12874:Philosopher / Physicist 12857:Arthur Stanley Eddington 12846:is in disagreement with 12827:thermodynamic operations 12667:the causal arrow of time 12540:take in radiative energy 11151:{\displaystyle \delta E} 10105:{\displaystyle \delta E} 9641:{\displaystyle \delta E} 9618:{\displaystyle \delta E} 9595:{\displaystyle \delta E} 8323:electrochemical gradient 8232:environmental accounting 3301:\delta S_{\text{NetRad}} 1921:{\displaystyle \delta Q} 1723:that was accepted as an 1334:Heterogeneous Substances 751:{\displaystyle \alpha =} 619:{\displaystyle \beta =-} 15895:Heat and Thermodynamics 15339:. xciii (12): 481–506. 15305:(VIII): 1–21, 102–119. 15256:(4): 368–397, 500–524. 15105:Buchdahl, H.A. (1966). 15048:Oxford University Press 14972:, de Paula, J. (2006). 14286:Entropy Sites — A Guide 13333:, Brooks Cole. p. 617. 13246:Mortimer, R.G. (2008). 13181:(1897/1903), pp. 40–41. 12683:thermodynamic processes 12656:Entropy (arrow of time) 11473:{\displaystyle \Omega } 11289:yields the expression: 11124:{\displaystyle \Omega } 10917:{\displaystyle \Omega } 10255:within a range between 9953:The generalized force, 9730:{\displaystyle \Omega } 9709:{\displaystyle \Omega } 9686:{\displaystyle \Omega } 9665:{\displaystyle \Omega } 9360:Kinetic theory of gases 8849:the sum of the rate of 8260:Heat can be transferred 8102:infinite-reservoir-like 3018:adiabatic accessibility 3006:Constantin Carathéodory 2480:Constantin Carathéodory 1667:energy interconversions 16310:Laws of thermodynamics 16271:, Vol,.1: p. 267. 16243:" – by Lawrence Sklar. 16119:Thurston, Robert Henry 15999:, Springer, New York, 15726:10.1098/rstl.1867.0004 15417:editions:PwR_Sbkwa8IC. 15196:at Kestin, J. (1976). 15085:Lectures on Gas Theory 15038:Blundell, Katherine M. 15002:Baierlein, R. (1999). 14943:Adkins, C. J. (1983). 14631:New Journal of Physics 14544:Brillouin, L. (2013). 13962:Dover Publications, NY 13733:Sychev, V. V. (1991). 13392:J. S. Dugdale (1996). 13110:Carroll, Sean (2010). 13039:Rao, Y. V. C. (1997). 12968:Quantum thermodynamics 12958:Laws of thermodynamics 12908: 12881: 12866: 12734: 12591:Non-equilibrium states 12501:cosmological inflation 12494:negative heat capacity 12460: 12241: 12211: 12117: 12021: 11913: 11740: 11668: 11595: 11474: 11451: 11272: 11223: 11185: 11152: 11125: 11102: 11025: 10976: 10947: 10918: 10898: 10869: 10849: 10811: 10695: 10666: 10646: 10602: 10573: 10549: 10495: 10405: 10336: 10304:. Calling this number 10298: 10269: 10249: 10205: 10171: 10106: 10080: 10024: 9981: 9924: 9821: 9759: 9731: 9710: 9687: 9666: 9642: 9619: 9596: 9573: 9544: 9524: 9490: 9422: 9306: 9274: 9232: 9127: 9105: 9070: 9028: 8943: 8875: 8843: 8804: 8762: 8676: 8623: 8595: 8543: 8470: 8422: 8382: 8192: 8147: 8080: 8029: 7923: 7777: 7677: 7578: 7446: 7306: 7277: 7241: 7175: 7054:for perfect crystals. 7033: 6986: 6941: 6844: 6700: 6624: 6383: 6343: 6313: 6046: 6014: 5984: 5084: 5057: 5030: 5003: 4965: 4838: 4711: 4490: 4290: 4099: 3957: 3852: 3558: 3441: 3422: 3333: 3302: 3266: 3057: 3014: 2986:irreversible phenomena 2886: 2859: 2800: 2714: 2645: 2593: 2432: 2302: 2276: 2180: 2089: 2061: 2028: 1951: 1922: 1895: 1855: 1816:conservation of energy 1787: 1690:conservation of energy 1151: 1096: 1041: 986: 985:{\displaystyle U(S,V)} 848: 824: 801: 777: 752: 716: 692: 669: 645: 620: 581: 557: 534: 510: 485: 464:Specific heat capacity 68:Quantum thermodynamics 16129:full text of 1897 ed. 16117:Carnot, Sadi (1890). 16039:, Ford, G.W. (1963). 15150:Mathematische Annalen 13140:The Physics of Energy 12882: 12867: 12836: 12732: 12559:Gravitational systems 12505:created spontaneously 12474:Further information: 12461: 12242: 12240:{\displaystyle P_{j}} 12212: 12118: 12022: 11914: 11741: 11669: 11596: 11475: 11452: 11273: 11224: 11186: 11153: 11126: 11103: 11026: 10977: 10948: 10919: 10899: 10870: 10850: 10812: 10696: 10667: 10647: 10603: 10574: 10550: 10496: 10406: 10337: 10299: 10270: 10250: 10206: 10172: 10107: 10081: 10025: 10023:{\displaystyle E_{r}} 9982: 9961:is defined such that 9925: 9822: 9760: 9732: 9711: 9688: 9667: 9643: 9620: 9597: 9574: 9545: 9525: 9491: 9423: 9406:fundamental postulate 9352:Further information: 9322:Statistical mechanics 9317:Statistical mechanics 9307: 9275: 9233: 9138:corresponding terms. 9128: 9106: 9071: 9029: 8944: 8876: 8874:{\displaystyle T_{a}} 8844: 8805: 8763: 8677: 8619: 8596: 8541: 8465: 8423: 8397:Helmholtz free energy 8383: 8220:second law efficiency 8193: 8148: 8081: 8030: 7924: 7778: 7678: 7579: 7447: 7307: 7278: 7242: 7176: 7034: 6987: 6942: 6845: 6701: 6625: 6384: 6344: 6342:{\displaystyle T_{1}} 6314: 6047: 6015: 6013:{\displaystyle q_{2}} 5985: 5085: 5083:{\displaystyle T_{2}} 5058: 5056:{\displaystyle q_{2}} 5031: 5029:{\displaystyle T_{2}} 5004: 5002:{\displaystyle q_{2}} 4966: 4839: 4712: 4491: 4291: 4100: 3955: 3853: 3559: 3442: 3423: 3334: 3303: 3267: 3058: 3010: 2933:heat engine statement 2887: 2860: 2801: 2715: 2643: 2589: 2578:The German scientist 2433: 2303: 2277: 2181: 2095:because entropy is a 2090: 2062: 2029: 1952: 1923: 1896: 1856: 1785: 1733:Statistical mechanics 1698:spontaneous processes 1332:On the Equilibrium of 1152: 1097: 1050:Helmholtz free energy 1042: 987: 849: 825: 802: 778: 753: 717: 693: 670: 646: 621: 582: 558: 535: 511: 486: 16305:Equations of physics 16286:, December 16, 2004) 16084:Institute of Physics 15873:Rao, Y.V.C. (2004). 15857:Quinn, T.J. (1983). 15768:Münster, A. (1970), 15470:Griem, H.R. (2005). 15034:Blundell, Stephen J. 14857:(1950), p. 192. 14288:Content selected by 13669:(1897/1903), p. 100. 13430:(1968), pp. 207–209. 12787:of the molecules in 12623:critical opalescence 12585:black-body radiation 12254: 12224: 12133: 12045: 11942: 11756: 11684: 11677:Combining this with 11612: 11491: 11464: 11296: 11233: 11195: 11166: 11139: 11115: 11038: 10986: 10957: 10928: 10908: 10879: 10859: 10824: 10735: 10676: 10656: 10612: 10583: 10563: 10528: 10421: 10349: 10308: 10279: 10259: 10215: 10184: 10119: 10093: 10037: 10007: 9999:is the volume, then 9965: 9837: 9790: 9741: 9721: 9700: 9677: 9656: 9629: 9606: 9583: 9554: 9534: 9503: 9435: 9412: 9287: 9242: 9148: 9117: 9086: 9038: 8959: 8885: 8858: 8817: 8772: 8713: 8643: 8561: 8482:James Prescott Joule 8403: 8363: 8157: 8115: 8100:In sum, if a proper 8045: 7952: 7820: 7701: 7610: 7505: 7387: 7362:Whatever changes to 7287: 7258: 7191: 7079: 7046:, which states that 7002: 6954: 6910: 6720: 6644: 6410: 6357: 6326: 6062: 6024: 5997: 5097: 5067: 5040: 5013: 4986: 4850: 4723: 4596: 4397: 4142: 4061: 3567: 3457: 3435: 3345: 3312: 3284: 3212: 3032: 2901:Planck's proposition 2869: 2810: 2728: 2669: 2323: 2301:{\displaystyle \xi } 2292: 2215: 2112: 2071: 2045: 1964: 1935: 1909: 1880: 1845: 1800:thermodynamic system 1729:thermodynamic theory 1692:as expressed in the 1686:thermodynamic system 1345:Motive Power of Fire 1111: 1056: 1001: 961: 913:Bridgman's equations 890:Fundamental relation 835: 814: 788: 767: 739: 703: 682: 656: 635: 604: 568: 547: 521: 500: 472: 16171:2011AIPC.1411..327K 15850:10.1155/2013/906136 15837:ISRN Thermodynamics 15690:(second ed.). 15688:Statistical physics 15656:1999PhR...310....1L 15345:1854AnP...169..481C 15262:1850AnP...155..500C 15017:Bailyn, M. (1994). 14987:Attard, P. (2012). 14915:2013Entrp..15.4432N 14653:2010NJPh...12a3013E 14466:1993PhT....46i..32L 14380:1985PhRvD..32.2489H 14337:2017SHPMP..57...53G 14225:Planck, M. (1945). 13993:1979JPhA...12..551L 13832:(1897/1903), p. 81. 13632:(1897/1903), p. 86. 13378:10.1155/2013/906136 13365:ISRN Thermodynamics 12938:Fluctuation theorem 12848:Maxwell's equations 12749:James Clerk Maxwell 12733:James Clerk Maxwell 12701:Loschmidt's paradox 12696:Loschmidt's paradox 12690:Loschmidt's paradox 12681:Irreversibility in 12486:observable universe 10508:at constant energy 9980:{\displaystyle Xdx} 9945:. According to the 9383:Loschmidt's paradox 9364:James Clerk Maxwell 8612:is temperature and 8468:École Polytechnique 8207:thermodynamic limit 7598:chemical potentials 7065:on this loop, with 7063:Clausius inequality 6834: 6819: 6796: 6778: 6041: 4046:Clausius inequality 2984:and G. W. Ford for 1950:{\displaystyle (T)} 1323:Source ... Friction 1255:Loschmidt's paradox 447:Material properties 325:Conjugate variables 16251:in the MIT Course 16161:Kostic, M (2011). 16138:2007-08-18 at the 15946:Also published in 15905:Proc. R. Ir. Acad. 15747:, Pitman, London, 15686:Mandl, F. (1988). 15457:Trans. Conn. Acad. 15337:Annalen der Physik 15279:2027/uc1.$ b242250 15250:Annalen der Physik 15162:10.1007/bf01450409 14875:www.britannica.com 14494:University Physics 14231:eq.(39) & (40) 13535:(1980), Chapter 5. 13273:Fermi, E. (2012). 13249:Physical Chemistry 13066:University Physics 12953:Jarzynski equality 12735: 12456: 12387: 12331: 12285: 12237: 12207: 12169: 12113: 12078: 12036:partition function 12017: 11933:canonical ensemble 11909: 11736: 11664: 11591: 11484:is thus given by: 11470: 11447: 11349: 11268: 11219: 11181: 11148: 11121: 11098: 11021: 10972: 10943: 10914: 10894: 10865: 10845: 10807: 10691: 10662: 10642: 10598: 10569: 10545: 10491: 10465: 10401: 10378: 10332: 10294: 10265: 10245: 10201: 10167: 10102: 10076: 10020: 9995:. For example, if 9977: 9920: 9817: 9755: 9727: 9706: 9683: 9662: 9638: 9615: 9592: 9569: 9540: 9520: 9486: 9418: 9391:boundary condition 9302: 9270: 9228: 9123: 9101: 9066: 9024: 8939: 8871: 8851:entropy production 8839: 8800: 8758: 8672: 8591: 8544: 8528:macroscopic system 8516:ergodic hypothesis 8471: 8458:History of entropy 8418: 8399:must be negative, 8378: 8188: 8143: 8076: 8025: 7945:of the subsystem, 7919: 7773: 7673: 7574: 7442: 7302: 7273: 7237: 7171: 7029: 6982: 6937: 6902:reversible process 6840: 6820: 6805: 6782: 6764: 6709:then the function 6696: 6620: 6379: 6339: 6309: 6042: 6027: 6010: 5980: 5978: 5080: 5053: 5026: 4999: 4961: 4834: 4707: 4486: 4346:| < 0 is waste 4286: 4095: 3958: 3848: 3554: 3418: 3262: 3186:partial derivative 3071:Planck's principle 3053: 3028:, in other words, 2960:Planck's statement 2882: 2855: 2796: 2710: 2646: 2585:Clausius statement 2574:Clausius statement 2486:Carnot's principle 2478:thermodynamics by 2428: 2374: 2298: 2272: 2176: 2085: 2057: 2024: 1947: 1918: 1891: 1851: 1788: 1587:Order and disorder 1343:Reflections on the 1250:Heat death paradox 1147: 1092: 1037: 982: 844: 820: 797: 773: 748: 712: 688: 665: 641: 616: 577: 553: 530: 506: 484:{\displaystyle c=} 481: 454:Property databases 430:Reduced properties 414:Chemical potential 378:Functions of state 301:Thermal efficiency 37:Carnot heat engine 16198:978-0-7354-0985-9 16189:10.1063/1.3665247 16108:978-0-521-56837-1 16092:978-0-585-49237-7 16074:978-0-674-75324-2 15886:978-81-7371-461-0 15701:978-0-471-91533-1 15626:978-3-540-74252-4 15514:978-0-19-954617-6 15437:Eu, B.C. (2002). 15100:978-0-470-04192-5 14997:978-0-19-966276-0 14982:978-0-7167-8759-4 14924:10.3390/e15104432 14909:(12): 4432–4483. 14840:978-0-521-56837-1 14623:Lindenberg, Katja 14557:978-0-486-49755-6 14431:978-0-375-41288-2 14374:(10): 2489–2495. 14274:978-0-19-954617-6 14145:10.1115/1.1636796 14030:(15): 1691–1706. 13933:(12): 1007–1016. 13883:978-0-444-87748-2 13744:978-1-56032-121-7 13566:(1998), pp.67–75. 13411:978-0-7484-0569-5 13286:978-0-486-13485-7 13259:978-0-12-370617-1 13150:978-1-107-01665-1 13123:978-0-525-95133-9 13050:978-81-7371-048-3 12799:and increases in 12518:Erwin Schrödinger 12454: 12436: 12378: 12376: 12322: 12320: 12276: 12274: 12160: 12069: 12015: 12004: 11906: 11882: 11869: 11835: 11791: 11733: 11710: 11661: 11638: 11578: 11531: 11434: 11383: 11340: 11322: 11285:and summing over 11031:. The difference 10868:{\displaystyle E} 10795: 10665:{\displaystyle Y} 10640: 10572:{\displaystyle E} 10456: 10454: 10369: 10268:{\displaystyle Y} 10243: 10160: 10074: 9947:adiabatic theorem 9918: 9862: 9815: 9543:{\displaystyle E} 9421:{\displaystyle E} 9299: 9255: 9219: 9203: 9189: 9184: 9169: 9126:{\displaystyle T} 9098: 9051: 9015: 9000: 8995: 8980: 8930: 8830: 8785: 8749: 8734: 8664: 8580: 8355:Gibbs free energy 8153:is equivalent to 7801:that can be done 7455:According to the 7252:adiabatic process 7235: 7163: 7126: 7027: 6980: 6929: 6898:Clausius equality 6896:According to the 6835: 6666: 6615: 6577: 6532: 6518: 6237: 6146: 5971: 5812: 5720: 5357: 5182: 4918: 4791: 4664: 4510: 4509: 4446: 4310: 4309: 4284: 4227: 4185: 4087: 4084: 3840: 3784: 3731: 3669: 3613: 3549: 3536: 3493: 3406: 3391: 3355: 3296: 3244: 3156:, and mol number 2947:thermal reservoir 2880: 2842: 2788: 2742: 2734: 2697: 2607:Kelvin statements 2426: 2365: 2363: 2350: 2270: 2242: 2174: 2146: 2143: 2097:function of state 2019: 1991: 1854:{\displaystyle S} 1721:empirical finding 1641: 1640: 1582:Self-organization 1407: 1406: 1105:Gibbs free energy 903:Maxwell relations 861: 860: 857: 856: 823:{\displaystyle V} 776:{\displaystyle 1} 731:Thermal expansion 725: 724: 691:{\displaystyle V} 644:{\displaystyle 1} 590: 589: 556:{\displaystyle N} 509:{\displaystyle T} 437: 436: 353:Process functions 339:Property diagrams 318:System properties 308: 307: 273:Endoreversibility 165:Equation of state 16327: 16222: 16216: 16212: 16210: 16202: 16182: 16126: 16112: 15969: 15967: 15965: 15945: 15890: 15854: 15852: 15737: 15705: 15692:Wiley & Sons 15675: 15649: 15647:cond-mat/9708200 15559:Guggenheim, E.A. 15545:Guggenheim, E.A. 15526: 15419: 15414: 15412: 15395: 15393: 15391: 15371: 15369: 15367: 15362:on 24 March 2014 15361: 15355:. Archived from 15334: 15321: 15319: 15317: 15290: 15288: 15286: 15281: 15187: 15182: 15181: 15172:. Archived from 15077: 14966: 14929: 14928: 14926: 14894: 14885: 14884: 14882: 14881: 14867: 14858: 14852: 14846: 14844: 14826: 14820: 14819: 14807: 14801: 14795: 14789: 14783: 14777: 14774: 14768: 14765: 14759: 14756: 14750: 14747: 14741: 14738: 14732: 14731: 14729: 14727: 14711: 14705: 14704: 14699: 14697: 14681: 14675: 14674: 14664: 14646: 14618: 14612: 14611: 14575: 14569: 14568: 14566: 14564: 14541: 14535: 14530: 14524: 14521: 14515: 14512: 14506: 14503: 14497: 14490: 14484: 14483: 14481: 14480: 14474:10.1063/1.881363 14451: 14442: 14436: 14435: 14419: 14406: 14400: 14399: 14363: 14357: 14356: 14330: 14310: 14304: 14298: 14292: 14290:Frank L. Lambert 14283: 14277: 14262: 14256: 14241: 14235: 14233: 14222: 14216: 14214:Wolfram Research 14209:Clausius theorem 14205: 14199: 14198: 14166: 14157: 14156: 14124: 14118: 14117: 14085: 14079: 14078: 14046: 14040: 14039: 14024:Int. J. Eng. Sci 14019: 14013: 14012: 13972: 13966: 13965: 13957: 13951: 13950: 13918: 13912: 13894: 13888: 13887: 13869: 13863: 13860: 13854: 13851: 13845: 13839: 13833: 13827: 13821: 13803: 13797: 13794: 13788: 13785: 13779: 13773: 13764: 13758: 13749: 13748: 13730: 13724: 13721: 13715: 13712:Carathéodory, C. 13709: 13703: 13697: 13691: 13688: 13682: 13676: 13670: 13664: 13658: 13648: 13642: 13639: 13633: 13627: 13621: 13615: 13609: 13603: 13597: 13591: 13585: 13582: 13576: 13573: 13567: 13560: 13554: 13551: 13545: 13542: 13536: 13530: 13524: 13521: 13515: 13512: 13506: 13503: 13497: 13491: 13485: 13479: 13473: 13467: 13461: 13460: 13458: 13457: 13446: 13440: 13437: 13431: 13425: 13419: 13418: 13399: 13389: 13383: 13382: 13380: 13356: 13350: 13347: 13341: 13323: 13314: 13311: 13300: 13297: 13291: 13290: 13270: 13264: 13263: 13243: 13232: 13229: 13223: 13220: 13214: 13208: 13202: 13197: 13191: 13188: 13182: 13176: 13170: 13169: 13161: 13155: 13154: 13134: 13128: 13127: 13107: 13101: 13098: 13092: 13091: 13076: 13070: 13061: 13055: 13054: 13036: 13027: 13026: 13005: 12906: 12879: 12864: 12553:ongoing research 12511:Living organisms 12465: 12463: 12462: 12457: 12455: 12450: 12442: 12437: 12432: 12415: 12410: 12409: 12397: 12396: 12386: 12377: 12369: 12364: 12360: 12359: 12358: 12349: 12348: 12330: 12321: 12313: 12308: 12307: 12295: 12294: 12284: 12275: 12267: 12246: 12244: 12243: 12238: 12236: 12235: 12216: 12214: 12213: 12208: 12206: 12205: 12193: 12189: 12188: 12168: 12159: 12158: 12157: 12122: 12120: 12119: 12114: 12112: 12108: 12107: 12088: 12087: 12077: 12068: 12067: 12066: 12026: 12024: 12023: 12018: 12016: 12011: 12010: 12006: 12005: 12003: 11999: 11998: 11997: 11986: 11985: 11976: 11959: 11954: 11953: 11918: 11916: 11915: 11910: 11907: 11902: 11894: 11883: 11875: 11870: 11865: 11857: 11846: 11845: 11840: 11836: 11834: 11826: 11818: 11802: 11801: 11796: 11792: 11790: 11782: 11774: 11745: 11743: 11742: 11737: 11734: 11726: 11721: 11720: 11715: 11711: 11709: 11701: 11693: 11673: 11671: 11670: 11665: 11662: 11654: 11649: 11648: 11643: 11639: 11637: 11629: 11621: 11600: 11598: 11597: 11592: 11589: 11588: 11583: 11579: 11577: 11569: 11561: 11542: 11541: 11536: 11532: 11530: 11522: 11521: 11500: 11480:with respect to 11479: 11477: 11476: 11471: 11456: 11454: 11453: 11448: 11445: 11444: 11439: 11435: 11433: 11425: 11424: 11420: 11404: 11394: 11393: 11388: 11384: 11382: 11374: 11373: 11372: 11359: 11348: 11333: 11332: 11327: 11323: 11321: 11313: 11305: 11277: 11275: 11274: 11269: 11267: 11263: 11245: 11244: 11228: 11226: 11225: 11220: 11218: 11207: 11206: 11190: 11188: 11187: 11182: 11157: 11155: 11154: 11149: 11130: 11128: 11127: 11122: 11107: 11105: 11104: 11099: 11096: 11092: 11074: 11073: 11061: 11050: 11049: 11030: 11028: 11027: 11022: 11020: 11016: 10998: 10997: 10981: 10979: 10978: 10973: 10952: 10950: 10949: 10944: 10923: 10921: 10920: 10915: 10903: 10901: 10900: 10895: 10874: 10872: 10871: 10866: 10854: 10852: 10851: 10846: 10816: 10814: 10813: 10808: 10796: 10794: 10786: 10785: 10774: 10773: 10763: 10758: 10747: 10746: 10720:move from below 10700: 10698: 10697: 10692: 10671: 10669: 10668: 10663: 10651: 10649: 10648: 10643: 10641: 10639: 10631: 10630: 10629: 10616: 10607: 10605: 10604: 10599: 10578: 10576: 10575: 10570: 10554: 10552: 10551: 10546: 10544: 10500: 10498: 10497: 10492: 10489: 10478: 10477: 10464: 10455: 10453: 10452: 10434: 10410: 10408: 10407: 10402: 10399: 10388: 10387: 10377: 10365: 10341: 10339: 10338: 10333: 10331: 10320: 10319: 10303: 10301: 10300: 10295: 10274: 10272: 10271: 10266: 10254: 10252: 10251: 10246: 10244: 10242: 10234: 10233: 10232: 10219: 10210: 10208: 10207: 10202: 10200: 10176: 10174: 10173: 10168: 10165: 10161: 10159: 10151: 10150: 10149: 10136: 10111: 10109: 10108: 10103: 10085: 10083: 10082: 10077: 10075: 10073: 10065: 10064: 10063: 10050: 10029: 10027: 10026: 10021: 10019: 10018: 9986: 9984: 9983: 9978: 9929: 9927: 9926: 9921: 9919: 9917: 9909: 9908: 9904: 9903: 9874: 9863: 9861: 9857: 9856: 9855: 9841: 9826: 9824: 9823: 9818: 9816: 9811: 9803: 9774: 9764: 9762: 9761: 9756: 9751: 9736: 9734: 9733: 9728: 9715: 9713: 9712: 9707: 9692: 9690: 9689: 9684: 9671: 9669: 9668: 9663: 9647: 9645: 9644: 9639: 9624: 9622: 9621: 9616: 9601: 9599: 9598: 9593: 9578: 9576: 9575: 9570: 9549: 9547: 9546: 9541: 9529: 9527: 9526: 9521: 9519: 9495: 9493: 9492: 9487: 9485: 9481: 9480: 9455: 9454: 9453: 9427: 9425: 9424: 9419: 9368:Ludwig Boltzmann 9338: 9337: 9311: 9309: 9308: 9303: 9301: 9300: 9292: 9279: 9277: 9276: 9271: 9263: 9262: 9257: 9256: 9248: 9237: 9235: 9234: 9229: 9227: 9226: 9221: 9220: 9212: 9205: 9204: 9196: 9190: 9185: 9177: 9175: 9170: 9168: 9160: 9152: 9132: 9130: 9129: 9124: 9110: 9108: 9107: 9102: 9100: 9099: 9091: 9075: 9073: 9072: 9067: 9059: 9058: 9053: 9052: 9044: 9033: 9031: 9030: 9025: 9023: 9022: 9017: 9016: 9008: 9001: 8996: 8988: 8986: 8981: 8979: 8971: 8963: 8948: 8946: 8945: 8940: 8938: 8937: 8932: 8931: 8923: 8919: 8918: 8906: 8905: 8880: 8878: 8877: 8872: 8870: 8869: 8848: 8846: 8845: 8840: 8838: 8837: 8832: 8831: 8823: 8809: 8807: 8806: 8801: 8793: 8792: 8787: 8786: 8778: 8767: 8765: 8764: 8759: 8757: 8756: 8751: 8750: 8742: 8735: 8733: 8725: 8717: 8681: 8679: 8678: 8673: 8665: 8663: 8655: 8647: 8600: 8598: 8597: 8592: 8581: 8576: 8568: 8427: 8425: 8424: 8419: 8387: 8385: 8384: 8379: 8315:active transport 8248:isolated systems 8213:process engineer 8197: 8195: 8194: 8189: 8181: 8180: 8152: 8150: 8149: 8144: 8136: 8135: 8085: 8083: 8082: 8077: 8069: 8068: 8034: 8032: 8031: 8026: 8024: 8023: 8014: 8013: 7992: 7991: 7976: 7975: 7928: 7926: 7925: 7920: 7918: 7914: 7913: 7912: 7903: 7902: 7881: 7880: 7865: 7864: 7835: 7834: 7782: 7780: 7779: 7774: 7772: 7771: 7759: 7758: 7734: 7733: 7682: 7680: 7679: 7674: 7666: 7665: 7650: 7649: 7631: 7630: 7583: 7581: 7580: 7575: 7573: 7569: 7568: 7567: 7558: 7557: 7479:the sub-system, 7451: 7449: 7448: 7443: 7435: 7434: 7410: 7409: 7408: 7311: 7309: 7308: 7303: 7282: 7280: 7279: 7274: 7246: 7244: 7243: 7238: 7236: 7234: 7233: 7215: 7207: 7180: 7178: 7177: 7172: 7164: 7162: 7161: 7143: 7135: 7127: 7125: 7124: 7106: 7098: 7038: 7036: 7035: 7030: 7028: 7023: 7015: 6991: 6989: 6988: 6983: 6981: 6976: 6968: 6966: 6965: 6946: 6944: 6943: 6938: 6930: 6925: 6917: 6849: 6847: 6846: 6841: 6836: 6833: 6828: 6818: 6813: 6804: 6795: 6790: 6777: 6772: 6751: 6750: 6738: 6737: 6705: 6703: 6702: 6697: 6686: 6685: 6667: 6664: 6656: 6655: 6637:* is defined by 6629: 6627: 6626: 6621: 6616: 6614: 6610: 6609: 6597: 6596: 6578: 6575: 6569: 6565: 6564: 6552: 6551: 6533: 6530: 6524: 6519: 6517: 6513: 6512: 6500: 6499: 6483: 6479: 6478: 6466: 6465: 6449: 6441: 6440: 6428: 6427: 6388: 6386: 6385: 6380: 6369: 6368: 6348: 6346: 6345: 6340: 6338: 6337: 6318: 6316: 6315: 6310: 6302: 6301: 6289: 6288: 6270: 6269: 6257: 6256: 6238: 6236: 6235: 6230: 6229: 6220: 6215: 6210: 6209: 6200: 6194: 6193: 6188: 6187: 6178: 6173: 6168: 6167: 6158: 6152: 6147: 6145: 6144: 6139: 6138: 6129: 6123: 6122: 6117: 6116: 6107: 6101: 6093: 6092: 6080: 6079: 6051: 6049: 6048: 6043: 6040: 6035: 6019: 6017: 6016: 6011: 6009: 6008: 5989: 5987: 5986: 5981: 5979: 5972: 5970: 5969: 5964: 5963: 5962: 5957: 5950: 5944: 5940: 5935: 5934: 5933: 5928: 5921: 5913: 5908: 5907: 5902: 5901: 5900: 5895: 5887: 5873: 5868: 5867: 5866: 5861: 5854: 5846: 5841: 5840: 5839: 5834: 5827: 5818: 5813: 5811: 5810: 5805: 5804: 5803: 5798: 5791: 5785: 5781: 5776: 5775: 5774: 5769: 5762: 5754: 5749: 5748: 5747: 5742: 5735: 5726: 5721: 5719: 5718: 5713: 5712: 5711: 5706: 5699: 5693: 5692: 5687: 5686: 5685: 5680: 5673: 5667: 5656: 5655: 5654: 5649: 5641: 5631: 5626: 5625: 5624: 5619: 5612: 5604: 5599: 5598: 5593: 5592: 5591: 5586: 5578: 5564: 5559: 5558: 5557: 5552: 5545: 5537: 5532: 5531: 5530: 5525: 5518: 5507: 5502: 5501: 5500: 5495: 5488: 5480: 5475: 5474: 5473: 5468: 5461: 5453: 5446: 5441: 5440: 5439: 5434: 5427: 5419: 5414: 5413: 5408: 5407: 5406: 5401: 5393: 5385: 5380: 5379: 5378: 5373: 5366: 5358: 5356: 5355: 5350: 5349: 5344: 5343: 5342: 5337: 5329: 5323: 5322: 5317: 5316: 5315: 5310: 5303: 5297: 5286: 5285: 5284: 5279: 5271: 5264: 5259: 5258: 5257: 5252: 5245: 5237: 5232: 5231: 5230: 5225: 5218: 5210: 5205: 5204: 5203: 5198: 5191: 5183: 5181: 5180: 5175: 5174: 5173: 5168: 5161: 5155: 5154: 5149: 5148: 5147: 5142: 5135: 5129: 5118: 5117: 5116: 5111: 5103: 5089: 5087: 5086: 5081: 5079: 5078: 5062: 5060: 5059: 5054: 5052: 5051: 5035: 5033: 5032: 5027: 5025: 5024: 5008: 5006: 5005: 5000: 4998: 4997: 4970: 4968: 4967: 4962: 4957: 4956: 4944: 4943: 4919: 4917: 4916: 4911: 4910: 4901: 4895: 4894: 4889: 4888: 4879: 4873: 4862: 4861: 4843: 4841: 4840: 4835: 4830: 4829: 4817: 4816: 4792: 4790: 4789: 4784: 4783: 4774: 4768: 4767: 4762: 4761: 4752: 4746: 4735: 4734: 4716: 4714: 4713: 4708: 4703: 4702: 4690: 4689: 4665: 4663: 4662: 4657: 4656: 4647: 4641: 4640: 4635: 4634: 4625: 4619: 4608: 4607: 4504: 4495: 4493: 4492: 4487: 4479: 4478: 4466: 4465: 4447: 4445: 4444: 4439: 4438: 4429: 4423: 4422: 4417: 4416: 4407: 4401: 4391: 4372:Carnot's theorem 4304: 4295: 4293: 4292: 4287: 4285: 4283: 4282: 4277: 4276: 4267: 4261: 4260: 4255: 4254: 4245: 4239: 4228: 4226: 4225: 4216: 4215: 4214: 4202: 4201: 4191: 4186: 4184: 4183: 4174: 4173: 4168: 4167: 4158: 4152: 4136: 4104: 4102: 4101: 4096: 4088: 4086: 4085: 4082: 4076: 4068: 4052:Clausius theorem 4006:Carnot's theorem 4001:Carnot's theorem 3988:Perpetual motion 3887:quantum theory. 3857: 3855: 3854: 3849: 3841: 3839: 3838: 3837: 3821: 3820: 3819: 3810: 3809: 3799: 3785: 3783: 3782: 3781: 3765: 3764: 3763: 3754: 3753: 3743: 3732: 3730: 3729: 3728: 3712: 3711: 3710: 3701: 3700: 3690: 3670: 3668: 3667: 3666: 3650: 3649: 3648: 3639: 3638: 3628: 3614: 3612: 3611: 3602: 3601: 3600: 3584: 3579: 3578: 3563: 3561: 3560: 3555: 3550: 3548: 3541: 3537: 3535: 3527: 3519: 3506: 3505: 3496: 3494: 3492: 3491: 3482: 3474: 3469: 3468: 3446: 3444: 3443: 3427: 3425: 3424: 3419: 3408: 3407: 3404: 3392: 3390: 3389: 3380: 3379: 3378: 3362: 3357: 3356: 3353: 3338: 3336: 3335: 3330: 3329: 3328: 3307: 3305: 3304: 3299: 3298: 3297: 3294: 3271: 3269: 3268: 3263: 3261: 3260: 3249: 3245: 3243: 3235: 3227: 3206:held constant): 3205: 3199: 3193: 3183: 3161: 3155: 3149: 3140: 3127: 3062: 3060: 3059: 3054: 3026:process function 2982:George Uhlenbeck 2891: 2889: 2888: 2883: 2881: 2873: 2864: 2862: 2861: 2856: 2854: 2850: 2843: 2835: 2822: 2821: 2805: 2803: 2802: 2797: 2789: 2781: 2773: 2772: 2743: 2740: 2735: 2732: 2719: 2717: 2716: 2711: 2709: 2705: 2698: 2690: 2437: 2435: 2434: 2429: 2427: 2424: 2399: 2398: 2385: 2384: 2373: 2364: 2356: 2351: 2346: 2338: 2330: 2312:and temperature 2307: 2305: 2304: 2299: 2281: 2279: 2278: 2273: 2271: 2268: 2243: 2238: 2230: 2222: 2204: 2195: 2185: 2183: 2182: 2177: 2175: 2172: 2147: 2145: 2144: 2141: 2135: 2127: 2119: 2094: 2092: 2091: 2086: 2081: 2066: 2064: 2063: 2058: 2033: 2031: 2030: 2025: 2020: 2017: 1992: 1987: 1979: 1971: 1956: 1954: 1953: 1948: 1927: 1925: 1924: 1919: 1903:transfer of heat 1900: 1898: 1897: 1892: 1887: 1860: 1858: 1857: 1852: 1753:Carnot's theorem 1702:isolated systems 1633: 1626: 1619: 1603: 1602: 1310:Key publications 1291: 1290:("living force") 1240:Brownian ratchet 1235:Entropy and life 1230:Entropy and time 1181: 1180: 1156: 1154: 1153: 1148: 1101: 1099: 1098: 1093: 1046: 1044: 1043: 1038: 991: 989: 988: 983: 885:Clausius theorem 880:Carnot's theorem 853: 851: 850: 845: 829: 827: 826: 821: 806: 804: 803: 798: 782: 780: 779: 774: 761: 760: 757: 755: 754: 749: 721: 719: 718: 713: 697: 695: 694: 689: 674: 672: 671: 666: 650: 648: 647: 642: 629: 628: 625: 623: 622: 617: 586: 584: 583: 578: 562: 560: 559: 554: 539: 537: 536: 531: 515: 513: 512: 507: 494: 493: 490: 488: 487: 482: 460: 459: 333: 332: 152: 151: 33: 19: 18: 16335: 16334: 16330: 16329: 16328: 16326: 16325: 16324: 16295: 16294: 16233: 16214: 16213: 16204: 16203: 16199: 16180:10.1.1.405.1945 16140:Wayback Machine 16109: 16061: 16059:Further reading 16056: 16037:Uhlenbeck, G.E. 15963: 15961: 15901:Schrödinger, E. 15887: 15702: 15634:Physics Reports 15597:Kondepudi, D., 15584:Thermal Physics 15515: 15410: 15408: 15389: 15387: 15365: 15363: 15359: 15332: 15315: 15313: 15284: 15282: 15179: 15177: 15142:C. Carathéodory 15066: 15004:Thermal Physics 14955: 14938: 14933: 14932: 14895: 14888: 14879: 14877: 14869: 14868: 14861: 14855:Schrödinger, E. 14853: 14849: 14841: 14827: 14823: 14808: 14804: 14796: 14792: 14784: 14780: 14775: 14771: 14766: 14762: 14757: 14753: 14748: 14744: 14739: 14735: 14725: 14723: 14712: 14708: 14695: 14693: 14682: 14678: 14619: 14615: 14576: 14572: 14562: 14560: 14558: 14542: 14538: 14531: 14527: 14522: 14518: 14513: 14509: 14504: 14500: 14491: 14487: 14478: 14476: 14449: 14443: 14439: 14432: 14407: 14403: 14364: 14360: 14311: 14307: 14301:Clausius (1867) 14299: 14295: 14284: 14280: 14263: 14259: 14242: 14238: 14223: 14219: 14206: 14202: 14167: 14160: 14125: 14121: 14086: 14082: 14047: 14043: 14020: 14016: 13973: 13969: 13958: 13954: 13919: 13915: 13895: 13891: 13884: 13870: 13866: 13861: 13857: 13852: 13848: 13840: 13836: 13828: 13824: 13804: 13800: 13795: 13791: 13786: 13782: 13774: 13767: 13759: 13752: 13745: 13731: 13727: 13722: 13718: 13710: 13706: 13700:Uhlenbeck, G.E. 13698: 13694: 13689: 13685: 13677: 13673: 13665: 13661: 13649: 13645: 13640: 13636: 13628: 13624: 13616: 13612: 13606:Clausius (1854) 13604: 13600: 13594:Clausius (1850) 13592: 13588: 13583: 13579: 13574: 13570: 13562:Kondepudi, D., 13561: 13557: 13552: 13548: 13543: 13539: 13531: 13527: 13522: 13518: 13513: 13509: 13504: 13500: 13492: 13488: 13480: 13476: 13468: 13464: 13455: 13453: 13448: 13447: 13443: 13438: 13434: 13426: 13422: 13412: 13390: 13386: 13357: 13353: 13348: 13344: 13324: 13317: 13312: 13303: 13298: 13294: 13287: 13271: 13267: 13260: 13244: 13235: 13230: 13226: 13221: 13217: 13209: 13205: 13198: 13194: 13189: 13185: 13177: 13173: 13162: 13158: 13151: 13135: 13131: 13124: 13108: 13104: 13099: 13095: 13084:www.web.mit.edu 13078: 13077: 13073: 13062: 13058: 13051: 13037: 13030: 13023: 13006: 13002: 12997: 12992: 12913: 12907: 12889: 12880: 12873: 12865: 12854: 12835: 12746: 12744:Maxwell's demon 12740: 12738:Maxwell's demon 12719: 12713: 12698: 12692: 12679: 12677:Irreversibility 12658: 12648: 12619:critical states 12599: 12593: 12561: 12513: 12478: 12476:Past hypothesis 12472: 12443: 12441: 12416: 12414: 12405: 12401: 12392: 12388: 12382: 12368: 12354: 12350: 12344: 12340: 12339: 12335: 12326: 12312: 12303: 12299: 12290: 12286: 12280: 12266: 12255: 12252: 12251: 12231: 12227: 12225: 12222: 12221: 12201: 12197: 12184: 12180: 12176: 12164: 12153: 12152: 12148: 12134: 12131: 12130: 12103: 12099: 12095: 12083: 12079: 12073: 12062: 12061: 12057: 12046: 12043: 12042: 11993: 11992: 11988: 11987: 11981: 11977: 11975: 11971: 11967: 11960: 11958: 11949: 11945: 11943: 11940: 11939: 11925: 11895: 11893: 11874: 11858: 11856: 11841: 11827: 11819: 11817: 11813: 11812: 11797: 11783: 11775: 11773: 11769: 11768: 11757: 11754: 11753: 11725: 11716: 11702: 11694: 11692: 11688: 11687: 11685: 11682: 11681: 11653: 11644: 11630: 11622: 11620: 11616: 11615: 11613: 11610: 11609: 11584: 11570: 11562: 11560: 11556: 11555: 11537: 11523: 11511: 11501: 11499: 11495: 11494: 11492: 11489: 11488: 11465: 11462: 11461: 11440: 11426: 11413: 11409: 11405: 11403: 11399: 11398: 11389: 11375: 11368: 11364: 11360: 11358: 11354: 11353: 11344: 11328: 11314: 11306: 11304: 11300: 11299: 11297: 11294: 11293: 11250: 11246: 11240: 11236: 11234: 11231: 11230: 11208: 11202: 11198: 11196: 11193: 11192: 11167: 11164: 11163: 11140: 11137: 11136: 11135:is larger than 11116: 11113: 11112: 11079: 11075: 11069: 11065: 11051: 11045: 11041: 11039: 11036: 11035: 11003: 10999: 10993: 10989: 10987: 10984: 10983: 10958: 10955: 10954: 10929: 10926: 10925: 10909: 10906: 10905: 10880: 10877: 10876: 10860: 10857: 10856: 10825: 10822: 10821: 10787: 10775: 10769: 10765: 10764: 10762: 10748: 10742: 10738: 10736: 10733: 10732: 10677: 10674: 10673: 10657: 10654: 10653: 10632: 10625: 10621: 10617: 10615: 10613: 10610: 10609: 10584: 10581: 10580: 10564: 10561: 10560: 10534: 10529: 10526: 10525: 10479: 10473: 10469: 10460: 10442: 10438: 10433: 10422: 10419: 10418: 10389: 10383: 10379: 10373: 10355: 10350: 10347: 10346: 10321: 10315: 10311: 10309: 10306: 10305: 10280: 10277: 10276: 10260: 10257: 10256: 10235: 10228: 10224: 10220: 10218: 10216: 10213: 10212: 10190: 10185: 10182: 10181: 10152: 10145: 10141: 10137: 10135: 10131: 10120: 10117: 10116: 10094: 10091: 10090: 10066: 10059: 10055: 10051: 10049: 10038: 10035: 10034: 10014: 10010: 10008: 10005: 10004: 9966: 9963: 9962: 9910: 9893: 9889: 9885: 9875: 9873: 9851: 9850: 9846: 9845: 9840: 9838: 9835: 9834: 9804: 9802: 9791: 9788: 9787: 9781: 9770: 9747: 9742: 9739: 9738: 9722: 9719: 9718: 9701: 9698: 9697: 9678: 9675: 9674: 9657: 9654: 9653: 9630: 9627: 9626: 9607: 9604: 9603: 9584: 9581: 9580: 9555: 9552: 9551: 9535: 9532: 9531: 9509: 9504: 9501: 9500: 9470: 9466: 9462: 9449: 9448: 9444: 9436: 9433: 9432: 9413: 9410: 9409: 9399:other scenarios 9356: 9350: 9333: 9331: 9319: 9291: 9290: 9288: 9285: 9284: 9258: 9247: 9246: 9245: 9243: 9240: 9239: 9222: 9211: 9210: 9209: 9195: 9194: 9176: 9174: 9161: 9153: 9151: 9149: 9146: 9145: 9118: 9115: 9114: 9090: 9089: 9087: 9084: 9083: 9054: 9043: 9042: 9041: 9039: 9036: 9035: 9018: 9007: 9006: 9005: 8987: 8985: 8972: 8964: 8962: 8960: 8957: 8956: 8933: 8922: 8921: 8920: 8914: 8910: 8892: 8888: 8886: 8883: 8882: 8865: 8861: 8859: 8856: 8855: 8833: 8822: 8821: 8820: 8818: 8815: 8814: 8788: 8777: 8776: 8775: 8773: 8770: 8769: 8752: 8741: 8740: 8739: 8726: 8718: 8716: 8714: 8711: 8710: 8656: 8648: 8646: 8644: 8641: 8640: 8634:isolated system 8569: 8567: 8562: 8559: 8558: 8548:Rudolf Clausius 8542:Rudolf Clausius 8536: 8486:Rudolf Clausius 8460: 8454: 8404: 8401: 8400: 8364: 8361: 8360: 8352: 8332: 8290: 8279: 8244: 8236:systems ecology 8203:design engineer 8176: 8172: 8158: 8155: 8154: 8125: 8121: 8116: 8113: 8112: 8064: 8060: 8046: 8043: 8042: 8019: 8015: 8006: 8002: 7987: 7983: 7971: 7967: 7953: 7950: 7949: 7908: 7904: 7895: 7891: 7876: 7872: 7860: 7856: 7849: 7845: 7830: 7826: 7821: 7818: 7817: 7810: 7799: 7767: 7763: 7751: 7747: 7729: 7725: 7702: 7699: 7698: 7661: 7657: 7645: 7641: 7626: 7622: 7611: 7608: 7607: 7595: 7563: 7559: 7550: 7546: 7542: 7538: 7506: 7503: 7502: 7496: 7492: 7430: 7426: 7398: 7397: 7393: 7388: 7385: 7384: 7379: 7371: 7357: 7350: 7343: 7336: 7324: 7318: 7288: 7285: 7284: 7259: 7256: 7255: 7220: 7216: 7208: 7206: 7192: 7189: 7188: 7148: 7144: 7136: 7134: 7111: 7107: 7099: 7097: 7080: 7077: 7076: 7071: 7016: 7014: 7003: 7000: 6999: 6969: 6967: 6961: 6957: 6955: 6952: 6951: 6918: 6916: 6911: 6908: 6907: 6894: 6888: 6877: 6870: 6860:* = 273.16 K × 6859: 6829: 6824: 6814: 6809: 6803: 6791: 6786: 6773: 6768: 6746: 6742: 6733: 6729: 6721: 6718: 6717: 6681: 6677: 6663: 6651: 6647: 6645: 6642: 6641: 6605: 6601: 6592: 6588: 6574: 6570: 6560: 6556: 6547: 6543: 6529: 6525: 6523: 6508: 6504: 6495: 6491: 6484: 6474: 6470: 6461: 6457: 6450: 6448: 6436: 6432: 6423: 6419: 6411: 6408: 6407: 6402: 6395: 6389:. Then for any 6364: 6360: 6358: 6355: 6354: 6333: 6329: 6327: 6324: 6323: 6297: 6293: 6284: 6280: 6265: 6261: 6252: 6248: 6231: 6225: 6221: 6216: 6211: 6205: 6201: 6196: 6195: 6189: 6183: 6179: 6174: 6169: 6163: 6159: 6154: 6153: 6151: 6140: 6134: 6130: 6125: 6124: 6118: 6112: 6108: 6103: 6102: 6100: 6088: 6084: 6075: 6071: 6063: 6060: 6059: 6036: 6031: 6025: 6022: 6021: 6004: 6000: 5998: 5995: 5994: 5977: 5976: 5965: 5958: 5953: 5952: 5951: 5946: 5945: 5936: 5929: 5924: 5923: 5922: 5917: 5909: 5903: 5896: 5891: 5890: 5889: 5888: 5883: 5869: 5862: 5857: 5856: 5855: 5850: 5842: 5835: 5830: 5829: 5828: 5823: 5819: 5817: 5806: 5799: 5794: 5793: 5792: 5787: 5786: 5777: 5770: 5765: 5764: 5763: 5758: 5750: 5743: 5738: 5737: 5736: 5731: 5727: 5725: 5714: 5707: 5702: 5701: 5700: 5695: 5694: 5688: 5681: 5676: 5675: 5674: 5669: 5668: 5666: 5650: 5645: 5644: 5643: 5639: 5638: 5627: 5620: 5615: 5614: 5613: 5608: 5600: 5594: 5587: 5582: 5581: 5580: 5579: 5574: 5560: 5553: 5548: 5547: 5546: 5541: 5533: 5526: 5521: 5520: 5519: 5514: 5503: 5496: 5491: 5490: 5489: 5484: 5476: 5469: 5464: 5463: 5462: 5457: 5451: 5450: 5442: 5435: 5430: 5429: 5428: 5423: 5415: 5409: 5402: 5397: 5396: 5395: 5394: 5389: 5381: 5374: 5369: 5368: 5367: 5362: 5351: 5345: 5338: 5333: 5332: 5331: 5330: 5325: 5324: 5318: 5311: 5306: 5305: 5304: 5299: 5298: 5296: 5280: 5275: 5274: 5273: 5269: 5268: 5260: 5253: 5248: 5247: 5246: 5241: 5233: 5226: 5221: 5220: 5219: 5214: 5206: 5199: 5194: 5193: 5192: 5187: 5176: 5169: 5164: 5163: 5162: 5157: 5156: 5150: 5143: 5138: 5137: 5136: 5131: 5130: 5128: 5112: 5107: 5106: 5105: 5100: 5098: 5095: 5094: 5074: 5070: 5068: 5065: 5064: 5047: 5043: 5041: 5038: 5037: 5020: 5016: 5014: 5011: 5010: 4993: 4989: 4987: 4984: 4983: 4981: 4952: 4948: 4939: 4935: 4912: 4906: 4902: 4897: 4896: 4890: 4884: 4880: 4875: 4874: 4872: 4857: 4853: 4851: 4848: 4847: 4825: 4821: 4812: 4808: 4785: 4779: 4775: 4770: 4769: 4763: 4757: 4753: 4748: 4747: 4745: 4730: 4726: 4724: 4721: 4720: 4698: 4694: 4685: 4681: 4658: 4652: 4648: 4643: 4642: 4636: 4630: 4626: 4621: 4620: 4618: 4603: 4599: 4597: 4594: 4593: 4588: 4581: 4573: 4566: 4559: 4553: 4546: 4539: 4532: 4525: 4518: 4474: 4470: 4461: 4457: 4440: 4434: 4430: 4425: 4424: 4418: 4412: 4408: 4403: 4402: 4400: 4398: 4395: 4394: 4387: 4380: 4367: 4358: 4345: 4336: 4327: 4318: 4278: 4272: 4268: 4263: 4262: 4256: 4250: 4246: 4241: 4240: 4238: 4221: 4217: 4210: 4206: 4197: 4193: 4192: 4190: 4179: 4175: 4169: 4163: 4159: 4154: 4153: 4151: 4143: 4140: 4139: 4131: 4125: 4114: 4081: 4077: 4069: 4067: 4062: 4059: 4058: 4048: 4038:), rather than 4003: 3990: 3984: 3979: 3946: 3921: 3914: 3907: 3896: 3885: 3878: 3833: 3829: 3822: 3815: 3811: 3805: 3801: 3800: 3798: 3777: 3773: 3766: 3759: 3755: 3749: 3745: 3744: 3742: 3724: 3720: 3713: 3706: 3702: 3696: 3692: 3691: 3689: 3662: 3658: 3651: 3644: 3640: 3634: 3630: 3629: 3627: 3607: 3603: 3596: 3592: 3585: 3583: 3574: 3570: 3568: 3565: 3564: 3528: 3520: 3518: 3514: 3507: 3501: 3497: 3495: 3487: 3483: 3475: 3473: 3464: 3460: 3458: 3455: 3454: 3433: 3432: 3403: 3399: 3385: 3381: 3371: 3367: 3363: 3361: 3352: 3348: 3346: 3343: 3342: 3321: 3317: 3313: 3310: 3309: 3293: 3289: 3285: 3282: 3281: 3277: 3250: 3236: 3228: 3226: 3222: 3221: 3213: 3210: 3209: 3201: 3195: 3189: 3163: 3157: 3151: 3145: 3136: 3134:internal energy 3130:convex function 3123: 3121:internal energy 3117: 3073: 3033: 3030: 3029: 3003: 2962: 2921: 2903: 2892:is obtained by 2872: 2870: 2867: 2866: 2834: 2833: 2829: 2817: 2813: 2811: 2808: 2807: 2806:, so therefore 2780: 2768: 2764: 2739: 2731: 2729: 2726: 2725: 2689: 2688: 2684: 2670: 2667: 2666: 2638: 2609: 2580:Rudolf Clausius 2576: 2488: 2468:Rudolf Clausius 2464: 2423: 2394: 2390: 2380: 2376: 2369: 2355: 2339: 2337: 2326: 2324: 2321: 2320: 2293: 2290: 2289: 2267: 2231: 2229: 2218: 2216: 2213: 2212: 2203: 2197: 2191: 2171: 2140: 2136: 2128: 2126: 2115: 2113: 2110: 2109: 2077: 2072: 2069: 2068: 2046: 2043: 2042: 2041:amount of heat 2016: 1980: 1978: 1967: 1965: 1962: 1961: 1936: 1933: 1932: 1910: 1907: 1906: 1883: 1881: 1878: 1877: 1846: 1843: 1842: 1796:internal energy 1780: 1761:Rudolf Clausius 1710:irreversibility 1637: 1592: 1591: 1567: 1559: 1558: 1557: 1417: 1409: 1408: 1387: 1373: 1348: 1344: 1337: 1333: 1326: 1322: 1289: 1282: 1264: 1245:Maxwell's demon 1207: 1178: 1177: 1161: 1160: 1159: 1112: 1109: 1108: 1107: 1057: 1054: 1053: 1052: 1002: 999: 998: 997: 962: 959: 958: 957: 955:Internal energy 950: 935: 925: 924: 899: 874: 864: 863: 862: 836: 833: 832: 815: 812: 811: 789: 786: 785: 768: 765: 764: 740: 737: 736: 704: 701: 700: 683: 680: 679: 657: 654: 653: 636: 633: 632: 605: 602: 601: 596:Compressibility 569: 566: 565: 548: 545: 544: 522: 519: 518: 501: 498: 497: 473: 470: 469: 449: 439: 438: 419:Particle number 372: 331: 320: 310: 309: 268:Irreversibility 180:State of matter 147:Isolated system 132: 122: 121: 120: 95: 85: 84: 80:Non-equilibrium 72: 47: 39: 17: 12: 11: 5: 16333: 16323: 16322: 16317: 16312: 16307: 16293: 16292: 16287: 16277: 16272: 16258: 16244: 16232: 16231:External links 16229: 16228: 16227: 16215:|journal= 16197: 16158: 16143: 16114: 16107: 16094: 16076: 16060: 16057: 16055: 16054: 16047:Zemansky, M.W. 16044: 16034: 16019: 16008: 15990: 15980: 15970: 15926: 15912: 15898: 15891: 15885: 15870: 15855: 15828: 15825: 15815: 15803: 15791: 15781: 15766: 15756: 15745:Thermodynamics 15738: 15706: 15700: 15683: 15676: 15629: 15614: 15595: 15573: 15566: 15556: 15542: 15527: 15513: 15498: 15483: 15468: 15450: 15435: 15420: 15396:Reprinted in: 15322: 15238: 15224: 15201: 15156:(3): 355–386. 15138: 15120: 15113:Bridgman, P.W. 15110: 15103: 15088: 15078: 15064: 15030: 15015: 15000: 14985: 14967: 14953: 14939: 14937: 14934: 14931: 14930: 14886: 14859: 14847: 14839: 14821: 14802: 14790: 14778: 14769: 14760: 14751: 14742: 14733: 14706: 14676: 14613: 14570: 14556: 14536: 14525: 14516: 14507: 14498: 14485: 14437: 14430: 14401: 14358: 14305: 14293: 14278: 14257: 14236: 14217: 14200: 14158: 14139:(1): 673–676. 14119: 14080: 14041: 14014: 13987:(4): 551–562. 13967: 13952: 13913: 13911:, pp. 146–148. 13889: 13882: 13864: 13855: 13846: 13834: 13822: 13798: 13789: 13780: 13765: 13750: 13743: 13725: 13716: 13704: 13692: 13683: 13671: 13659: 13657:(1966), p. 17. 13643: 13634: 13622: 13618:Thomson (1851) 13610: 13598: 13586: 13577: 13568: 13555: 13546: 13537: 13525: 13516: 13507: 13498: 13486: 13484:, p. 213. 13474: 13462: 13441: 13432: 13428:Zemansky, M.W. 13420: 13410: 13384: 13351: 13342: 13339:978-1305079113 13315: 13301: 13292: 13285: 13276:Thermodynamics 13265: 13258: 13233: 13224: 13215: 13203: 13192: 13183: 13171: 13156: 13149: 13129: 13122: 13102: 13093: 13071: 13056: 13049: 13028: 13021: 12999: 12998: 12996: 12993: 12991: 12990: 12985: 12980: 12975: 12970: 12965: 12960: 12955: 12950: 12945: 12940: 12935: 12930: 12925: 12920: 12914: 12912: 12909: 12887: 12871: 12852: 12840:laws of Nature 12834: 12831: 12812:Léon Brillouin 12783:. The average 12742:Main article: 12739: 12736: 12715:Main article: 12712: 12709: 12694:Main article: 12691: 12688: 12678: 12675: 12647: 12644: 12595:Main article: 12592: 12589: 12560: 12557: 12528:Léon Brillouin 12512: 12509: 12471: 12468: 12467: 12466: 12453: 12449: 12446: 12440: 12435: 12431: 12428: 12425: 12422: 12419: 12413: 12408: 12404: 12400: 12395: 12391: 12385: 12381: 12375: 12372: 12367: 12363: 12357: 12353: 12347: 12343: 12338: 12334: 12329: 12325: 12319: 12316: 12311: 12306: 12302: 12298: 12293: 12289: 12283: 12279: 12273: 12270: 12265: 12262: 12259: 12234: 12230: 12218: 12217: 12204: 12200: 12196: 12192: 12187: 12183: 12179: 12175: 12172: 12167: 12163: 12156: 12151: 12147: 12144: 12141: 12138: 12124: 12123: 12111: 12106: 12102: 12098: 12094: 12091: 12086: 12082: 12076: 12072: 12065: 12060: 12056: 12053: 12050: 12028: 12027: 12014: 12009: 12002: 11996: 11991: 11984: 11980: 11974: 11970: 11966: 11963: 11957: 11952: 11948: 11924: 11921: 11920: 11919: 11905: 11901: 11898: 11892: 11889: 11886: 11881: 11878: 11873: 11868: 11864: 11861: 11855: 11852: 11849: 11844: 11839: 11833: 11830: 11825: 11822: 11816: 11811: 11808: 11805: 11800: 11795: 11789: 11786: 11781: 11778: 11772: 11767: 11764: 11761: 11747: 11746: 11732: 11729: 11724: 11719: 11714: 11708: 11705: 11700: 11697: 11691: 11675: 11674: 11660: 11657: 11652: 11647: 11642: 11636: 11633: 11628: 11625: 11619: 11602: 11601: 11587: 11582: 11576: 11573: 11568: 11565: 11559: 11554: 11551: 11548: 11545: 11540: 11535: 11529: 11526: 11520: 11517: 11514: 11510: 11507: 11504: 11498: 11469: 11458: 11457: 11443: 11438: 11432: 11429: 11423: 11419: 11416: 11412: 11408: 11402: 11397: 11392: 11387: 11381: 11378: 11371: 11367: 11363: 11357: 11352: 11347: 11343: 11339: 11336: 11331: 11326: 11320: 11317: 11312: 11309: 11303: 11266: 11262: 11259: 11256: 11253: 11249: 11243: 11239: 11217: 11214: 11211: 11205: 11201: 11180: 11177: 11174: 11171: 11147: 11144: 11120: 11109: 11108: 11095: 11091: 11088: 11085: 11082: 11078: 11072: 11068: 11064: 11060: 11057: 11054: 11048: 11044: 11019: 11015: 11012: 11009: 11006: 11002: 10996: 10992: 10971: 10968: 10965: 10962: 10942: 10939: 10936: 10933: 10913: 10893: 10890: 10887: 10884: 10864: 10844: 10841: 10838: 10835: 10832: 10829: 10818: 10817: 10805: 10802: 10799: 10793: 10790: 10784: 10781: 10778: 10772: 10768: 10761: 10757: 10754: 10751: 10745: 10741: 10690: 10687: 10684: 10681: 10661: 10638: 10635: 10628: 10624: 10620: 10597: 10594: 10591: 10588: 10568: 10543: 10540: 10537: 10533: 10502: 10501: 10488: 10485: 10482: 10476: 10472: 10468: 10463: 10459: 10451: 10448: 10445: 10441: 10437: 10432: 10429: 10426: 10412: 10411: 10398: 10395: 10392: 10386: 10382: 10376: 10372: 10368: 10364: 10361: 10358: 10354: 10330: 10327: 10324: 10318: 10314: 10293: 10290: 10287: 10284: 10264: 10241: 10238: 10231: 10227: 10223: 10199: 10196: 10193: 10189: 10178: 10177: 10164: 10158: 10155: 10148: 10144: 10140: 10134: 10130: 10127: 10124: 10101: 10098: 10087: 10086: 10072: 10069: 10062: 10058: 10054: 10048: 10045: 10042: 10017: 10013: 9976: 9973: 9970: 9931: 9930: 9916: 9913: 9907: 9902: 9899: 9896: 9892: 9888: 9884: 9881: 9878: 9872: 9869: 9866: 9860: 9854: 9849: 9844: 9828: 9827: 9814: 9810: 9807: 9801: 9798: 9795: 9780: 9777: 9754: 9750: 9746: 9726: 9705: 9682: 9661: 9637: 9634: 9614: 9611: 9591: 9588: 9568: 9565: 9562: 9559: 9539: 9518: 9515: 9512: 9508: 9497: 9496: 9484: 9479: 9476: 9473: 9469: 9465: 9461: 9458: 9452: 9447: 9443: 9440: 9417: 9349: 9346: 9318: 9315: 9298: 9295: 9281: 9280: 9269: 9266: 9261: 9254: 9251: 9225: 9218: 9215: 9208: 9202: 9199: 9193: 9188: 9183: 9180: 9173: 9167: 9164: 9159: 9156: 9135: 9134: 9122: 9112: 9097: 9094: 9077: 9076: 9065: 9062: 9057: 9050: 9047: 9021: 9014: 9011: 9004: 8999: 8994: 8991: 8984: 8978: 8975: 8970: 8967: 8936: 8929: 8926: 8917: 8913: 8909: 8904: 8901: 8898: 8895: 8891: 8868: 8864: 8836: 8829: 8826: 8811: 8810: 8799: 8796: 8791: 8784: 8781: 8755: 8748: 8745: 8738: 8732: 8729: 8724: 8721: 8704: 8703: 8693: 8683: 8682: 8671: 8668: 8662: 8659: 8654: 8651: 8602: 8601: 8590: 8587: 8584: 8579: 8575: 8572: 8566: 8535: 8532: 8494:caloric theory 8453: 8450: 8417: 8414: 8411: 8408: 8389: 8388: 8377: 8374: 8371: 8368: 8350: 8331: 8328: 8327: 8326: 8311: 8304: 8288: 8277: 8270: 8269: 8266: 8263: 8243: 8240: 8199: 8198: 8187: 8184: 8179: 8175: 8171: 8168: 8165: 8162: 8142: 8139: 8134: 8131: 8128: 8124: 8120: 8087: 8086: 8075: 8072: 8067: 8063: 8059: 8056: 8053: 8050: 8036: 8035: 8022: 8018: 8012: 8009: 8005: 8001: 7998: 7995: 7990: 7986: 7982: 7979: 7974: 7970: 7966: 7963: 7960: 7957: 7930: 7929: 7917: 7911: 7907: 7901: 7898: 7894: 7890: 7887: 7884: 7879: 7875: 7871: 7868: 7863: 7859: 7855: 7852: 7848: 7844: 7841: 7838: 7833: 7829: 7825: 7808: 7797: 7784: 7783: 7770: 7766: 7762: 7757: 7754: 7750: 7746: 7743: 7740: 7737: 7732: 7728: 7724: 7721: 7718: 7715: 7712: 7709: 7706: 7684: 7683: 7672: 7669: 7664: 7660: 7656: 7653: 7648: 7644: 7640: 7637: 7634: 7629: 7625: 7621: 7618: 7615: 7591: 7585: 7584: 7572: 7566: 7562: 7556: 7553: 7549: 7545: 7541: 7537: 7534: 7531: 7528: 7525: 7522: 7519: 7516: 7513: 7510: 7494: 7490: 7453: 7452: 7441: 7438: 7433: 7429: 7425: 7422: 7419: 7416: 7413: 7407: 7404: 7401: 7396: 7392: 7377: 7369: 7355: 7348: 7341: 7334: 7317: 7314: 7301: 7298: 7295: 7292: 7272: 7269: 7266: 7263: 7248: 7247: 7232: 7229: 7226: 7223: 7219: 7214: 7211: 7205: 7202: 7199: 7196: 7182: 7181: 7170: 7167: 7160: 7157: 7154: 7151: 7147: 7142: 7139: 7133: 7130: 7123: 7120: 7117: 7114: 7110: 7105: 7102: 7096: 7093: 7090: 7087: 7084: 7069: 7040: 7039: 7026: 7022: 7019: 7013: 7010: 7007: 6979: 6975: 6972: 6964: 6960: 6948: 6947: 6936: 6933: 6928: 6924: 6921: 6915: 6890:Main article: 6887: 6884: 6875: 6868: 6857: 6851: 6850: 6839: 6832: 6827: 6823: 6817: 6812: 6808: 6802: 6799: 6794: 6789: 6785: 6781: 6776: 6771: 6767: 6763: 6760: 6757: 6754: 6749: 6745: 6741: 6736: 6732: 6728: 6725: 6707: 6706: 6695: 6692: 6689: 6684: 6680: 6676: 6673: 6670: 6662: 6659: 6654: 6650: 6631: 6630: 6619: 6613: 6608: 6604: 6600: 6595: 6591: 6587: 6584: 6581: 6573: 6568: 6563: 6559: 6555: 6550: 6546: 6542: 6539: 6536: 6528: 6522: 6516: 6511: 6507: 6503: 6498: 6494: 6490: 6487: 6482: 6477: 6473: 6469: 6464: 6460: 6456: 6453: 6447: 6444: 6439: 6435: 6431: 6426: 6422: 6418: 6415: 6400: 6393: 6378: 6375: 6372: 6367: 6363: 6336: 6332: 6320: 6319: 6308: 6305: 6300: 6296: 6292: 6287: 6283: 6279: 6276: 6273: 6268: 6264: 6260: 6255: 6251: 6247: 6244: 6241: 6234: 6228: 6224: 6219: 6214: 6208: 6204: 6199: 6192: 6186: 6182: 6177: 6172: 6166: 6162: 6157: 6150: 6143: 6137: 6133: 6128: 6121: 6115: 6111: 6106: 6099: 6096: 6091: 6087: 6083: 6078: 6074: 6070: 6067: 6039: 6034: 6030: 6007: 6003: 5991: 5990: 5975: 5968: 5961: 5956: 5949: 5943: 5939: 5932: 5927: 5920: 5916: 5912: 5906: 5899: 5894: 5886: 5882: 5879: 5876: 5872: 5865: 5860: 5853: 5849: 5845: 5838: 5833: 5826: 5822: 5816: 5809: 5802: 5797: 5790: 5784: 5780: 5773: 5768: 5761: 5757: 5753: 5746: 5741: 5734: 5730: 5724: 5717: 5710: 5705: 5698: 5691: 5684: 5679: 5672: 5665: 5662: 5659: 5653: 5648: 5642: 5640: 5637: 5634: 5630: 5623: 5618: 5611: 5607: 5603: 5597: 5590: 5585: 5577: 5573: 5570: 5567: 5563: 5556: 5551: 5544: 5540: 5536: 5529: 5524: 5517: 5513: 5510: 5506: 5499: 5494: 5487: 5483: 5479: 5472: 5467: 5460: 5456: 5454: 5452: 5449: 5445: 5438: 5433: 5426: 5422: 5418: 5412: 5405: 5400: 5392: 5388: 5384: 5377: 5372: 5365: 5361: 5354: 5348: 5341: 5336: 5328: 5321: 5314: 5309: 5302: 5295: 5292: 5289: 5283: 5278: 5272: 5270: 5267: 5263: 5256: 5251: 5244: 5240: 5236: 5229: 5224: 5217: 5213: 5209: 5202: 5197: 5190: 5186: 5179: 5172: 5167: 5160: 5153: 5146: 5141: 5134: 5127: 5124: 5121: 5115: 5110: 5104: 5102: 5077: 5073: 5050: 5046: 5023: 5019: 4996: 4992: 4979: 4973: 4972: 4960: 4955: 4951: 4947: 4942: 4938: 4934: 4931: 4928: 4925: 4922: 4915: 4909: 4905: 4900: 4893: 4887: 4883: 4878: 4871: 4868: 4865: 4860: 4856: 4845: 4833: 4828: 4824: 4820: 4815: 4811: 4807: 4804: 4801: 4798: 4795: 4788: 4782: 4778: 4773: 4766: 4760: 4756: 4751: 4744: 4741: 4738: 4733: 4729: 4718: 4706: 4701: 4697: 4693: 4688: 4684: 4680: 4677: 4674: 4671: 4668: 4661: 4655: 4651: 4646: 4639: 4633: 4629: 4624: 4617: 4614: 4611: 4606: 4602: 4586: 4579: 4571: 4564: 4557: 4551: 4544: 4537: 4530: 4523: 4516: 4508: 4507: 4498: 4496: 4485: 4482: 4477: 4473: 4469: 4464: 4460: 4456: 4453: 4450: 4443: 4437: 4433: 4428: 4421: 4415: 4411: 4406: 4385: 4378: 4363: 4354: 4348:heat given off 4341: 4332: 4323: 4316: 4308: 4307: 4298: 4296: 4281: 4275: 4271: 4266: 4259: 4253: 4249: 4244: 4237: 4234: 4231: 4224: 4220: 4213: 4209: 4205: 4200: 4196: 4189: 4182: 4178: 4172: 4166: 4162: 4157: 4150: 4147: 4127:Main article: 4124: 4121: 4112: 4106: 4105: 4094: 4091: 4080: 4075: 4072: 4066: 4047: 4044: 4036:caloric theory 4021: 4020: 4017: 4002: 3999: 3986:Main article: 3983: 3980: 3978: 3975: 3945: 3942: 3919: 3912: 3905: 3894: 3883: 3876: 3847: 3844: 3836: 3832: 3828: 3825: 3818: 3814: 3808: 3804: 3797: 3794: 3791: 3788: 3780: 3776: 3772: 3769: 3762: 3758: 3752: 3748: 3741: 3738: 3735: 3727: 3723: 3719: 3716: 3709: 3705: 3699: 3695: 3688: 3685: 3682: 3679: 3676: 3673: 3665: 3661: 3657: 3654: 3647: 3643: 3637: 3633: 3626: 3623: 3620: 3617: 3610: 3606: 3599: 3595: 3591: 3588: 3582: 3577: 3573: 3553: 3547: 3544: 3540: 3534: 3531: 3526: 3523: 3517: 3513: 3510: 3504: 3500: 3490: 3486: 3481: 3478: 3472: 3467: 3463: 3438: 3417: 3414: 3411: 3402: 3398: 3395: 3388: 3384: 3377: 3374: 3370: 3366: 3360: 3351: 3327: 3324: 3320: 3316: 3292: 3288: 3276: 3273: 3259: 3256: 3253: 3248: 3242: 3239: 3234: 3231: 3225: 3220: 3217: 3116: 3113: 3109: 3108: 3107: 3106: 3085: 3084: 3083: 3082: 3072: 3069: 3052: 3049: 3046: 3043: 3040: 3037: 3002: 2999: 2998: 2997: 2996: 2995: 2978: 2977: 2976: 2975: 2961: 2958: 2957: 2956: 2955: 2954: 2920: 2917: 2916: 2915: 2914: 2913: 2902: 2899: 2879: 2876: 2853: 2849: 2846: 2841: 2838: 2832: 2828: 2825: 2820: 2816: 2795: 2792: 2787: 2784: 2779: 2776: 2771: 2767: 2763: 2760: 2757: 2753: 2749: 2746: 2738: 2708: 2704: 2701: 2696: 2693: 2687: 2683: 2680: 2677: 2674: 2637: 2634: 2633: 2632: 2631: 2630: 2624: 2623: 2622: 2621: 2608: 2605: 2575: 2572: 2571: 2570: 2569: 2568: 2554: 2553: 2552: 2551: 2543: 2542: 2541: 2540: 2527: 2526: 2525: 2524: 2508:caloric theory 2498:, is an ideal 2487: 2484: 2463: 2460: 2439: 2438: 2397: 2393: 2389: 2383: 2379: 2372: 2368: 2362: 2359: 2354: 2349: 2345: 2342: 2336: 2333: 2329: 2297: 2283: 2282: 2241: 2237: 2234: 2228: 2225: 2221: 2201: 2187: 2186: 2139: 2134: 2131: 2125: 2122: 2118: 2084: 2080: 2076: 2056: 2053: 2050: 2035: 2034: 2023: 1990: 1986: 1983: 1977: 1974: 1970: 1946: 1943: 1940: 1917: 1914: 1890: 1886: 1850: 1835:entropy change 1779: 1776: 1749:caloric theory 1675:cyclic process 1639: 1638: 1636: 1635: 1628: 1621: 1613: 1610: 1609: 1608: 1607: 1594: 1593: 1590: 1589: 1584: 1579: 1574: 1568: 1565: 1564: 1561: 1560: 1556: 1555: 1550: 1545: 1540: 1535: 1530: 1525: 1520: 1515: 1510: 1505: 1500: 1495: 1490: 1485: 1480: 1475: 1470: 1465: 1460: 1455: 1450: 1445: 1440: 1435: 1430: 1425: 1419: 1418: 1415: 1414: 1411: 1410: 1405: 1404: 1403: 1402: 1397: 1389: 1388: 1386: 1385: 1382: 1378: 1375: 1374: 1372: 1371: 1366: 1364:Thermodynamics 1360: 1357: 1356: 1352: 1351: 1350: 1349: 1340: 1338: 1329: 1327: 1318: 1313: 1312: 1306: 1305: 1304: 1303: 1298: 1293: 1281: 1280: 1278:Caloric theory 1274: 1271: 1270: 1266: 1265: 1263: 1262: 1257: 1252: 1247: 1242: 1237: 1232: 1226: 1223: 1222: 1216: 1215: 1214: 1213: 1206: 1205: 1200: 1195: 1189: 1186: 1185: 1179: 1176: 1175: 1172: 1168: 1167: 1166: 1163: 1162: 1158: 1157: 1146: 1143: 1140: 1137: 1134: 1131: 1128: 1125: 1122: 1119: 1116: 1102: 1091: 1088: 1085: 1082: 1079: 1076: 1073: 1070: 1067: 1064: 1061: 1047: 1036: 1033: 1030: 1027: 1024: 1021: 1018: 1015: 1012: 1009: 1006: 992: 981: 978: 975: 972: 969: 966: 951: 949: 948: 943: 937: 936: 931: 930: 927: 926: 923: 922: 915: 910: 905: 898: 897: 892: 887: 882: 876: 875: 870: 869: 866: 865: 859: 858: 855: 854: 843: 840: 830: 819: 808: 807: 796: 793: 783: 772: 758: 747: 744: 734: 727: 726: 723: 722: 711: 708: 698: 687: 676: 675: 664: 661: 651: 640: 626: 615: 612: 609: 599: 592: 591: 588: 587: 576: 573: 563: 552: 541: 540: 529: 526: 516: 505: 491: 480: 477: 467: 458: 457: 456: 450: 445: 444: 441: 440: 435: 434: 433: 432: 427: 422: 411: 400: 381: 380: 374: 373: 371: 370: 365: 359: 356: 355: 349: 348: 347: 346: 341: 322: 321: 316: 315: 312: 311: 306: 305: 304: 303: 298: 293: 285: 284: 278: 277: 276: 275: 270: 265: 260: 258:Free expansion 255: 250: 245: 240: 235: 230: 225: 220: 212: 211: 205: 204: 203: 202: 197: 195:Control volume 192: 187: 185:Phase (matter) 182: 177: 172: 167: 159: 158: 150: 149: 144: 139: 133: 128: 127: 124: 123: 119: 118: 113: 108: 103: 97: 96: 91: 90: 87: 86: 83: 82: 71: 70: 65: 60: 55: 49: 48: 45: 44: 41: 40: 35:The classical 34: 26: 25: 23:Thermodynamics 15: 9: 6: 4: 3: 2: 16332: 16321: 16318: 16316: 16313: 16311: 16308: 16306: 16303: 16302: 16300: 16291: 16288: 16285: 16281: 16278: 16276: 16273: 16270: 16266: 16262: 16259: 16256: 16255: 16250: 16249: 16245: 16242: 16238: 16235: 16234: 16225: 16220: 16208: 16200: 16194: 16190: 16186: 16181: 16176: 16172: 16168: 16164: 16159: 16156: 16155:1-928729-01-0 16152: 16148: 16144: 16141: 16137: 16134: 16130: 16124: 16120: 16115: 16110: 16104: 16101:. Cambridge. 16100: 16095: 16093: 16089: 16085: 16081: 16077: 16075: 16071: 16067: 16063: 16062: 16052: 16048: 16045: 16042: 16038: 16035: 16032: 16031:0-691-11338-6 16028: 16024: 16020: 16018:(3): 305–394. 16017: 16013: 16009: 16006: 16005:0-387-90403-4 16002: 15998: 15994: 15993:Truesdell, C. 15991: 15988: 15984: 15981: 15978: 15974: 15971: 15959: 15955: 15951: 15943: 15939: 15935: 15931: 15927: 15924: 15920: 15919:Wergeland, H. 15916: 15913: 15910: 15906: 15902: 15899: 15896: 15892: 15888: 15882: 15878: 15877: 15871: 15868: 15867:0-12-569680-9 15864: 15860: 15856: 15851: 15846: 15842: 15838: 15834: 15829: 15826: 15823: 15819: 15816: 15813: 15812: 15807: 15804: 15802: 15800: 15796:(1897/1903). 15795: 15792: 15789: 15786:(1957/1966). 15785: 15784:Pippard, A.B. 15782: 15779: 15778:0-471-62430-6 15775: 15771: 15767: 15764: 15760: 15757: 15754: 15753:0-273-08577-8 15750: 15746: 15742: 15739: 15735: 15731: 15727: 15723: 15719: 15715: 15711: 15710:Maxwell, J.C. 15707: 15703: 15697: 15693: 15689: 15684: 15681: 15677: 15673: 15669: 15665: 15661: 15657: 15653: 15648: 15643: 15639: 15635: 15630: 15627: 15623: 15619: 15615: 15612: 15611:0-471-97393-9 15608: 15604: 15600: 15599:Prigogine, I. 15596: 15593: 15592:0-7167-1088-9 15589: 15585: 15582:(1969/1980). 15581: 15577: 15574: 15571: 15567: 15564: 15560: 15557: 15554: 15550: 15546: 15543: 15540: 15539:0-691-11338-6 15536: 15532: 15528: 15524: 15520: 15516: 15510: 15506: 15505: 15499: 15496: 15495:0-471-30280-5 15492: 15488: 15484: 15481: 15480:0-521-61941-6 15477: 15473: 15469: 15466: 15462: 15458: 15454: 15451: 15448: 15447:1-4020-0788-4 15444: 15440: 15436: 15433: 15432:0-521-23682-7 15429: 15425: 15421: 15418: 15406: 15405: 15400: 15385: 15381: 15377: 15358: 15354: 15350: 15346: 15342: 15338: 15331: 15327: 15323: 15312: 15308: 15304: 15300: 15296: 15280: 15275: 15271: 15267: 15263: 15259: 15255: 15251: 15247: 15243: 15239: 15236: 15233:(1939/1970). 15232: 15231:Cowling, T.G. 15228: 15225: 15223: 15219: 15218:0-7190-1741-6 15215: 15211: 15210: 15206:(1824/1986). 15205: 15202: 15199: 15195: 15191: 15186: 15176:on 2016-03-04 15175: 15171: 15167: 15163: 15159: 15155: 15151: 15147: 15143: 15139: 15136: 15135:0-471-86256-8 15132: 15128: 15125:(1960/1985). 15124: 15121: 15118: 15114: 15111: 15108: 15104: 15101: 15097: 15093: 15089: 15086: 15083:(1896/1964). 15082: 15081:Boltzmann, L. 15079: 15075: 15071: 15067: 15065:9780199562107 15061: 15057: 15053: 15049: 15045: 15044: 15039: 15035: 15031: 15028: 15027:0-88318-797-3 15024: 15020: 15016: 15013: 15012:0-521-59082-5 15009: 15005: 15001: 14998: 14994: 14990: 14986: 14983: 14979: 14975: 14971: 14968: 14964: 14960: 14956: 14954:0-521-25445-0 14950: 14946: 14941: 14940: 14925: 14920: 14916: 14912: 14908: 14904: 14900: 14893: 14891: 14876: 14872: 14866: 14864: 14856: 14851: 14842: 14836: 14833:. Cambridge. 14832: 14825: 14817: 14813: 14806: 14799: 14794: 14787: 14782: 14773: 14764: 14755: 14746: 14737: 14721: 14717: 14710: 14703: 14691: 14687: 14680: 14672: 14668: 14663: 14658: 14654: 14650: 14645: 14640: 14637:(1): 013013. 14636: 14632: 14628: 14624: 14617: 14609: 14605: 14601: 14597: 14593: 14589: 14585: 14581: 14574: 14559: 14553: 14549: 14548: 14540: 14534: 14529: 14520: 14511: 14502: 14495: 14489: 14475: 14471: 14467: 14463: 14459: 14455: 14454:Physics Today 14448: 14441: 14433: 14427: 14423: 14418: 14417: 14411: 14410:Greene, Brian 14405: 14397: 14393: 14389: 14385: 14381: 14377: 14373: 14369: 14362: 14354: 14350: 14346: 14342: 14338: 14334: 14329: 14324: 14320: 14316: 14309: 14302: 14297: 14291: 14287: 14282: 14275: 14271: 14267: 14261: 14254: 14253:0-521-25677-1 14250: 14246: 14240: 14232: 14228: 14221: 14215: 14211: 14210: 14204: 14196: 14192: 14188: 14184: 14180: 14176: 14172: 14165: 14163: 14154: 14150: 14146: 14142: 14138: 14134: 14130: 14123: 14115: 14111: 14107: 14103: 14099: 14095: 14091: 14084: 14076: 14072: 14068: 14064: 14060: 14056: 14052: 14045: 14037: 14033: 14029: 14025: 14018: 14010: 14006: 14002: 13998: 13994: 13990: 13986: 13982: 13978: 13971: 13963: 13956: 13948: 13944: 13940: 13936: 13932: 13928: 13924: 13917: 13910: 13909:0-471-86256-8 13906: 13902: 13899:(1960/1985), 13898: 13893: 13885: 13879: 13875: 13868: 13859: 13850: 13843: 13838: 13831: 13826: 13819: 13818:0-12-701350-4 13815: 13811: 13807: 13806:Truesdell, C. 13802: 13793: 13784: 13777: 13772: 13770: 13763:, p. 49. 13762: 13757: 13755: 13746: 13740: 13736: 13729: 13720: 13713: 13708: 13701: 13696: 13687: 13680: 13675: 13668: 13663: 13656: 13655:Wergeland, H. 13652: 13647: 13638: 13631: 13626: 13619: 13614: 13608:, p. 86. 13607: 13602: 13595: 13590: 13581: 13572: 13565: 13564:Prigogine, I. 13559: 13550: 13541: 13534: 13533:Truesdell, C. 13529: 13520: 13511: 13502: 13495: 13490: 13483: 13478: 13471: 13466: 13452:. web.mit.edu 13451: 13445: 13436: 13429: 13424: 13417: 13413: 13407: 13403: 13398: 13397: 13388: 13379: 13374: 13370: 13366: 13362: 13355: 13346: 13340: 13336: 13332: 13328: 13327:Butler, L. J. 13322: 13320: 13310: 13308: 13306: 13296: 13288: 13282: 13278: 13277: 13269: 13261: 13255: 13251: 13250: 13242: 13240: 13238: 13228: 13219: 13212: 13207: 13201: 13196: 13187: 13180: 13175: 13167: 13160: 13152: 13146: 13142: 13141: 13133: 13125: 13119: 13115: 13114: 13106: 13097: 13089: 13085: 13081: 13075: 13068: 13067: 13060: 13052: 13046: 13042: 13035: 13033: 13024: 13022:0-7131-2789-9 13018: 13014: 13010: 13009:Reichl, Linda 13004: 13000: 12989: 12986: 12984: 12983:Thermal diode 12981: 12979: 12976: 12974: 12971: 12969: 12966: 12964: 12961: 12959: 12956: 12954: 12951: 12949: 12946: 12944: 12941: 12939: 12936: 12934: 12931: 12929: 12926: 12924: 12921: 12919: 12916: 12915: 12904: 12903:0-12-701350-4 12900: 12896: 12892: 12891:Truesdell, C. 12886: 12877: 12876:P.W. Bridgman 12870: 12862: 12858: 12851: 12849: 12845: 12841: 12830: 12828: 12824: 12820: 12815: 12813: 12810:and later by 12809: 12804: 12802: 12798: 12794: 12790: 12786: 12782: 12778: 12774: 12770: 12766: 12762: 12758: 12754: 12750: 12745: 12731: 12727: 12724: 12718: 12708: 12704: 12702: 12697: 12687: 12684: 12674: 12672: 12668: 12664: 12657: 12653: 12652:Arrow of time 12646:Arrow of time 12643: 12640: 12636: 12633: 12629: 12626: 12624: 12620: 12616: 12612: 12607: 12604: 12598: 12588: 12586: 12582: 12578: 12574: 12568: 12566: 12565:heat capacity 12556: 12554: 12548: 12544: 12541: 12537: 12531: 12529: 12525: 12524: 12523:What is Life? 12520:(in his book 12519: 12508: 12506: 12502: 12497: 12495: 12489: 12487: 12483: 12477: 12451: 12447: 12444: 12438: 12433: 12429: 12426: 12423: 12420: 12417: 12411: 12406: 12402: 12398: 12393: 12389: 12383: 12379: 12373: 12370: 12365: 12361: 12355: 12351: 12345: 12341: 12336: 12332: 12327: 12323: 12317: 12314: 12309: 12304: 12300: 12296: 12291: 12287: 12281: 12277: 12271: 12268: 12263: 12260: 12257: 12250: 12249: 12248: 12232: 12228: 12202: 12198: 12194: 12190: 12185: 12181: 12177: 12173: 12170: 12165: 12161: 12149: 12145: 12142: 12139: 12136: 12129: 12128: 12127: 12109: 12104: 12100: 12096: 12092: 12089: 12084: 12080: 12074: 12070: 12058: 12054: 12051: 12048: 12041: 12040: 12039: 12037: 12033: 12012: 12007: 12000: 11989: 11982: 11978: 11972: 11968: 11964: 11961: 11955: 11950: 11946: 11938: 11937: 11936: 11934: 11930: 11903: 11899: 11896: 11890: 11887: 11884: 11879: 11876: 11871: 11866: 11862: 11859: 11853: 11850: 11847: 11842: 11837: 11831: 11823: 11814: 11809: 11806: 11803: 11798: 11793: 11787: 11779: 11770: 11765: 11762: 11759: 11752: 11751: 11750: 11730: 11727: 11722: 11717: 11712: 11706: 11698: 11689: 11680: 11679: 11678: 11658: 11655: 11650: 11645: 11640: 11634: 11626: 11617: 11608: 11607: 11606: 11585: 11580: 11574: 11566: 11557: 11552: 11549: 11546: 11543: 11538: 11533: 11527: 11518: 11512: 11508: 11505: 11496: 11487: 11486: 11485: 11483: 11441: 11436: 11430: 11421: 11417: 11410: 11400: 11395: 11390: 11385: 11379: 11369: 11355: 11350: 11345: 11341: 11337: 11334: 11329: 11324: 11318: 11301: 11292: 11291: 11290: 11288: 11284: 11279: 11264: 11260: 11257: 11254: 11251: 11247: 11241: 11237: 11215: 11212: 11209: 11203: 11199: 11178: 11175: 11172: 11169: 11161: 11145: 11142: 11134: 11093: 11089: 11086: 11083: 11080: 11076: 11070: 11066: 11062: 11058: 11055: 11052: 11046: 11042: 11034: 11033: 11032: 11017: 11013: 11010: 11007: 11004: 11000: 10994: 10990: 10969: 10966: 10963: 10960: 10940: 10937: 10934: 10931: 10891: 10888: 10885: 10882: 10862: 10842: 10839: 10836: 10833: 10830: 10827: 10803: 10800: 10797: 10791: 10788: 10782: 10779: 10776: 10770: 10759: 10755: 10752: 10749: 10743: 10739: 10731: 10730: 10729: 10727: 10723: 10719: 10715: 10712: 10708: 10704: 10688: 10685: 10682: 10679: 10659: 10636: 10633: 10626: 10622: 10618: 10595: 10592: 10589: 10586: 10566: 10558: 10541: 10538: 10535: 10523: 10519: 10515: 10511: 10507: 10486: 10483: 10480: 10474: 10466: 10461: 10457: 10449: 10446: 10443: 10435: 10430: 10427: 10424: 10417: 10416: 10415: 10396: 10393: 10390: 10384: 10374: 10370: 10366: 10362: 10359: 10356: 10345: 10344: 10343: 10328: 10325: 10322: 10316: 10291: 10288: 10285: 10282: 10262: 10239: 10236: 10229: 10225: 10221: 10197: 10194: 10191: 10162: 10156: 10153: 10146: 10142: 10138: 10132: 10128: 10125: 10122: 10115: 10114: 10113: 10099: 10096: 10070: 10067: 10060: 10056: 10052: 10046: 10043: 10040: 10033: 10032: 10031: 10030:is given by: 10015: 10011: 10002: 9998: 9994: 9990: 9974: 9971: 9968: 9960: 9956: 9951: 9948: 9944: 9940: 9936: 9914: 9911: 9905: 9900: 9897: 9894: 9886: 9882: 9879: 9876: 9870: 9867: 9864: 9858: 9847: 9842: 9833: 9832: 9831: 9812: 9808: 9805: 9799: 9796: 9793: 9786: 9785: 9784: 9776: 9773: 9768: 9748: 9744: 9694: 9649: 9635: 9632: 9612: 9609: 9589: 9586: 9566: 9563: 9560: 9557: 9537: 9516: 9513: 9510: 9482: 9477: 9474: 9471: 9463: 9459: 9456: 9445: 9441: 9438: 9431: 9430: 9429: 9415: 9407: 9402: 9400: 9396: 9392: 9388: 9384: 9379: 9377: 9373: 9369: 9365: 9361: 9355: 9345: 9342: 9336: 9328: 9323: 9314: 9296: 9293: 9267: 9264: 9259: 9252: 9249: 9223: 9216: 9213: 9206: 9200: 9197: 9191: 9186: 9181: 9178: 9171: 9165: 9162: 9157: 9154: 9144: 9143: 9142: 9139: 9120: 9113: 9095: 9092: 9082: 9081: 9080: 9063: 9060: 9055: 9048: 9045: 9019: 9012: 9009: 9002: 8997: 8992: 8989: 8982: 8976: 8973: 8968: 8965: 8955: 8954: 8953: 8950: 8934: 8927: 8924: 8915: 8911: 8907: 8902: 8899: 8896: 8893: 8889: 8866: 8862: 8852: 8834: 8827: 8824: 8797: 8794: 8789: 8782: 8779: 8753: 8746: 8743: 8736: 8730: 8727: 8722: 8719: 8709: 8708: 8707: 8701: 8697: 8694: 8691: 8688: 8687: 8686: 8669: 8666: 8660: 8657: 8652: 8649: 8639: 8638: 8637: 8635: 8630: 8628: 8622: 8618: 8615: 8611: 8607: 8588: 8585: 8582: 8577: 8573: 8570: 8564: 8557: 8556: 8555: 8553: 8549: 8540: 8531: 8529: 8524: 8521: 8517: 8512: 8510: 8506: 8502: 8497: 8495: 8491: 8490:spontaneously 8487: 8483: 8478: 8476: 8469: 8464: 8459: 8449: 8447: 8443: 8439: 8435: 8431: 8415: 8412: 8409: 8398: 8394: 8375: 8372: 8369: 8359: 8358: 8357: 8356: 8349: 8345: 8341: 8337: 8324: 8320: 8316: 8312: 8309: 8305: 8302: 8298: 8294: 8293: 8292: 8287: 8283: 8276: 8267: 8264: 8261: 8257: 8256: 8255: 8253: 8249: 8239: 8237: 8233: 8229: 8224: 8222: 8221: 8215: 8214: 8208: 8204: 8185: 8182: 8177: 8173: 8169: 8166: 8163: 8160: 8140: 8137: 8132: 8129: 8126: 8122: 8118: 8111: 8110: 8109: 8107: 8103: 8098: 8096: 8092: 8073: 8070: 8065: 8061: 8057: 8054: 8051: 8048: 8041: 8040: 8039: 8020: 8016: 8010: 8007: 8003: 7999: 7996: 7993: 7988: 7984: 7980: 7977: 7972: 7968: 7964: 7961: 7958: 7955: 7948: 7947: 7946: 7944: 7941: 7940: 7935: 7915: 7909: 7905: 7899: 7896: 7892: 7888: 7885: 7882: 7877: 7873: 7869: 7866: 7861: 7857: 7853: 7850: 7846: 7842: 7839: 7836: 7831: 7827: 7823: 7816: 7815: 7814: 7812: 7804: 7800: 7793: 7789: 7768: 7764: 7760: 7755: 7752: 7748: 7744: 7741: 7738: 7735: 7730: 7726: 7722: 7719: 7716: 7713: 7710: 7707: 7704: 7697: 7696: 7695: 7693: 7688: 7670: 7667: 7662: 7658: 7654: 7646: 7642: 7638: 7635: 7627: 7623: 7619: 7616: 7613: 7606: 7605: 7604: 7601: 7599: 7594: 7590: 7570: 7564: 7560: 7554: 7551: 7547: 7543: 7539: 7535: 7532: 7529: 7526: 7523: 7520: 7517: 7514: 7511: 7508: 7501: 7500: 7499: 7497: 7486: 7482: 7478: 7474: 7470: 7466: 7462: 7459:, the change 7458: 7439: 7436: 7431: 7427: 7423: 7420: 7417: 7414: 7411: 7394: 7390: 7383: 7382: 7381: 7376: 7372: 7365: 7360: 7358: 7351: 7344: 7338:and pressure 7337: 7330: 7323: 7313: 7299: 7296: 7293: 7270: 7267: 7264: 7261: 7253: 7230: 7227: 7224: 7221: 7217: 7212: 7209: 7203: 7200: 7197: 7187: 7186: 7185: 7168: 7165: 7158: 7155: 7152: 7149: 7145: 7140: 7137: 7131: 7128: 7121: 7118: 7115: 7112: 7108: 7103: 7100: 7094: 7091: 7088: 7082: 7075: 7074: 7073: 7068: 7064: 7059: 7055: 7053: 7052:absolute zero 7049: 7045: 7024: 7020: 7017: 7011: 7008: 7005: 6998: 6997: 6996: 6993: 6977: 6973: 6970: 6962: 6958: 6934: 6931: 6926: 6922: 6919: 6913: 6906: 6905: 6904: 6903: 6899: 6893: 6883: 6881: 6874: 6867: 6863: 6856: 6837: 6830: 6825: 6821: 6815: 6810: 6806: 6800: 6792: 6787: 6783: 6779: 6774: 6769: 6765: 6758: 6755: 6747: 6743: 6739: 6734: 6730: 6723: 6716: 6715: 6714: 6712: 6690: 6687: 6682: 6678: 6671: 6668: 6660: 6657: 6652: 6648: 6640: 6639: 6638: 6636: 6617: 6606: 6602: 6598: 6593: 6589: 6582: 6579: 6571: 6561: 6557: 6553: 6548: 6544: 6537: 6534: 6526: 6520: 6509: 6505: 6501: 6496: 6492: 6485: 6475: 6471: 6467: 6462: 6458: 6451: 6445: 6437: 6433: 6429: 6424: 6420: 6413: 6406: 6405: 6404: 6399: 6392: 6376: 6373: 6370: 6365: 6361: 6352: 6334: 6330: 6306: 6298: 6294: 6290: 6285: 6281: 6274: 6266: 6262: 6258: 6253: 6249: 6242: 6239: 6226: 6222: 6206: 6202: 6184: 6180: 6164: 6160: 6148: 6135: 6131: 6113: 6109: 6097: 6089: 6085: 6081: 6076: 6072: 6065: 6058: 6057: 6056: 6053: 6037: 6032: 6028: 6005: 6001: 5973: 5959: 5954: 5930: 5925: 5914: 5904: 5897: 5892: 5877: 5863: 5858: 5847: 5836: 5831: 5814: 5800: 5795: 5771: 5766: 5755: 5744: 5739: 5722: 5708: 5703: 5682: 5677: 5663: 5660: 5657: 5651: 5646: 5635: 5621: 5616: 5605: 5595: 5588: 5583: 5568: 5554: 5549: 5538: 5527: 5522: 5508: 5497: 5492: 5481: 5470: 5465: 5455: 5447: 5436: 5431: 5420: 5410: 5403: 5398: 5386: 5375: 5370: 5346: 5339: 5334: 5312: 5307: 5293: 5290: 5287: 5281: 5276: 5265: 5254: 5249: 5238: 5227: 5222: 5211: 5200: 5195: 5170: 5165: 5144: 5139: 5125: 5122: 5119: 5113: 5108: 5093: 5092: 5091: 5075: 5071: 5048: 5044: 5021: 5017: 4994: 4990: 4978: 4953: 4949: 4945: 4940: 4936: 4929: 4926: 4923: 4920: 4907: 4903: 4885: 4881: 4869: 4866: 4863: 4858: 4854: 4846: 4826: 4822: 4818: 4813: 4809: 4802: 4799: 4796: 4793: 4780: 4776: 4758: 4754: 4742: 4739: 4736: 4731: 4727: 4719: 4699: 4695: 4691: 4686: 4682: 4675: 4672: 4669: 4666: 4653: 4649: 4631: 4627: 4615: 4612: 4609: 4604: 4600: 4592: 4591: 4590: 4585: 4578: 4574: 4567: 4560: 4550: 4543: 4536: 4529: 4522: 4515: 4506: 4499: 4497: 4483: 4475: 4471: 4467: 4462: 4458: 4451: 4448: 4435: 4431: 4413: 4409: 4393: 4392: 4389: 4384: 4377: 4373: 4369: 4366: 4362: 4357: 4353: 4349: 4344: 4340: 4335: 4331: 4326: 4322: 4315: 4306: 4299: 4297: 4273: 4269: 4251: 4247: 4235: 4232: 4229: 4222: 4218: 4211: 4207: 4203: 4198: 4194: 4187: 4180: 4176: 4164: 4160: 4148: 4145: 4138: 4137: 4134: 4130: 4120: 4118: 4111: 4092: 4089: 4078: 4073: 4070: 4064: 4057: 4056: 4055: 4053: 4043: 4041: 4037: 4032: 4030: 4026: 4018: 4015: 4014:Carnot engine 4011: 4010: 4009: 4007: 3998: 3995: 3989: 3974: 3970: 3966: 3962: 3954: 3950: 3941: 3938: 3934: 3930: 3926: 3918: 3911: 3904: 3900: 3893: 3888: 3882: 3875: 3871: 3867: 3863: 3858: 3834: 3830: 3826: 3823: 3816: 3812: 3806: 3802: 3792: 3789: 3778: 3774: 3770: 3767: 3760: 3756: 3750: 3746: 3736: 3725: 3721: 3717: 3714: 3707: 3703: 3697: 3693: 3686: 3683: 3677: 3674: 3663: 3659: 3655: 3652: 3645: 3641: 3635: 3631: 3624: 3621: 3608: 3604: 3597: 3593: 3589: 3586: 3580: 3575: 3571: 3551: 3545: 3542: 3538: 3532: 3529: 3524: 3521: 3515: 3511: 3508: 3502: 3498: 3488: 3484: 3479: 3476: 3470: 3465: 3461: 3452: 3448: 3436: 3428: 3415: 3412: 3400: 3396: 3393: 3386: 3382: 3375: 3372: 3368: 3364: 3349: 3340: 3332:\delta Q_{CC} 3325: 3322: 3318: 3314: 3290: 3286: 3272: 3257: 3254: 3251: 3246: 3240: 3232: 3223: 3218: 3215: 3207: 3204: 3198: 3194:equation for 3192: 3187: 3182: 3178: 3174: 3170: 3166: 3160: 3154: 3148: 3144: 3139: 3135: 3131: 3128:defined as a 3126: 3122: 3112: 3104: 3103: 3102: 3101: 3100: 3097: 3095: 3089: 3080: 3079: 3078: 3077: 3076: 3068: 3064: 3050: 3047: 3044: 3041: 3038: 3035: 3027: 3023: 3019: 3013: 3009: 3007: 2993: 2992: 2991: 2990: 2989: 2987: 2983: 2972: 2971: 2970: 2969: 2968: 2966: 2952: 2948: 2944: 2940: 2939: 2938: 2937: 2936: 2934: 2930: 2926: 2911: 2910: 2909: 2908: 2907: 2898: 2895: 2877: 2874: 2851: 2847: 2844: 2839: 2836: 2830: 2826: 2823: 2818: 2814: 2793: 2790: 2785: 2782: 2777: 2769: 2765: 2761: 2758: 2747: 2744: 2736: 2723: 2706: 2702: 2699: 2694: 2691: 2685: 2681: 2678: 2675: 2664: 2660: 2656: 2652: 2651:Carnot engine 2642: 2628: 2627: 2626: 2625: 2619: 2618: 2617: 2616: 2615: 2613: 2604: 2602: 2601:refrigeration 2597: 2592: 2588: 2586: 2581: 2567:temperatures. 2565: 2561: 2560: 2559: 2558: 2557: 2550: 2547: 2546: 2545: 2544: 2539: 2535: 2534:steam engines 2531: 2530: 2529: 2528: 2523: 2519: 2518: 2517: 2516: 2515: 2513: 2509: 2505: 2501: 2497: 2496:Carnot engine 2493: 2483: 2481: 2477: 2473: 2469: 2459: 2457: 2452: 2447: 2445: 2395: 2391: 2387: 2381: 2370: 2366: 2360: 2357: 2352: 2347: 2343: 2340: 2334: 2331: 2319: 2318: 2317: 2315: 2311: 2295: 2286: 2239: 2235: 2232: 2226: 2223: 2211: 2210: 2209: 2206: 2200: 2194: 2137: 2132: 2129: 2123: 2120: 2108: 2107: 2106: 2105: 2100: 2098: 2051: 2040: 2039:infinitesimal 2021: 1988: 1984: 1981: 1975: 1972: 1960: 1959: 1958: 1941: 1931: 1915: 1912: 1904: 1888: 1875: 1871: 1867: 1862: 1861:, increases. 1848: 1840: 1836: 1832: 1828: 1823: 1819: 1817: 1813: 1809: 1805: 1804:closed system 1801: 1797: 1793: 1784: 1775: 1773: 1769: 1764: 1762: 1758: 1754: 1750: 1746: 1742: 1738: 1734: 1730: 1726: 1722: 1717: 1715: 1714:arrow of time 1711: 1707: 1703: 1699: 1695: 1691: 1687: 1683: 1678: 1676: 1672: 1668: 1664: 1660: 1657: 1654: 1650: 1646: 1634: 1629: 1627: 1622: 1620: 1615: 1614: 1612: 1611: 1606: 1598: 1597: 1596: 1595: 1588: 1585: 1583: 1580: 1578: 1577:Self-assembly 1575: 1573: 1570: 1569: 1563: 1562: 1554: 1551: 1549: 1548:van der Waals 1546: 1544: 1541: 1539: 1536: 1534: 1531: 1529: 1526: 1524: 1521: 1519: 1516: 1514: 1511: 1509: 1506: 1504: 1501: 1499: 1496: 1494: 1491: 1489: 1486: 1484: 1481: 1479: 1476: 1474: 1473:von Helmholtz 1471: 1469: 1466: 1464: 1461: 1459: 1456: 1454: 1451: 1449: 1446: 1444: 1441: 1439: 1436: 1434: 1431: 1429: 1426: 1424: 1421: 1420: 1413: 1412: 1401: 1398: 1396: 1393: 1392: 1391: 1390: 1383: 1380: 1379: 1377: 1376: 1370: 1367: 1365: 1362: 1361: 1359: 1358: 1354: 1353: 1347: 1346: 1339: 1336: 1335: 1328: 1325: 1324: 1317: 1316: 1315: 1314: 1311: 1308: 1307: 1302: 1299: 1297: 1294: 1292: 1288: 1284: 1283: 1279: 1276: 1275: 1273: 1272: 1268: 1267: 1261: 1258: 1256: 1253: 1251: 1248: 1246: 1243: 1241: 1238: 1236: 1233: 1231: 1228: 1227: 1225: 1224: 1221: 1218: 1217: 1212: 1209: 1208: 1204: 1201: 1199: 1196: 1194: 1191: 1190: 1188: 1187: 1183: 1182: 1173: 1170: 1169: 1165: 1164: 1144: 1141: 1138: 1135: 1132: 1126: 1123: 1120: 1114: 1106: 1103: 1089: 1086: 1083: 1080: 1077: 1071: 1068: 1065: 1059: 1051: 1048: 1034: 1031: 1028: 1025: 1022: 1016: 1013: 1010: 1004: 996: 993: 976: 973: 970: 964: 956: 953: 952: 947: 944: 942: 939: 938: 934: 929: 928: 921: 920: 916: 914: 911: 909: 906: 904: 901: 900: 896: 895:Ideal gas law 893: 891: 888: 886: 883: 881: 878: 877: 873: 868: 867: 841: 831: 817: 810: 809: 794: 784: 770: 763: 762: 759: 745: 742: 735: 732: 729: 728: 709: 699: 685: 678: 677: 662: 652: 638: 631: 630: 627: 613: 610: 607: 600: 597: 594: 593: 574: 564: 550: 543: 542: 527: 517: 503: 496: 495: 492: 478: 475: 468: 465: 462: 461: 455: 452: 451: 448: 443: 442: 431: 428: 426: 425:Vapor quality 423: 421: 420: 415: 412: 410: 409: 404: 401: 398: 394: 393: 388: 385: 384: 383: 382: 379: 376: 375: 369: 366: 364: 361: 360: 358: 357: 354: 351: 350: 345: 342: 340: 337: 336: 335: 334: 330: 326: 319: 314: 313: 302: 299: 297: 294: 292: 289: 288: 287: 286: 283: 280: 279: 274: 271: 269: 266: 264: 263:Reversibility 261: 259: 256: 254: 251: 249: 246: 244: 241: 239: 236: 234: 231: 229: 226: 224: 221: 219: 216: 215: 214: 213: 210: 207: 206: 201: 198: 196: 193: 191: 188: 186: 183: 181: 178: 176: 173: 171: 168: 166: 163: 162: 161: 160: 157: 154: 153: 148: 145: 143: 140: 138: 137:Closed system 135: 134: 131: 126: 125: 117: 114: 112: 109: 107: 104: 102: 99: 98: 94: 89: 88: 81: 77: 74: 73: 69: 66: 64: 61: 59: 56: 54: 51: 50: 43: 42: 38: 32: 28: 27: 24: 21: 20: 16283: 16268: 16253: 16247: 16162: 16146: 16122: 16113:(technical). 16098: 16079: 16065: 16050: 16040: 16022: 16015: 16011: 15996: 15986: 15976: 15962:. Retrieved 15957: 15953: 15941: 15937: 15922: 15915:ter Haar, D. 15908: 15904: 15894: 15875: 15858: 15840: 15836: 15821: 15810: 15798: 15787: 15769: 15762: 15744: 15717: 15713: 15687: 15679: 15637: 15633: 15617: 15602: 15583: 15569: 15562: 15552: 15548: 15530: 15503: 15486: 15471: 15464: 15460: 15456: 15438: 15423: 15416: 15409:. Retrieved 15403: 15399:Clausius, R. 15388:. Retrieved 15383: 15379: 15364:. Retrieved 15357:the original 15336: 15326:Clausius, R. 15314:. Retrieved 15302: 15298: 15283:. Retrieved 15253: 15249: 15242:Clausius, R. 15234: 15208: 15197: 15184: 15178:. Retrieved 15174:the original 15153: 15149: 15126: 15123:Callen, H.B. 15116: 15106: 15091: 15084: 15042: 15018: 15003: 14988: 14973: 14970:Atkins, P.W. 14944: 14906: 14902: 14878:. Retrieved 14874: 14850: 14830: 14824: 14815: 14805: 14793: 14781: 14772: 14763: 14754: 14745: 14736: 14724:. Retrieved 14719: 14709: 14701: 14694:. Retrieved 14689: 14679: 14634: 14630: 14616: 14583: 14579: 14573: 14561:. Retrieved 14546: 14539: 14528: 14519: 14510: 14501: 14493: 14488: 14477:. Retrieved 14460:(9): 32–38. 14457: 14453: 14440: 14415: 14404: 14371: 14368:Phys. Rev. D 14367: 14361: 14318: 14314: 14308: 14296: 14281: 14276:, pp. 55–58. 14265: 14260: 14255:, pp. 43–44. 14244: 14239: 14230: 14226: 14220: 14208: 14203: 14178: 14174: 14136: 14132: 14122: 14100:(2): 69–77. 14097: 14093: 14083: 14061:(1): 24–33. 14058: 14054: 14044: 14027: 14023: 14017: 13984: 13980: 13970: 13961: 13955: 13930: 13926: 13916: 13900: 13897:Callen, H.B. 13892: 13873: 13867: 13858: 13849: 13837: 13825: 13809: 13801: 13792: 13783: 13734: 13728: 13719: 13707: 13695: 13686: 13674: 13662: 13651:ter Haar, D. 13646: 13637: 13625: 13613: 13601: 13589: 13580: 13571: 13558: 13549: 13540: 13528: 13519: 13510: 13501: 13496:(1824/1986). 13489: 13477: 13465: 13454:. Retrieved 13444: 13435: 13423: 13415: 13395: 13387: 13368: 13364: 13354: 13345: 13330: 13295: 13275: 13268: 13248: 13227: 13218: 13206: 13195: 13186: 13174: 13159: 13139: 13132: 13111: 13105: 13096: 13083: 13074: 13064: 13059: 13040: 13012: 13003: 12894: 12883: 12868: 12860: 12837: 12822: 12818: 12816: 12805: 12800: 12796: 12792: 12788: 12780: 12776: 12772: 12756: 12752: 12747: 12720: 12705: 12699: 12680: 12663:CPT symmetry 12659: 12641: 12637: 12634: 12630: 12627: 12615:fluctuations 12608: 12600: 12569: 12562: 12549: 12545: 12532: 12521: 12514: 12498: 12490: 12479: 12219: 12125: 12031: 12029: 11928: 11926: 11748: 11676: 11603: 11481: 11459: 11286: 11282: 11280: 11159: 11132: 11110: 10982:is given by 10819: 10728:. There are 10725: 10721: 10717: 10713: 10710: 10706: 10702: 10556: 10521: 10517: 10513: 10509: 10505: 10503: 10413: 10179: 10088: 10000: 9996: 9992: 9988: 9958: 9954: 9952: 9942: 9938: 9932: 9829: 9782: 9771: 9695: 9650: 9498: 9403: 9387:uncorrelated 9380: 9357: 9340: 9334: 9320: 9282: 9140: 9136: 9078: 8951: 8812: 8705: 8695: 8689: 8684: 8631: 8624: 8620: 8613: 8609: 8605: 8603: 8545: 8525: 8513: 8498: 8489: 8479: 8472: 8445: 8441: 8437: 8433: 8429: 8392: 8390: 8347: 8343: 8339: 8333: 8297:refrigerator 8285: 8281: 8274: 8271: 8251: 8245: 8225: 8217: 8210: 8200: 8105: 8101: 8099: 8094: 8090: 8088: 8037: 7942: 7937: 7934:availability 7933: 7931: 7806: 7802: 7795: 7791: 7787: 7785: 7691: 7689: 7685: 7602: 7592: 7588: 7586: 7488: 7484: 7480: 7476: 7472: 7468: 7464: 7460: 7454: 7374: 7367: 7363: 7361: 7353: 7346: 7339: 7332: 7328: 7325: 7249: 7183: 7066: 7060: 7056: 7047: 7041: 6994: 6949: 6901: 6895: 6872: 6865: 6861: 6854: 6852: 6710: 6708: 6634: 6632: 6397: 6390: 6351:triple point 6321: 6054: 5992: 4976: 4974: 4583: 4576: 4569: 4562: 4555: 4548: 4541: 4534: 4527: 4520: 4513: 4511: 4500: 4382: 4375: 4370: 4364: 4360: 4355: 4351: 4342: 4338: 4333: 4329: 4324: 4320: 4313: 4311: 4300: 4132: 4109: 4107: 4049: 4033: 4029:Carnot cycle 4022: 4004: 3991: 3971: 3967: 3963: 3959: 3947: 3936: 3932: 3928: 3924: 3916: 3909: 3902: 3898: 3891: 3889: 3880: 3873: 3869: 3865: 3861: 3859: 3453: 3449: 3429: 3341: 3278: 3208: 3202: 3196: 3190: 3180: 3176: 3172: 3168: 3164: 3158: 3152: 3146: 3137: 3124: 3118: 3110: 3098: 3094:mole numbers 3090: 3086: 3074: 3065: 3015: 3011: 3004: 2985: 2979: 2963: 2932: 2922: 2904: 2662: 2658: 2647: 2610: 2598: 2594: 2590: 2584: 2577: 2564:Carnot cycle 2555: 2548: 2537: 2521: 2489: 2465: 2448: 2443: 2440: 2313: 2309: 2287: 2284: 2207: 2198: 2192: 2188: 2101: 2036: 1870:quasi-static 1863: 1824: 1820: 1806:in terms of 1789: 1778:Introduction 1765: 1718: 1679: 1649:physical law 1644: 1642: 1438:Carathéodory 1369:Heat engines 1341: 1330: 1319: 1301:Motive power 1286: 946:Free entropy 917: 417: 416: / 406: 405: / 397:introduction 390: 389: / 328: 291:Heat engines 110: 78: / 16284:In Our Time 16261:E.T. Jaynes 15973:Thomson, W. 15954:Philos. Mag 15930:Thomson, W. 15859:Temperature 15640:(1): 1–96. 15580:Kroemer, H. 15453:Gibbs, J.W. 15227:Chapman, S. 12808:Leó Szilárd 10342:, we have: 8308:heat engine 8228:engineering 7498:, so that: 3977:Corollaries 2612:Lord Kelvin 2500:heat engine 2492:Sadi Carnot 2472:Lord Kelvin 1757:Sadi Carnot 1661:concerning 1659:observation 1260:Synergetics 941:Free energy 387:Temperature 248:Quasistatic 243:Isenthalpic 200:Instruments 190:Equilibrium 142:Open system 76:Equilibrium 58:Statistical 16299:Categories 15911:: 189–195. 15824:: 453–463. 15818:Planck, M. 15806:Planck. M. 15794:Planck, M. 15759:Müller, I. 15741:Müller, I. 15576:Kittel, C. 15555:: 450–454. 15222:Also here. 15204:Carnot, S. 15180:2014-02-18 14880:2023-03-14 14798:Müller, I. 14786:Müller, I. 14479:2013-02-22 14328:1702.01411 13842:Planck, M. 13830:Planck, M. 13776:Planck, M. 13679:Planck, M. 13667:Planck, M. 13630:Planck, M. 13494:Carnot, S. 13482:Rao (2004) 13456:2010-10-07 13211:Planck, M. 13200:Mandl 1988 13179:Planck, M. 13116:. Dutton. 12995:References 12833:Quotations 12650:See also: 12577:protostars 12536:metabolism 9397:), though 9327:microstate 8456:See also: 8230:practice, 8211:Also, see 7320:See also: 2974:unchanged. 2965:Max Planck 2943:cyclically 2655:efficiency 2104:inequality 1866:reversible 1572:Nucleation 1416:Scientists 1220:Philosophy 933:Potentials 296:Heat pumps 253:Polytropic 238:Isentropic 228:Isothermal 16263:, 1988, " 16217:ignored ( 16207:cite book 16175:CiteSeerX 15983:Tisza, L. 15720:: 49–88. 15672:119620408 15523:190843367 15170:118230148 15074:607907330 14845:chapter 6 14671:1367-2630 14644:0908.1125 14600:1879-4912 14321:: 53–65. 14195:0020-7225 14181:: 12–18. 14153:0199-6231 14114:1164-0235 14075:1164-0235 14009:0305-4470 13947:0020-7225 12765:molecules 12671:causality 12445:δ 12427:δ 12380:∑ 12366:− 12324:∑ 12278:∑ 12174:⁡ 12162:∑ 12146:− 12093:⁡ 12071:∑ 12055:− 11973:− 11965:⁡ 11897:δ 11829:∂ 11821:∂ 11785:∂ 11777:∂ 11704:∂ 11696:∂ 11632:∂ 11624:∂ 11572:∂ 11564:∂ 11547:β 11525:∂ 11516:Ω 11509:⁡ 11503:∂ 11468:Ω 11428:∂ 11415:Ω 11407:∂ 11377:∂ 11366:Ω 11362:∂ 11342:∑ 11338:− 11316:∂ 11311:Ω 11308:∂ 11258:δ 11176:δ 11162:to above 11143:δ 11119:Ω 11087:δ 11063:− 11011:δ 10967:δ 10953:to above 10938:δ 10912:Ω 10889:δ 10840:δ 10837:≤ 10789:δ 10767:Ω 10724:to above 10686:δ 10593:δ 10532:Ω 10471:Ω 10458:∑ 10440:Ω 10431:− 10381:Ω 10371:∑ 10353:Ω 10313:Ω 10289:δ 10188:Ω 10129:− 10097:δ 10047:− 9891:Ω 9883:⁡ 9871:≡ 9868:β 9865:≡ 9806:δ 9767:H-theorem 9753:Ω 9725:Ω 9704:Ω 9681:Ω 9660:Ω 9633:δ 9610:δ 9587:δ 9564:δ 9507:Ω 9468:Ω 9460:⁡ 9372:H-theorem 9370:with his 9366:in 1860; 9354:H-theorem 9297:˙ 9265:≥ 9253:˙ 9217:˙ 9201:˙ 9182:˙ 9096:˙ 9061:≥ 9049:˙ 9013:˙ 8993:˙ 8928:˙ 8828:˙ 8795:≥ 8783:˙ 8747:˙ 8667:≥ 8608:is heat, 8586:− 8571:δ 8565:∫ 8520:Boltzmann 8509:reservoir 8407:Δ 8367:Δ 8321:or by an 8301:heat pump 8183:≤ 8170:δ 8138:≥ 8071:≤ 8058:δ 8004:μ 8000:∑ 7997:− 7965:− 7893:μ 7889:∑ 7886:− 7854:− 7840:− 7837:≤ 7824:δ 7749:μ 7745:∑ 7714:− 7711:≤ 7705:δ 7655:≤ 7636:− 7614:δ 7548:μ 7544:∑ 7527:δ 7524:− 7518:δ 7471:any work 7437:≥ 7329:unlimited 7297:≥ 7291:Δ 7262:δ 7210:δ 7204:∫ 7201:≥ 7195:Δ 7166:≤ 7138:δ 7132:∮ 7101:δ 7095:∫ 7086:Δ 7083:− 7018:δ 6971:δ 6959:∫ 6920:δ 6914:∮ 6831:∗ 6816:∗ 6793:∗ 6775:∗ 6669:⋅ 6653:∗ 6580:⋅ 6535:⋅ 6038:∗ 5915:− 5905:∗ 5848:− 5664:− 5647:η 5606:− 5596:∗ 5539:− 5421:− 5411:∗ 5360:→ 5347:∗ 5294:− 5277:η 5239:− 5185:→ 5126:− 5109:η 4927:− 4870:− 4855:η 4800:− 4743:− 4728:η 4673:− 4616:− 4601:η 4236:− 4146:η 4090:≤ 4071:δ 4065:∮ 3831:ν 3817:ν 3793:⁡ 3775:ν 3761:ν 3737:− 3722:ν 3708:ν 3678:⁡ 3660:ν 3646:ν 3594:ν 3576:ν 3543:− 3525:ν 3512:⁡ 3499:ν 3466:ν 3437:δ 3397:δ 3365:δ 3350:∫ 3315:δ 3287:δ 3238:∂ 3230:∂ 3150:, volume 3036:δ 2929:Wergeland 2878:η 2845:− 2840:η 2786:η 2778:− 2752:⟹ 2700:− 2695:η 2673:Δ 2476:axiomatic 2392:ξ 2388:δ 2378:Ξ 2367:∑ 2353:− 2341:δ 2296:ξ 2233:δ 2130:δ 2052:δ 1982:δ 1913:δ 1831:phenomena 1827:radiation 1745:molecules 1656:empirical 1653:universal 1651:based on 1553:Waterston 1503:von Mayer 1458:de Donder 1448:Clapeyron 1428:Boltzmann 1423:Bernoulli 1384:Education 1355:Timelines 1139:− 1084:− 872:Equations 839:∂ 792:∂ 743:α 707:∂ 660:∂ 614:− 608:β 572:∂ 525:∂ 233:Adiabatic 223:Isochoric 209:Processes 170:Ideal gas 53:Classical 16223:also at 16136:Archived 16049:(1968). 15995:(1980). 15985:(1966). 15975:(1852). 15960:(22): 13 15932:(1851). 15921:(1966). 15808:(1914). 15743:(1985). 15734:96568430 15601:(1998). 15561:(1967). 15549:Research 15401:(1867). 15390:24 March 15366:24 March 15328:(1854). 15244:(1850). 15144:(1909). 15115:(1943). 15040:(2010). 14608:18787276 14563:26 March 14412:(2004). 14353:38272381 13820:, p. 15. 13011:(1980). 12911:See also 12905:, p. 17. 12888:— 12878:, (1941) 12872:— 12853:— 12844:universe 12482:Big Bang 10163:⟩ 10133:⟨ 9395:Big Bang 8627:universe 8299:or in a 7596:are the 6900:, for a 6882:scale.) 4554:, where 2925:ter Haar 1605:Category 1543:Thompson 1453:Clausius 1433:Bridgman 1287:Vis viva 1269:Theories 1203:Gas laws 995:Enthalpy 403:Pressure 218:Isobaric 175:Real gas 63:Chemical 46:Branches 16167:Bibcode 16121:(ed.). 16023:Entropy 15964:25 June 15843:: 1–9. 15763:Entropy 15680:Entropy 15652:Bibcode 15531:Entropy 15411:19 June 15382:. 4th. 15341:Bibcode 15316:26 June 15301:. 4th. 15285:26 June 15258:Bibcode 14963:9132054 14936:Sources 14911:Bibcode 14903:Entropy 14800:(2003). 14788:(1985). 14649:Bibcode 14462:Bibcode 14396:9956019 14376:Bibcode 14333:Bibcode 13989:Bibcode 13778:(1926). 13714:(1909). 13371:: 1–9. 13329:(2015). 12581:Jupiter 11749:gives: 10524:. Then 9579:. Here 9381:Due to 9332:√ 8452:History 7254:, then 7050:= 0 at 6886:Entropy 6665: K 6576: K 6531: K 4117:entropy 4040:entropy 3162:, i.e. 3143:entropy 1682:entropy 1528:Smeaton 1523:Rankine 1513:Onsager 1498:Maxwell 1493:Massieu 1198:Entropy 1193:General 1184:History 1174:Culture 1171:History 395: ( 392:Entropy 329:italics 130:Systems 16195: 16177: 16153: 16105: 16090: 16072: 16029: 16003: 15883: 15865: 15776: 15751: 15732: 15698: 15670: 15624: 15609: 15590: 15537: 15521: 15511: 15493: 15478: 15445: 15430: 15216: 15168: 15133: 15098: 15072: 15062: 15025: 15010: 14995: 14980: 14961: 14951: 14837: 14726:7 June 14696:7 June 14669: 14606: 14598: 14554: 14428: 14394: 14351: 14272: 14251: 14193: 14151: 14112: 14094:Exergy 14073: 14055:Exergy 14007: 13945: 13907: 13880: 13816: 13741: 13408: 13337: 13283: 13256: 13147: 13120: 13047: 13019: 12901: 12863:(1927) 12526:) and 9499:where 9339:where 8685:where 8604:where 8334:For a 7939:exergy 7792:useful 7587:where 7322:Exergy 7184:Thus, 6880:Kelvin 6661:273.16 6572:273.16 6527:273.16 6374:273.16 4312:where 3860:where 3440:\delta 3405:NetRad 3295:NetRad 2741:Output 1874:closed 1518:Planck 1508:Nernst 1483:Kelvin 1443:Carnot 733: 598: 466: 408:Volume 323:Note: 282:Cycles 111:Second 101:Zeroth 15956:. 4. 15730:S2CID 15668:S2CID 15642:arXiv 15360:(PDF) 15333:(PDF) 15166:S2CID 14639:arXiv 14604:S2CID 14450:(PDF) 14349:S2CID 14323:arXiv 12785:speed 12769:demon 12669:, or 12126:that 12030:Here 11131:. If 9283:Here 9238:with 9079:Here 9034:with 8813:with 8768:with 8505:cycle 8448:= 0. 8346:> 7794:work 7475:done 7469:minus 7283:, so 6055:Then 4568:> 4561:> 4359:| / | 4337:= - | 3413:<= 3354:cycle 2733:Input 1864:In a 1798:of a 1751:, is 1741:atoms 1725:axiom 1673:in a 1647:is a 1566:Other 1533:Stahl 1488:Lewis 1478:Joule 1468:Gibbs 1463:Duhem 156:State 116:Third 106:First 16219:help 16193:ISBN 16151:ISBN 16133:html 16103:ISBN 16088:ISBN 16070:ISBN 16027:ISBN 16001:ISBN 15966:2012 15881:ISBN 15863:ISBN 15841:2013 15774:ISBN 15749:ISBN 15696:ISBN 15622:ISBN 15607:ISBN 15588:ISBN 15535:ISBN 15519:OCLC 15509:ISBN 15491:ISBN 15476:ISBN 15443:ISBN 15428:ISBN 15413:2012 15392:2014 15386:: 86 15368:2014 15318:2012 15287:2012 15214:ISBN 15190:here 15131:ISBN 15096:ISBN 15070:OCLC 15060:ISBN 15023:ISBN 15008:ISBN 14993:ISBN 14978:ISBN 14959:OCLC 14949:ISBN 14835:ISBN 14728:2020 14698:2020 14667:ISSN 14596:ISSN 14565:2021 14552:ISBN 14426:ISBN 14392:PMID 14270:ISBN 14249:ISBN 14191:ISSN 14149:ISSN 14110:ISSN 14071:ISSN 14005:ISSN 13943:ISSN 13905:ISBN 13878:ISBN 13814:ISBN 13739:ISBN 13406:ISBN 13369:2013 13335:ISBN 13281:ISBN 13254:ISBN 13145:ISBN 13118:ISBN 13045:ISBN 13017:ISBN 12899:ISBN 12855:Sir 12821:and 12755:and 12721:The 12654:and 11229:and 11133:Y dx 10875:and 10703:Y dx 10672:and 10579:and 10275:and 9935:here 9933:See 9550:and 9428:is: 8700:time 8514:The 8440:and 8413:< 8391:or d 8373:< 8351:surr 8218:See 7481:plus 7366:and 7070:surr 6396:and 4582:and 4547:and 4519:and 4381:and 4113:surr 4083:surr 4050:The 3879:and 3200:and 2951:work 2927:and 2449:The 2202:surr 2142:surr 2124:> 1812:heat 1810:and 1808:work 1790:The 1671:work 1665:and 1663:heat 1643:The 1538:Tait 368:Heat 363:Work 93:Laws 16239:: " 16185:doi 16131:) ( 15909:A53 15845:doi 15722:doi 15718:157 15660:doi 15638:310 15349:doi 15307:doi 15274:hdl 15266:doi 15158:doi 15052:doi 14919:doi 14657:doi 14588:doi 14470:doi 14422:171 14384:doi 14341:doi 14212:at 14183:doi 14179:111 14141:doi 14137:126 14102:doi 14063:doi 14032:doi 13997:doi 13935:doi 13373:doi 12779:to 12761:gas 12673:). 11962:exp 10716:to 10516:to 8698:is 8432:or 8348:Q/T 8319:ATP 8284:+ Δ 8280:= Δ 8278:tot 8258:1) 8223:.) 7936:or 7378:tot 4368:|. 3929:L/K 3870:, h 3866:, k 3509:exp 3191:TdS 2520:... 2205:). 1868:or 1743:or 1727:of 1677:." 1381:Art 327:in 16301:: 16211:: 16209:}} 16205:{{ 16191:. 16183:. 16173:. 16086:. 16016:32 16014:, 15958:IV 15952:. 15942:XX 15940:. 15936:. 15917:, 15907:, 15839:. 15835:. 15728:. 15716:. 15694:. 15666:. 15658:. 15650:. 15636:. 15578:, 15551:, 15517:. 15459:, 15415:. 15378:. 15347:. 15335:. 15297:. 15272:. 15264:. 15254:79 15252:. 15248:. 15229:, 15220:. 15183:. 15164:. 15154:67 15152:. 15148:. 15068:. 15058:. 15050:. 15036:; 14957:. 14917:. 14907:15 14905:. 14901:. 14889:^ 14873:. 14862:^ 14814:. 14718:. 14700:. 14688:. 14665:. 14655:. 14647:. 14635:12 14633:. 14629:. 14602:. 14594:. 14582:. 14468:. 14458:46 14456:. 14452:. 14424:. 14390:. 14382:. 14372:32 14370:. 14347:. 14339:. 14331:. 14319:57 14317:. 14189:. 14177:. 14173:. 14161:^ 14147:. 14135:. 14131:. 14108:. 14096:. 14092:. 14069:. 14057:. 14053:. 14028:39 14026:. 14003:. 13995:. 13985:12 13983:. 13979:. 13941:. 13931:45 13929:. 13925:. 13768:^ 13753:^ 13653:, 13414:. 13404:. 13402:13 13367:. 13363:. 13318:^ 13304:^ 13236:^ 13086:. 13082:. 13031:^ 12859:, 12555:. 12530:. 12171:ln 12090:ln 11935:: 11506:ln 10714:dx 10709:– 10522:dx 10520:+ 9993:dx 9880:ln 9648:. 9457:ln 9378:. 8949:. 8340:PV 8234:, 8095:on 8091:by 7811:dV 7803:by 7796:δw 7788:δw 7692:δw 7593:iR 7491:iR 7477:by 7473:δw 7465:δq 7461:dU 7368:dS 7364:dS 7359:. 7312:. 6403:, 4093:0. 3899:T) 3790:ln 3675:ln 3179:, 3175:, 3167:= 3063:. 2988:. 2587:: 1774:. 1731:. 1716:. 16226:. 16221:) 16201:. 16187:: 16169:: 16157:. 16142:) 16127:( 16111:. 16033:. 16007:. 15968:. 15889:. 15869:. 15853:. 15847:: 15780:. 15755:. 15736:. 15724:: 15704:. 15674:. 15662:: 15654:: 15644:: 15628:. 15613:. 15594:. 15553:2 15541:. 15525:. 15497:. 15482:. 15461:3 15449:. 15434:. 15394:. 15384:2 15370:. 15351:: 15343:: 15320:. 15309:: 15303:2 15289:. 15276:: 15268:: 15260:: 15160:: 15137:. 15102:. 15076:. 15054:: 15029:. 15014:. 14999:. 14984:. 14965:. 14927:. 14921:: 14913:: 14883:. 14843:. 14818:. 14730:. 14673:. 14659:: 14651:: 14641:: 14610:. 14590:: 14584:3 14567:. 14482:. 14472:: 14464:: 14434:. 14398:. 14386:: 14378:: 14355:. 14343:: 14335:: 14325:: 14303:. 14234:. 14197:. 14185:: 14155:. 14143:: 14116:. 14104:: 14098:2 14077:. 14065:: 14059:2 14038:. 14034:: 14011:. 13999:: 13991:: 13964:. 13949:. 13937:: 13886:. 13747:. 13620:. 13596:. 13472:. 13459:. 13381:. 13375:: 13289:. 13262:. 13168:. 13153:. 13126:. 13090:. 13053:. 13025:. 12823:B 12819:A 12801:B 12797:A 12793:A 12789:B 12781:B 12777:A 12773:A 12757:B 12753:A 12452:T 12448:Q 12439:= 12434:T 12430:W 12424:+ 12421:E 12418:d 12412:= 12407:j 12403:E 12399:d 12394:j 12390:P 12384:j 12374:T 12371:1 12362:) 12356:j 12352:P 12346:j 12342:E 12337:( 12333:d 12328:j 12318:T 12315:1 12310:= 12305:j 12301:P 12297:d 12292:j 12288:E 12282:j 12272:T 12269:1 12264:= 12261:S 12258:d 12233:j 12229:P 12203:j 12199:P 12195:d 12191:) 12186:j 12182:P 12178:( 12166:j 12155:B 12150:k 12143:= 12140:S 12137:d 12110:) 12105:j 12101:P 12097:( 12085:j 12081:P 12075:j 12064:B 12059:k 12052:= 12049:S 12032:Z 12013:Z 12008:) 12001:T 11995:B 11990:k 11983:j 11979:E 11969:( 11956:= 11951:j 11947:P 11929:T 11904:T 11900:Q 11891:= 11888:x 11885:d 11880:T 11877:X 11872:+ 11867:T 11863:E 11860:d 11854:= 11851:x 11848:d 11843:E 11838:) 11832:x 11824:S 11815:( 11810:+ 11807:E 11804:d 11799:x 11794:) 11788:E 11780:S 11771:( 11766:= 11763:S 11760:d 11731:T 11728:1 11723:= 11718:x 11713:) 11707:E 11699:S 11690:( 11659:T 11656:X 11651:= 11646:E 11641:) 11635:x 11627:S 11618:( 11586:x 11581:) 11575:E 11567:X 11558:( 11553:+ 11550:X 11544:= 11539:E 11534:) 11528:x 11519:) 11513:( 11497:( 11482:x 11442:x 11437:) 11431:E 11422:) 11418:X 11411:( 11401:( 11396:= 11391:x 11386:) 11380:E 11370:Y 11356:( 11351:Y 11346:Y 11335:= 11330:E 11325:) 11319:x 11302:( 11287:Y 11283:E 11265:) 11261:E 11255:+ 11252:E 11248:( 11242:Y 11238:N 11216:) 11213:E 11210:( 11204:Y 11200:N 11179:E 11173:+ 11170:E 11160:E 11146:E 11094:) 11090:E 11084:+ 11081:E 11077:( 11071:Y 11067:N 11059:) 11056:E 11053:( 11047:Y 11043:N 11018:) 11014:E 11008:+ 11005:E 11001:( 10995:Y 10991:N 10970:E 10964:+ 10961:E 10941:E 10935:+ 10932:E 10892:E 10886:+ 10883:E 10863:E 10843:E 10834:x 10831:d 10828:Y 10804:x 10801:d 10798:Y 10792:E 10783:) 10780:E 10777:( 10771:Y 10760:= 10756:) 10753:E 10750:( 10744:Y 10740:N 10726:E 10722:E 10718:E 10711:Y 10707:E 10689:Y 10683:+ 10680:Y 10660:Y 10637:x 10634:d 10627:r 10623:E 10619:d 10596:E 10590:+ 10587:E 10567:E 10557:x 10542:) 10539:E 10536:( 10518:x 10514:x 10510:E 10506:x 10487:) 10484:E 10481:( 10475:Y 10467:Y 10462:Y 10450:) 10447:E 10444:( 10436:1 10428:= 10425:X 10397:) 10394:E 10391:( 10385:Y 10375:Y 10367:= 10363:) 10360:E 10357:( 10329:) 10326:E 10323:( 10317:Y 10292:Y 10286:+ 10283:Y 10263:Y 10240:x 10237:d 10230:r 10226:E 10222:d 10198:) 10195:E 10192:( 10157:x 10154:d 10147:r 10143:E 10139:d 10126:= 10123:X 10100:E 10071:x 10068:d 10061:r 10057:E 10053:d 10044:= 10041:X 10016:r 10012:E 10001:X 9997:x 9989:x 9975:x 9972:d 9969:X 9959:x 9955:X 9943:x 9939:x 9915:E 9912:d 9906:] 9901:) 9898:E 9895:( 9887:[ 9877:d 9859:T 9853:B 9848:k 9843:1 9813:T 9809:Q 9800:= 9797:S 9794:d 9772:H 9749:/ 9745:1 9636:E 9613:E 9590:E 9567:E 9561:+ 9558:E 9538:E 9517:) 9514:E 9511:( 9483:] 9478:) 9475:E 9472:( 9464:[ 9451:B 9446:k 9442:= 9439:S 9416:E 9341:N 9335:N 9294:S 9268:0 9260:i 9250:S 9224:i 9214:S 9207:+ 9198:S 9192:+ 9187:T 9179:Q 9172:= 9166:t 9163:d 9158:S 9155:d 9121:T 9093:Q 9064:0 9056:i 9046:S 9020:i 9010:S 9003:+ 8998:T 8990:Q 8983:= 8977:t 8974:d 8969:S 8966:d 8935:i 8925:S 8916:a 8912:T 8908:= 8903:s 8900:s 8897:i 8894:d 8890:P 8867:a 8863:T 8835:i 8825:S 8798:0 8790:i 8780:S 8754:i 8744:S 8737:= 8731:t 8728:d 8723:S 8720:d 8702:. 8696:t 8690:S 8670:0 8661:t 8658:d 8653:S 8650:d 8614:N 8610:T 8606:Q 8589:N 8583:= 8578:T 8574:Q 8446:G 8442:p 8438:T 8434:A 8430:G 8416:0 8410:A 8393:G 8376:0 8370:G 8344:S 8325:. 8289:R 8286:S 8282:S 8275:S 8252:S 8186:0 8178:u 8174:w 8167:+ 8164:E 8161:d 8141:0 8133:t 8130:o 8127:t 8123:S 8119:d 8106:E 8074:0 8066:u 8062:w 8055:+ 8052:E 8049:d 8021:i 8017:N 8011:R 8008:i 7994:V 7989:R 7985:p 7981:+ 7978:S 7973:R 7969:T 7962:U 7959:= 7956:E 7943:E 7916:) 7910:i 7906:N 7900:R 7897:i 7883:V 7878:R 7874:p 7870:+ 7867:S 7862:R 7858:T 7851:U 7847:( 7843:d 7832:u 7828:w 7809:R 7807:p 7798:u 7769:i 7765:N 7761:d 7756:R 7753:i 7742:+ 7739:S 7736:d 7731:R 7727:T 7723:+ 7720:U 7717:d 7708:w 7671:S 7668:d 7663:R 7659:T 7652:) 7647:R 7643:S 7639:d 7633:( 7628:R 7624:T 7620:= 7617:q 7589:μ 7571:) 7565:i 7561:N 7555:R 7552:i 7540:( 7536:d 7533:+ 7530:w 7521:q 7515:= 7512:U 7509:d 7495:i 7493:N 7489:μ 7487:Σ 7485:d 7440:0 7432:R 7428:S 7424:d 7421:+ 7418:S 7415:d 7412:= 7406:t 7403:o 7400:t 7395:S 7391:d 7375:S 7370:R 7356:R 7354:P 7349:R 7347:T 7342:R 7340:P 7335:R 7333:T 7300:0 7294:S 7271:0 7268:= 7265:Q 7231:r 7228:r 7225:u 7222:s 7218:T 7213:Q 7198:S 7169:0 7159:r 7156:r 7153:u 7150:s 7146:T 7141:Q 7129:= 7122:r 7119:r 7116:u 7113:s 7109:T 7104:Q 7092:+ 7089:S 7067:T 7048:S 7025:T 7021:Q 7012:= 7009:S 7006:d 6978:T 6974:Q 6963:L 6935:0 6932:= 6927:T 6923:Q 6876:1 6873:T 6871:, 6869:1 6866:T 6864:( 6862:f 6858:1 6855:T 6838:, 6826:2 6822:T 6811:3 6807:T 6801:= 6798:) 6788:3 6784:T 6780:, 6770:2 6766:T 6762:( 6759:f 6756:= 6753:) 6748:3 6744:T 6740:, 6735:2 6731:T 6727:( 6724:f 6711:f 6694:) 6691:T 6688:, 6683:1 6679:T 6675:( 6672:f 6658:= 6649:T 6635:T 6618:. 6612:) 6607:2 6603:T 6599:, 6594:1 6590:T 6586:( 6583:f 6567:) 6562:3 6558:T 6554:, 6549:1 6545:T 6541:( 6538:f 6521:= 6515:) 6510:2 6506:T 6502:, 6497:1 6493:T 6489:( 6486:f 6481:) 6476:3 6472:T 6468:, 6463:1 6459:T 6455:( 6452:f 6446:= 6443:) 6438:3 6434:T 6430:, 6425:2 6421:T 6417:( 6414:f 6401:3 6398:T 6394:2 6391:T 6377:K 6371:= 6366:1 6362:T 6335:1 6331:T 6307:. 6304:) 6299:3 6295:T 6291:, 6286:2 6282:T 6278:( 6275:f 6272:) 6267:2 6263:T 6259:, 6254:1 6250:T 6246:( 6243:f 6240:= 6233:| 6227:2 6223:q 6218:| 6213:| 6207:1 6203:q 6198:| 6191:| 6185:3 6181:q 6176:| 6171:| 6165:2 6161:q 6156:| 6149:= 6142:| 6136:1 6132:q 6127:| 6120:| 6114:3 6110:q 6105:| 6098:= 6095:) 6090:3 6086:T 6082:, 6077:1 6073:T 6069:( 6066:f 6033:2 6029:q 6006:2 6002:q 5974:. 5967:| 5960:1 5955:q 5948:| 5942:) 5938:| 5931:3 5926:q 5919:| 5911:| 5898:2 5893:q 5885:| 5881:( 5878:+ 5875:) 5871:| 5864:2 5859:q 5852:| 5844:| 5837:1 5832:q 5825:| 5821:( 5815:= 5808:| 5801:1 5796:q 5789:| 5783:) 5779:| 5772:3 5767:w 5760:| 5756:+ 5752:| 5745:2 5740:w 5733:| 5729:( 5723:= 5716:| 5709:1 5704:q 5697:| 5690:| 5683:3 5678:q 5671:| 5661:1 5658:= 5652:1 5636:, 5633:) 5629:| 5622:3 5617:q 5610:| 5602:| 5589:2 5584:q 5576:| 5572:( 5569:+ 5566:) 5562:| 5555:2 5550:q 5543:| 5535:| 5528:1 5523:q 5516:| 5512:( 5509:= 5505:| 5498:3 5493:w 5486:| 5482:+ 5478:| 5471:2 5466:w 5459:| 5448:, 5444:| 5437:3 5432:q 5425:| 5417:| 5404:2 5399:q 5391:| 5387:= 5383:| 5376:3 5371:w 5364:| 5353:| 5340:2 5335:q 5327:| 5320:| 5313:3 5308:q 5301:| 5291:1 5288:= 5282:3 5266:, 5262:| 5255:2 5250:q 5243:| 5235:| 5228:1 5223:q 5216:| 5212:= 5208:| 5201:2 5196:w 5189:| 5178:| 5171:1 5166:q 5159:| 5152:| 5145:2 5140:q 5133:| 5123:1 5120:= 5114:2 5076:2 5072:T 5049:2 5045:q 5022:2 5018:T 4995:2 4991:q 4980:2 4977:T 4971:. 4959:) 4954:3 4950:T 4946:, 4941:2 4937:T 4933:( 4930:f 4924:1 4921:= 4914:| 4908:2 4904:q 4899:| 4892:| 4886:3 4882:q 4877:| 4867:1 4864:= 4859:3 4844:, 4832:) 4827:2 4823:T 4819:, 4814:1 4810:T 4806:( 4803:f 4797:1 4794:= 4787:| 4781:1 4777:q 4772:| 4765:| 4759:2 4755:q 4750:| 4740:1 4737:= 4732:2 4717:, 4705:) 4700:3 4696:T 4692:, 4687:1 4683:T 4679:( 4676:f 4670:1 4667:= 4660:| 4654:1 4650:q 4645:| 4638:| 4632:3 4628:q 4623:| 4613:1 4610:= 4605:1 4587:3 4584:T 4580:1 4577:T 4572:3 4570:T 4565:2 4563:T 4558:1 4556:T 4552:3 4549:T 4545:2 4542:T 4538:2 4535:T 4531:1 4528:T 4524:3 4521:T 4517:1 4514:T 4505:) 4503:2 4501:( 4484:. 4481:) 4476:C 4472:T 4468:, 4463:H 4459:T 4455:( 4452:f 4449:= 4442:| 4436:H 4432:q 4427:| 4420:| 4414:C 4410:q 4405:| 4386:C 4383:T 4379:H 4376:T 4365:H 4361:q 4356:C 4352:q 4343:C 4339:q 4334:C 4330:q 4325:H 4321:q 4317:n 4314:W 4305:) 4303:1 4301:( 4280:| 4274:H 4270:q 4265:| 4258:| 4252:C 4248:q 4243:| 4233:1 4230:= 4223:H 4219:q 4212:C 4208:q 4204:+ 4199:H 4195:q 4188:= 4181:H 4177:q 4171:| 4165:n 4161:W 4156:| 4149:= 4110:T 4079:T 4074:Q 3937:T 3935:/ 3933:q 3925:L 3920:v 3917:L 3913:v 3910:K 3906:v 3903:L 3895:v 3892:K 3884:v 3881:L 3877:v 3874:K 3862:c 3846:) 3843:) 3835:3 3827:h 3824:2 3813:K 3807:2 3803:c 3796:( 3787:) 3779:3 3771:h 3768:2 3757:K 3751:2 3747:c 3740:( 3734:) 3726:3 3718:h 3715:2 3704:K 3698:2 3694:c 3687:+ 3684:1 3681:( 3672:) 3664:3 3656:h 3653:2 3642:K 3636:2 3632:c 3625:+ 3622:1 3619:( 3616:( 3609:2 3605:c 3598:2 3590:k 3587:2 3581:= 3572:L 3552:, 3546:1 3539:) 3533:T 3530:k 3522:h 3516:( 3503:3 3489:2 3485:c 3480:h 3477:2 3471:= 3462:K 3416:0 3410:) 3401:S 3394:+ 3387:b 3383:T 3376:C 3373:C 3369:Q 3359:( 3326:C 3323:C 3319:Q 3291:S 3258:N 3255:, 3252:V 3247:) 3241:S 3233:U 3224:( 3219:= 3216:T 3203:N 3197:V 3181:N 3177:V 3173:S 3171:( 3169:U 3165:U 3159:N 3153:V 3147:S 3138:U 3125:U 3051:S 3048:d 3045:T 3042:= 3039:Q 2953:. 2875:Q 2852:) 2848:1 2837:1 2831:( 2827:Q 2824:= 2819:c 2815:Q 2794:0 2791:= 2783:Q 2775:) 2770:c 2766:Q 2762:+ 2759:Q 2756:( 2748:0 2745:= 2737:+ 2707:) 2703:1 2692:1 2686:( 2682:Q 2679:= 2676:Q 2663:η 2659:η 2396:j 2382:j 2371:j 2361:T 2358:1 2348:T 2344:Q 2335:= 2332:S 2328:d 2314:T 2310:P 2240:T 2236:Q 2227:= 2224:S 2220:d 2199:T 2193:T 2138:T 2133:Q 2121:S 2117:d 2083:) 2079:d 2075:( 2055:) 2049:( 2022:. 1989:T 1985:Q 1976:= 1973:S 1969:d 1945:) 1942:T 1939:( 1916:Q 1905:( 1889:S 1885:d 1849:S 1632:e 1625:t 1618:v 1145:S 1142:T 1136:H 1133:= 1130:) 1127:p 1124:, 1121:T 1118:( 1115:G 1090:S 1087:T 1081:U 1078:= 1075:) 1072:V 1069:, 1066:T 1063:( 1060:A 1035:V 1032:p 1029:+ 1026:U 1023:= 1020:) 1017:p 1014:, 1011:S 1008:( 1005:H 980:) 977:V 974:, 971:S 968:( 965:U 842:T 818:V 795:V 771:1 746:= 710:p 686:V 663:V 639:1 611:= 575:T 551:N 528:S 504:T 479:= 476:c 399:)

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Index