First law of thermodynamics

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collection which is the contiguous surrounding subsystem. Some internal energy will accompany the vapor that leaves the system, but it will not make sense to try to uniquely identify part of that internal energy as heat and part of it as work. Consequently, the energy transfer that accompanies the transfer of matter between the system and its surrounding subsystem cannot be uniquely split into heat and work transfers to or from the open system. The component of total energy transfer that accompanies the transfer of vapor into the surrounding subsystem is customarily called 'latent heat of evaporation', but this use of the word heat is a quirk of customary historical language, not in strict compliance with the thermodynamic definition of transfer of energy as heat. In this example, kinetic energy of bulk flow and potential energy with respect to long-range external forces such as gravity are both considered to be zero. The first law of thermodynamics refers to the change of internal energy of the open system, between its initial and final states of internal equilibrium.

2919:

that no adiabatic process can reduce the internal energy of a system at constant volume. Carathéodory's paper asserts that its statement of the first law corresponds exactly to Joule's experimental arrangement, regarded as an instance of adiabatic work. It does not point out that Joule's experimental arrangement performed essentially irreversible work, through friction of paddles in a liquid, or passage of electric current through a resistance inside the system, driven by motion of a coil and inductive heating, or by an external current source, which can access the system only by the passage of electrons, and so is not strictly adiabatic, because electrons are a form of matter, which cannot penetrate adiabatic walls. The paper goes on to base its main argument on the possibility of quasi-static adiabatic work, which is essentially reversible. The paper asserts that it will avoid reference to Carnot cycles, and then proceeds to base its argument on cycles of forward and backward quasi-static adiabatic stages, with isothermal stages of zero magnitude.

8750:

defined in the so-called Lagrangian way, moving with the local center of mass. The flow of matter across the boundary is zero when considered as a flow of total mass. Nevertheless, if the material constitution is of several chemically distinct components that can diffuse with respect to one another, the system is considered to be open, the diffusive flows of the components being defined with respect to the center of mass of the system, and balancing one another as to mass transfer. Still there can be a distinction between bulk flow of internal energy and diffusive flow of internal energy in this case, because the internal energy density does not have to be constant per unit mass of material, and allowing for non-conservation of internal energy because of local conversion of kinetic energy of bulk flow to internal energy by viscosity.

8754:

with historical custom, that often enough did not clearly distinguish between heat and internal energy; he writes "that this relation must be considered to be the exact definition of the concept of heat flow, fairly loosely used in experimental physics and heat technics". Apparently in a different frame of thinking from that of the above-mentioned paradoxical usage in the earlier sections of the historic 1947 work by Prigogine, about discrete systems, this usage of Gyarmati is consistent with the later sections of the same 1947 work by Prigogine, about continuous-flow systems, which use the term "heat flux" in just this way. This usage is also followed by Glansdorff and Prigogine in their 1971 text about continuous-flow systems. They write: "Again the flow of internal energy may be split into a convection flow

2907:

version of the first law of thermodynamics was stated in an axiom which refrained from defining or mentioning temperature or quantity of heat transferred. That axiom stated that the internal energy of a phase in equilibrium is a function of state, that the sum of the internal energies of the phases is the total internal energy of the system, and that the value of the total internal energy of the system is changed by the amount of work done adiabatically on it, considering work as a form of energy. That article considered this statement to be an expression of the law of conservation of energy for such systems. This version is nowadays widely accepted as authoritative, but is stated in slightly varied ways by different authors.

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The irreversibility is often due to mechanisms known as dissipative, that transform bulk kinetic energy into internal energy. Examples are friction and viscosity. If the process is performed more slowly, the frictional or viscous dissipation is less. In the limit of infinitely slow performance, the dissipation tends to zero and then the limiting process, though fictional rather than actual, is notionally reversible, and is called quasi-static. Throughout the course of the fictional limiting quasi-static process, the internal intensive variables of the system are equal to the external intensive variables, those that describe the reactive forces exerted by the surroundings. This can be taken to justify the formula

8742:

Except for the special case mentioned above when there is no actual transfer of matter, which can be treated as if for a closed system, in strictly defined thermodynamic terms, it follows that transfer of energy as heat is not defined. In this sense, there is no such thing as 'heat flow' for a continuous-flow open system. Properly, for closed systems, one speaks of transfer of internal energy as heat, but in general, for open systems, one can speak safely only of transfer of internal energy. A factor here is that there are often cross-effects between distinct transfers, for example that transfer of one substance may cause transfer of another even when the latter has zero chemical potential gradient.

7133:

as heat through the diathermic walls, and of the energy transferred to the system as work through the adiabatic walls, including the energy transferred to the system by long-range forces. These simultaneously transferred quantities of energy are defined by events in the surroundings of the system. Because the internal energy transferred with matter is not in general uniquely resolvable into heat and work components, the total energy transfer cannot in general be uniquely resolved into heat and work components. Under these conditions, the following formula can describe the process in terms of externally defined thermodynamic variables, as a statement of the first law of thermodynamics:

6345:

such systems, the principle of conservation of energy is expressed in terms not only of internal energy as defined for homogeneous systems, but also in terms of kinetic energy and potential energies of parts of the inhomogeneous system with respect to each other and with respect to long-range external forces. How the total energy of a system is allocated between these three more specific kinds of energy varies according to the purposes of different writers; this is because these components of energy are to some extent mathematical artefacts rather than actually measured physical quantities. For any closed homogeneous component of an inhomogeneous closed system, if

6832:, the transfer of matter and energy across an open connection "cannot be reduced to mechanics". In contrast to the case of closed systems, for open systems, in the presence of diffusion, there is no unconstrained and unconditional physical distinction between convective transfer of internal energy by bulk flow of matter, the transfer of internal energy without transfer of matter (usually called heat conduction and work transfer), and change of various potential energies. The older traditional way and the conceptually revised (Carathéodory) way agree that there is no physically unique definition of heat and work transfer processes between open systems. 4272:, at temperatures fixed by the occurrence of phase changes under specified conditions in bodies of known latent heat of phase change. The calorimeter can be calibrated by transferring an externally determined amount of heat into it, for instance from a resistive electrical heater inside the calorimeter through which a precisely known electric current is passed at a precisely known voltage for a precisely measured period of time. The calibration allows comparison of calorimetric measurement of quantity of heat transferred with quantity of energy transferred as (surroundings-based) work. According to one textbook, "The most common device for measuring 2994:

that the time order of the stages, and their relative magnitudes, does not affect the amount of adiabatic work that needs to be done for the change of state. According to one respected scholar: "Unfortunately, it does not seem that experiments of this kind have ever been carried out carefully. ... We must therefore admit that the statement which we have enunciated here, and which is equivalent to the first law of thermodynamics, is not well founded on direct experimental evidence." Another expression of this view is "no systematic precise experiments to verify this generalization directly have ever been attempted".

7129:

transferred matter, but immovable, and separate connections through adiabatic walls with others, and separate connections through diathermic walls impermeable to matter with yet others. Because there are physically separate connections that are permeable to energy but impermeable to matter, between the system and its surroundings, energy transfers between them can occur with definite heat and work characters. Conceptually essential here is that the internal energy transferred with the transfer of matter is measured by a variable that is mathematically independent of the variables that measure heat and work.

2497:, who had in 1909 stated the first law without defining quantity of heat. Born's definition was specifically for transfers of energy without transfer of matter, and it has been widely followed in textbooks (examples:). Born observes that a transfer of matter between two systems is accompanied by a transfer of internal energy that cannot be resolved into heat and work components. There can be pathways to other systems, spatially separate from that of the matter transfer, that allow heat and work transfer independent of and simultaneous with the matter transfer. Energy is conserved in such transfers. 8801:

one is dealing with a system effectively closed to the transfer of matter. But still one can validly talk of a distinction between bulk flow and diffusive flow of internal energy, the latter driven by a temperature gradient within the flowing material, and being defined with respect to the local center of mass of the bulk flow. In this case of a virtually closed system, because of the zero matter transfer, as noted above, one can safely distinguish between transfer of energy as work, and transfer of internal energy as heat.

2341:, defined by calorimetry. It was presupposed as logically prior to the theoretical development of thermodynamics. Jointly primitive with this notion of heat were the notions of empirical temperature and thermal equilibrium. This framework also took as primitive the notion of transfer of energy as work. This framework did not presume a concept of energy in general, but regarded it as derived or synthesized from the prior notions of heat and work. By one author, this framework has been called the "thermodynamic" approach. 2452:, especially adiabatic walls and non-adiabatic walls, defined as follows. Temporarily, only for purpose of this definition, one can prohibit transfer of energy as work across a wall of interest. Then walls of interest fall into two classes, (a) those such that arbitrary systems separated by them remain independently in their own previously established respective states of internal thermodynamic equilibrium; they are defined as adiabatic; and (b) those without such independence; they are defined as non-adiabatic. 2982:

returned to its initial state, isolated again, and the same amount of work is done on the tank using different devices (an electric motor, a chemical battery, a spring,...). In every case, the amount of work can be measured independently. The return to the initial state is not conducted by doing adiabatic work on the system. The evidence shows that the final state of the water (in particular, its temperature and volume) is the same in every case. It is irrelevant if the work is

33: 1603: 3628:) above. Moreover, it deals to some extent with the problem of lack of direct experimental evidence that the time order of stages of a process does not matter in the determination of internal energy. This way does not provide theoretical purity in terms of adiabatic work processes, but is empirically feasible, and is in accord with experiments actually done, such as the Joule experiments mentioned just above, and with older traditions. 4211: 4260:. Adynamic transfer of energy as heat can be measured empirically by changes in the surroundings of the system of interest by calorimetry. This again requires the existence of adiabatic enclosure of the entire process, system and surroundings, though the separating wall between the surroundings and the system is thermally conductive or radiatively permeable, not adiabatic. A calorimeter can rely on measurement of 3069:

conservation of energy, though that did not deal with forces that cannot be described by a potential, and thus did not fully justify the principle. Moreover, that paper was critical of the early work of Joule that had by then been performed. A great merit of the internal energy concept is that it frees thermodynamics from a restriction to cyclic processes, and allows a treatment in terms of thermodynamic states.

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experiment being considered as testing the accuracy of the law, it is more practical and realistic to think of the law as testing the accuracy of experiment. An experimental result that seems to violate the law may be assumed to be inaccurate or wrongly conceived, for example due to failure to account for an important physical factor. Thus, some may regard it as a principle more abstract than a law.

7660: 5471:. These variables are important throughout thermodynamics, though not necessary for the statement of the first law. Rigorously, they are defined only when the system is in its own state of internal thermodynamic equilibrium. For some purposes, the concepts provide good approximations for scenarios sufficiently near to the system's internal thermodynamic equilibrium. 2176:, while change in internal energy depends only on the initial and final states of the system, not on the path between. Thermodynamic work is measured by change in the system, and is not necessarily the same as work measured by forces and distances in the surroundings, though, ideally, such can sometimes be arranged; this distinction is noted in the term ' 3704: 6155:

phases: liquid water and water vapor. There is a generalized "force" of evaporation that drives water molecules out of the liquid. There is a generalized "force" of condensation that drives vapor molecules out of the vapor. Only when these two "forces" (or chemical potentials) are equal is there equilibrium, and the net rate of transfer zero.

7869: 6839:. This principle allows a composite isolated system to be derived from two other component non-interacting isolated systems, in such a way that the total energy of the composite isolated system is equal to the sum of the total energies of the two component isolated systems. Two previously isolated systems can be subjected to the 7231: 8723: 6334: 8800:

In the case of a flowing system of only one chemical constituent, in the Lagrangian representation, there is no distinction between bulk flow and diffusion of matter. Moreover, the flow of matter is zero into or out of the cell that moves with the local center of mass. In effect, in this description,

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Usually transfer between a system and its surroundings applies to transfer of a state variable, and obeys a balance law, that the amount lost by the donor system is equal to the amount gained by the receptor system. Heat is not a state variable. For his 1947 definition of "heat transfer" for discrete

7132:

With such independence of variables, the total increase of internal energy in the process is then determined as the sum of the internal energy transferred from the surroundings with the transfer of matter through the walls that are permeable to it, and of the internal energy transferred to the system

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A thermodynamic process might be initiated by a thermodynamic operation in the surroundings, that mechanically increases in the controlled volume of the vapor. Some mechanical work will be done within the surroundings by the vapor, but also some of the parent liquid will evaporate and enter the vapor

6827:

Since the revised and more rigorous definition of the internal energy of a closed system rests upon the possibility of processes by which adiabatic work takes the system from one state to another, this leaves a problem for the definition of internal energy for an open system, for which adiabatic work

6814:

For the first law of thermodynamics, there is no trivial passage of physical conception from the closed system view to an open system view. For closed systems, the concepts of an adiabatic enclosure and of an adiabatic wall are fundamental. Matter and internal energy cannot permeate or penetrate such

2468:

The revised statement of the first law postulates that a change in the internal energy of a system due to any arbitrary process, that takes the system from a given initial thermodynamic state to a given final equilibrium thermodynamic state, can be determined through the physical existence, for those

1688:

of the first kind are impossible; work done by a system on its surroundings requires that the system's internal energy be consumed, so that the amount of internal energy lost by that work must be resupplied as heat by an external energy source or as work by an external machine acting on the system to

8753:

Gyarmati shows that his definition of "the heat flow vector" is strictly speaking a definition of flow of internal energy, not specifically of heat, and so it turns out that his use here of the word heat is contrary to the strict thermodynamic definition of heat, though it is more or less compatible

7527:

Nevertheless, a conditional correspondence exists. There are three relevant kinds of wall here: purely diathermal, adiabatic, and permeable to matter. If two of those kinds of wall are sealed off, leaving only one that permits transfers of energy, as work, as heat, or with matter, then the remaining

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There is a sense in which this kind of additivity expresses a fundamental postulate that goes beyond the simplest ideas of classical closed system thermodynamics; the extensivity of some variables is not obvious, and needs explicit expression; indeed one author goes so far as to say that it could be

2993:

A change from one state to another, for example an increase of both temperature and volume, may be conducted in several stages, for example by externally supplied electrical work on a resistor in the body, and adiabatic expansion allowing the body to do work on the surroundings. It needs to be shown

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The 1909 Carathéodory statement of the law in axiomatic form does not mention heat or temperature, but the equilibrium states to which it refers are explicitly defined by variable sets that necessarily include "non-deformation variables", such as pressures, which, within reasonable restrictions, can

2906:

Carathéodory's celebrated presentation of equilibrium thermodynamics refers to closed systems, which are allowed to contain several phases connected by internal walls of various kinds of impermeability and permeability (explicitly including walls that are permeable only to heat). Carathéodory's 1909

2518:

In a cyclic process in which the system does net work on its surroundings, it is observed to be physically necessary not only that heat be taken into the system, but also, importantly, that some heat leave the system. The difference is the heat converted by the cycle into work. In each repetition of

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and with N. K. Adam. From this, Denbigh concludes "It seems, however, that when a system is able to exchange both heat and matter with its environment, it is impossible to make an unambiguous distinction between energy transported as heat and by the migration of matter, without already assuming the

8792:

denotes the energy per unit mass. " This usage is followed also by other writers on non-equilibrium thermodynamics such as Lebon, Jou, and Casas-Vásquez, and de Groot and Mazur. This usage is described by Bailyn as stating the non-convective flow of internal energy, and is listed as his definition

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The transfer of energy between an open system and a single contiguous subsystem of its surroundings is considered also in non-equilibrium thermodynamics. The problem of definition arises also in this case. It may be allowed that the wall between the system and the subsystem is not only permeable to

6843:

of placement between them of a wall permeable to matter and energy, followed by a time for establishment of a new thermodynamic state of internal equilibrium in the new single unpartitioned system. The internal energies of the initial two systems and of the final new system, considered respectively

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Similarly, a difference in chemical potential between groups of particles in the system drives a chemical reaction that changes the numbers of particles, and the corresponding product is the amount of chemical potential energy transformed in process. For example, consider a system consisting of two

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depends upon the particular path taken through the space of thermodynamic parameters while the integral of an exact differential depends only upon the initial and final states. If the initial and final states are the same, then the integral of an inexact differential may or may not be zero, but the

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by Helmholtz. If only adiabatic processes were of interest, and heat could be ignored, the concept of internal energy would hardly arise or be needed. The relevant physics would be largely covered by the concept of potential energy, as was intended in the 1847 paper of Helmholtz on the principle of

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In an adiabatic process, there is transfer of energy as work but not as heat. For all adiabatic process that takes a system from a given initial state to a given final state, irrespective of how the work is done, the respective eventual total quantities of energy transferred as work are one and the

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The first law of thermodynamics for closed systems was originally induced from empirically observed evidence, including calorimetric evidence. It is nowadays, however, taken to provide the definition of heat via the law of conservation of energy and the definition of work in terms of changes in the

2941:

A respected text disregards the Carathéodory's exclusion of mention of heat from the statement of the first law for closed systems, and admits heat calorimetrically defined along with work and internal energy. Another respected text defines heat exchange as determined by temperature difference, but

2925:

Sometimes the existence of the internal energy is made explicit but work is not explicitly mentioned in the statement of the first postulate of thermodynamics. Heat supplied is then defined as the residual change in internal energy after work has been taken into account, in a non-adiabatic process.

8741:

Methods for study of non-equilibrium processes mostly deal with spatially continuous flow systems. In this case, the open connection between system and surroundings is usually taken to fully surround the system, so that there are no separate connections impermeable to matter but permeable to heat.

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of transfer of matter can be made to occur between them if the surrounding subsystem is subjected to some thermodynamic operation, for example, removal of a partition between it and some further surrounding subsystem. The removal of the partition in the surroundings initiates a process of exchange

6801:

The distinction between internal and kinetic energy is hard to make in the presence of turbulent motion within the system, as friction gradually dissipates macroscopic kinetic energy of localised bulk flow into molecular random motion of molecules that is classified as internal energy. The rate of

6110:

For an open system, there can be transfers of particles as well as energy into or out of the system during a process. For this case, the first law of thermodynamics still holds, in the form that the internal energy is a function of state and the change of internal energy in a process is a function

4388:

Heat transfer is practically reversible when it is driven by practically negligibly small temperature gradients. Work transfer is practically reversible when it occurs so slowly that there are no frictional effects within the system; frictional effects outside the system should also be zero if the

3531:

Since the work of Bryan (1907), the most accepted way to deal with it nowadays, followed by Carathéodory, is to rely on the previously established concept of quasi-static processes, as follows. Actual physical processes of transfer of energy as work are always at least to some degree irreversible.

2918:

According to A. Münster (1970), "A somewhat unsatisfactory aspect of Carathéodory's theory is that a consequence of the Second Law must be considered at this point , i.e. that it is not always possible to reach any state 2 from any other state 1 by means of an adiabatic process." Münster instances

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For a closed system, in any arbitrary process of interest that takes it from an initial to a final state of internal thermodynamic equilibrium, the change of internal energy is the same as that for a reference adiabatic work process that links those two states. This is so regardless of the path of

2437:

Energy can also be transferred from one thermodynamic system to another in association with transfer of matter. Born points out that in general such energy transfer is not resolvable uniquely into work and heat moieties. In general, when there is transfer of energy associated with matter transfer,

6926:

denote the changes in internal energy of the system and of its surroundings respectively. This is a statement of the first law of thermodynamics for a transfer between two otherwise isolated open systems, that fits well with the conceptually revised and rigorous statement of the law stated above.

6344:

Classical thermodynamics is initially focused on closed homogeneous systems (e.g. Planck 1897/1903), which might be regarded as 'zero-dimensional' in the sense that they have no spatial variation. But it is desired to study also systems with distinct internal motion and spatial inhomogeneity. For

6139:

is the displacement (with units of distance times area). We may say, with respect to this work term, that a pressure difference forces a transfer of volume, and that the product of the two (work) is the amount of energy transferred out of the system as a result of the process. If one were to make

2445:

as work, and that energy can be held as the internal energy of a thermodynamic system. It also postulates that energy can be transferred from one thermodynamic system to another by a path that is non-adiabatic, and is unaccompanied by matter transfer. Initially, it "cleverly" (according to Martin

2374:

The concept of internal energy is considered by Bailyn to be of "enormous interest". Its quantity cannot be immediately measured, but can only be inferred, by differencing actual immediate measurements. Bailyn likens it to the energy states of an atom, that were revealed by Bohr's energy relation

2370:

Because of its definition in terms of increments, the value of the internal energy of a system is not uniquely defined. It is defined only up to an arbitrary additive constant of integration, which can be adjusted to give arbitrary reference zero levels. This non-uniqueness is in keeping with the

8749:

The situation is clarified by Gyarmati, who shows that his definition of "heat transfer", for continuous-flow systems, really refers not specifically to heat, but rather to transfer of internal energy, as follows. He considers a conceptual small cell in a situation of continuous-flow as a system

5363:

The first law of thermodynamics is so general that its predictions cannot all be directly tested. In many properly conducted experiments it has been precisely supported, and never violated. Indeed, within its scope of applicability, the law is so reliably established, that, nowadays, rather than

2929:

A respected modern author states the first law of thermodynamics as "Heat is a form of energy", which explicitly mentions neither internal energy nor adiabatic work. Heat is defined as energy transferred by thermal contact with a reservoir, which has a temperature, and is generally so large that

2485:

This statement is much less close to the empirical basis than are the original statements, but is often regarded as conceptually parsimonious in that it rests only on the concepts of adiabatic work and of non-adiabatic processes, not on the concepts of transfer of energy as heat and of empirical

7128:

This includes cases in which there is contact equilibrium between the system, and several subsystems in its surroundings, including separate connections with subsystems through walls that are permeable to the transfer of matter and internal energy as heat and allowing friction of passage of the

7112:

An example is evaporation. One may consider an open system consisting of a collection of liquid, enclosed except where it is allowed to evaporate into or to receive condensate from its vapor above it, which may be considered as its contiguous surrounding subsystem, and subject to control of its

4868:

If, in a process of change of state of a closed system, the energy transfer is not under a practically zero temperature gradient, practically frictionless, and with nearly balanced forces, then the process is irreversible. Then the heat and work transfers may be difficult to calculate with high

2910:

Such statements of the first law for closed systems assert the existence of internal energy as a function of state defined in terms of adiabatic work. Thus heat is not defined calorimetrically or as due to temperature difference. It is defined as a residual difference between change of internal

6818:

There are some cases in which a process for an open system can, for particular purposes, be considered as if it were for a closed system. In an open system, by definition hypothetically or potentially, matter can pass between the system and its surroundings. But when, in a particular case, the

5543: 5307: 2997:

This kind of evidence, of independence of sequence of stages, combined with the above-mentioned evidence, of independence of qualitative kind of work, would show the existence of an important state variable that corresponds with adiabatic work, but not that such a state variable represented a

2981:

For instance, in Joule's experiment, the initial system is a tank of water with a paddle wheel inside. If we isolate the tank thermally, and move the paddle wheel with a pulley and a weight, we can relate the increase in temperature with the distance descended by the mass. Next, the system is

2510:

The first law of thermodynamics for a closed system was expressed in two ways by Clausius. One way referred to cyclic processes and the inputs and outputs of the system, but did not refer to increments in the internal state of the system. The other way referred to an incremental change in the

1692:

The ideal isolated system, of which the entire universe is an example, is often only used as a model. Many systems in practical applications require the consideration of internal chemical or nuclear reactions, as well as transfers of matter into or out of the system. For such considerations,

7531:

For the special fictive case of quasi-static transfers, there is a simple correspondence. For this, it is supposed that the system has multiple areas of contact with its surroundings. There are pistons that allow adiabatic work, purely diathermal walls, and open connections with surrounding

4810: 2262:

Heat is simply motive power, or rather motion which has changed its form. It is a movement among the particles of bodies. Whereever there is destruction of motive power, there is at the same time production of heat in quantity exactly proportional to the quantity of motive power destroyed.

2978:

same, determined just by the given initial and final states. The work done on the system is defined and measured by changes in mechanical or quasi-mechanical variables external to the system. Physically, adiabatic transfer of energy as work requires the existence of adiabatic enclosures.

6752: 10303:

Jan T. Knuiman, Peter A. Barneveld, and Nicolaas A. M. Besseling, "On the Relation between the Fundamental Equation of Thermodynamics and the Energy Balance Equation in the Context of Closed and Open Systems," Journal of Chemical Education 2012 89 (8), 968-972 DOI: 10.1021/ed200405k,

8564: 4206:{\displaystyle -W_{A\to B}^{\mathrm {adiabatic,\,quasi-static} }=-W_{A\to O}^{\mathrm {adiabatic,\,quasi-static} }-W_{O\to B}^{\mathrm {adiabatic,\,quasi-static} }=W_{O\to A}^{\mathrm {adiabatic,\,quasi-static} }-W_{O\to B}^{\mathrm {adiabatic,\,quasi-static} }=-U(A)+U(B)=\Delta U} 4869:

accuracy, although the simple equations for reversible processes still hold to a good approximation in the absence of composition changes. Importantly, the first law still holds and provides a check on the measurements and calculations of the work done irreversibly on the system,

9928: 2514:

A cyclic process is one that can be repeated indefinitely often, returning the system to its initial state. Of particular interest for single cycle of a cyclic process are the net work done, and the net heat taken in (or 'consumed', in Clausius' statement), by the system.

8362: 2989:

Evidence of this kind shows that to increase the temperature of the water in the tank, the qualitative kind of adiabatically performed work does not matter. No qualitative kind of adiabatic work has ever been observed to decrease the temperature of the water in the tank.

8061: 6815:

a wall. For an open system, there is a wall that allows penetration by matter. In general, matter in diffusive motion carries with it some internal energy, and some microscopic potential energy changes accompany the motion. An open system is not adiabatically enclosed.

3398: 8989:, translated and edited by R. H. Thurston, and published by Macmillan and Company in 1890. Further editing by E. Mendoza, who added a new Appendix, "Selections from the Posthumous Manuscripts of Carnot," translated by R. H. Thurston and E. Mendoza. Dover, Mineola, NY. 2455:

This approach derives the notions of transfer of energy as heat, and of temperature, as theoretical developments, not taking them as primitives. It regards calorimetry as a derived theory. It has an early origin in the nineteenth century, for example in the work of

7457: 7753: 2569:

This physical statement is restricted neither to closed systems nor to systems with states that are strictly defined only for thermodynamic equilibrium; it has meaning also for open systems and for systems with states that are not in thermodynamic equilibrium.

2306:(1980) as "in a process at constant pressure, the heat used to produce expansion is universally interconvertible with work", but this is not a general statement of the first law, for it does not express the concept of the thermodynamic state variable, the 6797:

in general lacks an assignment to either subsystem in a way that is not arbitrary, and this stands in the way of a general non-arbitrary definition of transfer of energy as work. On occasions, authors make their various respective arbitrary assignments.

2954:

The following is an account in terms of changes of state of a closed system through compound processes that are not necessarily cyclic. This account first considers processes for which the first law is easily verified because of their simplicity, namely

2318:, in which he specified a numerical value for the amount of mechanical work required to "produce a unit of heat", based on heat production by friction in the passage of electricity through a resistor and in the rotation of a paddle in a vat of water. 7141: 3603: 2795: 5744: 5661: 2538:

The law is of great importance and generality and is consequently thought of from several points of view. Most careful textbook statements of the law express it for closed systems. It is stated in several ways, sometimes even by the same author.

8241: 7336:), and if the process can be described in the quasi-static formalism, in terms of the internal state variables of the system, then the process can also be described by a combination of the first and second laws of thermodynamics, by the formula 7298:

denotes the energy transferred from the system to the surrounding subsystems that are in adiabatic connection with it. The case of a wall that is permeable to matter and can move so as to allow transfer of energy as work is not considered here.

6118:

A useful idea from mechanics is that the energy gained by a particle is equal to the force applied to the particle multiplied by the displacement of the particle while that force is applied. Now consider the first law without the heating term:

9924: 2564:

It is in no way possible, either by mechanical, thermal, chemical, or other devices, to obtain perpetual motion, i.e. it is impossible to construct an engine which will work in a cycle and produce continuous work, or kinetic energy, from

2406:. In each case, an unmeasurable quantity (the internal energy, the atomic energy level) is revealed by considering the difference of measured quantities (increments of internal energy, quantities of emitted or absorbed radiative energy). 8587: 2490:, it is often regarded as theoretically preferable because of this conceptual parsimony. Born particularly observes that the revised approach avoids thinking in terms of what he calls the "imported engineering" concept of heat engines. 6175: 1862:, often replace the subtraction with addition, and consider all net energy transfers to the system as positive and all net energy transfers from the system as negative, irrespective of the use of the system, for example as an engine. 5826:

In the case of a closed system in which the particles of the system are of different types and, because chemical reactions may occur, their respective numbers are not necessarily constant, the fundamental thermodynamic relation for

7655:{\displaystyle \delta Q\,=\,T\,\mathrm {d} S-T\textstyle {\sum _{i}}s_{i}\,dN_{i}\,{\text{ and }}\delta W\,=\,P\,\mathrm {d} V\,\,\,\,\,\,{\text{(suitably defined surrounding subsystems, quasi-static transfers of energy)}},} 2294:

during chemical transformations. This law was later recognized as a consequence of the first law of thermodynamics, but Hess's statement was not explicitly concerned with the relation between energy exchanges by heat and work.

2365:

In all cases in which work is produced by the agency of heat, a quantity of heat is consumed which is proportional to the work done; and conversely, by the expenditure of an equal quantity of work an equal quantity of heat is

5480: 5106: 2689: 5071: 4969: 2356:

In a thermodynamic process involving a closed system (no transfer of matter), the increment in the internal energy is equal to the difference between the heat accumulated by the system and the thermodynamic work done by

4621: 4583: 4487: 3021:

by Clausius in 1850, but he did not then name it, and he defined it in terms not only of work but also of heat transfer in the same process. It was also independently recognized in 1850 by Rankine, who also denoted it

7103:

A system connected to its surroundings only through contact by a single permeable wall, but otherwise isolated, is an open system. If it is initially in a state of contact equilibrium with a surrounding subsystem, a

4220:

For all adiabatic processes between two specified states of a closed system of any nature, the net work done is the same regardless the details of the process, and determines a state function called internal energy,

6581: 6070: 2257:

came to understand that the caloric theory of heat was restricted to mere calorimetry, and that heat and "motive power" are interconvertible. This is known only from his posthumously published notes. He wrote:

8438: 4302:

When the system evolves with transfer of energy as heat, without energy being transferred as work, in an adynamic process, the heat transferred to the system is equal to the increase in its internal energy:

2479:

the process of interest, and regardless of whether it is an adiabatic or a non-adiabatic process. The reference adiabatic work process may be chosen arbitrarily from amongst the class of all such processes.

7528:

permitted terms correspond precisely. If two of the kinds of wall are left unsealed, then energy transfer can be shared between them, so that the two remaining permitted terms do not correspond precisely.

9567:, (first edition 1949), fifth edition 1967, North-Holland, Amsterdam, pp. 9–10. Guggenheim 1949/1965 is recommended by Buchdahl, H. A. (1966), p. 218. It is also recommended by Münster, A. (1970), p. 376. 4378: 8145:

Formula (6) is valid in general case, both for quasi-static and for irreversible processes. The situation of the quasi-static process is considered in the previous Section, which in our terms defines

6158:

The two thermodynamic parameters that form a generalized force-displacement pair are called "conjugate variables". The two most familiar pairs are, of course, pressure-volume, and temperature-entropy.

6434: 8264: 7954: 2434:. Largely through Born's influence, this revised conceptual approach to the definition of heat came to be preferred by many twentieth-century writers. It might be called the "mechanical approach". 1322: 3216: 2942:

also mentions that the Born (1921) version is "completely rigorous". These versions follow the traditional approach that is now considered out of date, exemplified by that of Planck (1897/1903).

7943:

matter and to internal energy, but also may be movable so as to allow work to be done when the two systems have different pressures. In this case, the transfer of energy as heat is not defined.

5918: 2934:

is the exchange of thermal energy between a system and its surroundings caused by a temperature difference." The author then explains how heat is defined or measured by calorimetry, in terms of

2856: 8380:

To describe deviation of the thermodynamic system from equilibrium, in addition to fundamental variables that are used to fix the equilibrium state, as was described above, a set of variables

7864:{\displaystyle \mathrm {d} U_{0}\,=\,\delta Q\,-\,\delta W\,+\,\sum _{j=1}^{n}h_{j}\,\mathrm {d} N_{j}\,\,\,\,\,\,\,{\text{(suitably defined surrounding subsystems, quasi-static transfers)}}.} 7344: 4264:, which requires the existence of thermometers and measurement of temperature change in bodies of known sensible heat capacity under specified conditions; or it can rely on the measurement of 3522: 2542:

For the thermodynamics of closed systems, the distinction between transfers of energy as work and as heat is central and is within the scope of the present article. For the thermodynamics of

7066: 6901: 3524:

is empirically feasible by a simple application of externally supplied work. The reason for this is given as the second law of thermodynamics and is not considered in the present article.

3460: 2951:

external parameters of a system. The original discovery of the law was gradual over a period of perhaps half a century or more, and some early studies were in terms of cyclic processes.

9297:, in his most widely cited text, Pippard's text gives a "scholarly and rigorous treatment"; see Callen, H. B. (1960/1985), p. 485. It is also recommended by Münster, A. (1970), p. 376. 8424: 6795: 6573: 2915:

be rightly interpreted as empirical temperatures, and the walls connecting the phases of the system are explicitly defined as possibly impermeable to heat or permeable only to heat.

2053: 7226:{\displaystyle \Delta U_{0}\,=\,Q\,-\,W\,-\,\sum _{i=1}^{m}\Delta U_{i}\,\,\,\,\,{\text{(suitably defined surrounding subsystems, general process, quasi-static or irreversible),}}} 7745:

For fictive quasi-static transfers for which the chemical potentials in the connected surrounding subsystems are suitably controlled, these can be put into equation (4) to yield

6507: 6472: 5959:

is expressed in J/mol. If the system has more external mechanical variables than just the volume that can change, the fundamental thermodynamic relation further generalizes to:

3539: 2700: 5692: 5597: 3042: ; and in 1851 by Kelvin who then called it "mechanical energy", and later "intrinsic energy". In 1865, after some hesitation, Clausius began calling his state function 8153: 6532:

Potential energy can be exchanged with the surroundings of the system when the surroundings impose a force field, such as gravitational or electromagnetic, on the system.

4849: 2986:, mechanical, chemical,... or if done suddenly or slowly, as long as it is performed in an adiabatic way, that is to say, without heat transfer into or out of the system. 2371:

abstract mathematical nature of the internal energy. The internal energy is customarily stated relative to a conventionally chosen standard reference state of the system.

1848: 4299:." According to another textbook, "Calorimetry is widely used in present day laboratories." According to one opinion, "Most thermodynamic data come from calorimetry...". 1999: 1157: 1102: 1047: 7532:

subsystems of completely controllable chemical potential (or equivalent controls for charged species). Then, for a suitable fictive quasi-static transfer, one can write

2207: 1924: 854: 807: 722: 675: 587: 540: 8889: 5559:

changes, such that there is at each instant negligible departure from thermodynamic equilibrium within the system and between system and surroundings. Then, mechanical

6151:

term in the same light: here the temperature is known as a "generalized" force (rather than an actual mechanical force) and the entropy is a generalized displacement.

5353: 4293: 2170: 1967: 1810: 758: 626: 8718:{\displaystyle \mathrm {d} S={\frac {\Delta E}{T}},\quad \Delta E=\Delta Q-\sum _{j}\,\Xi _{j}\,\Delta \xi _{j}+\sum _{\alpha }\,\eta _{\alpha }\,\Delta n_{\alpha }.} 2493:

Basing his thinking on the mechanical approach, Born in 1921, and again in 1949, proposed to revise the definition of heat. In particular, he referred to the work of

8911:

Gislason, E. A.; Craig, N. C. (2005). "Cementing the foundations of thermodynamics: comparison of system-based and surroundings-based definitions of work and heat".

7693: 6329:{\displaystyle {\frac {DE_{t}}{Dt}}={\frac {DW}{Dt}}+{\frac {DQ}{Dt}}\to {\frac {DE_{t}}{Dt}}=\nabla \cdot ({\mathbf {\sigma } \cdot v})-\nabla \cdot {\mathbf {q} }} 4585:

are not required to occur respectively adiabatically or adynamically, but they must belong to the same particular process defined by its particular reversible path,

992: 8120: 7912: 7740: 5098: 4610: 3168: 3119: 2441:

The "mechanical" approach postulates the law of conservation of energy. It also postulates that energy can be transferred from one thermodynamic system to another

1677:

for taking account of the balance of heat and work in the system. Energy cannot be created or destroyed, but it can be transformed from one form to another. In an

6835:

In particular, between two otherwise isolated open systems an adiabatic wall is by definition impossible. This problem is solved by recourse to the principle of

2911:

energy and work done on the system, when that work does not account for the whole of the change of internal energy and the system is not adiabatically isolated.

2271:

had not been formulated. Carnot was aware that heat could be produced by friction and by percussion, as forms of dissipation of "motive power". As late as 1847,

491: 8140: 7932: 7713: 6802:

dissipation by friction of kinetic energy of localised bulk flow into internal energy, whether in turbulent or in streamlined flow, is an important quantity in

6527: 6363: 5330: 4239: 3696: 3676: 3656: 3208: 3188: 3139: 3090: 3060: 3040: 3019: 2143: 2123: 2103: 2076: 1944: 1891: 1775: 1755: 1735: 830: 783: 698: 651: 563: 516: 8746:

open systems, the author Prigogine carefully explains at some length that his definition of it does not obey a balance law. He describes this as paradoxical.

6819:

process of interest involves only hypothetical or potential but no actual passage of matter, the process can be considered as if it were for a closed system.

2553:

There are two main ways of stating a law of thermodynamics, physically or mathematically. They should be logically coherent and consistent with one another.

2422:

When energy flows from one system or part of a system to another otherwise than by the performance of mechanical work, the energy so transferred is called

4269: 2882:, uses the sign convention of IUPAC, not that of Clausius. Though it does not explicitly say so, this statement refers to closed systems. Internal energy 5538:{\displaystyle dU=\delta Q-\delta W\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{(closed system, general process, quasi-static or irreversible).}}} 5302:{\displaystyle -W_{A\to B}^{\mathrm {path} \,P_{1},\,\mathrm {irreversible} }+Q_{A\to B}^{\mathrm {path} \,P_{1},\,\mathrm {irreversible} }=\Delta U\,.} 5404:

The first law for a closed homogeneous system may be stated in terms that include concepts that are established in the second law. The internal energy

2519:

a cyclic process, the net work done by the system, measured in mechanical units, is proportional to the heat consumed, measured in calorimetric units.

6998:

should be specified accordingly, maintaining also that the internal energy of a system be proportional to its mass, so that the internal energies are

10257: 10189: 9539:, Oppenheim, I. (1961), pp. 17–18. Kirkwood & Oppenheim 1961 is recommended by Münster, A. (1970), p. 376. It is also cited by Eu, B. C. (2002), 2606: 4805:{\displaystyle -W_{A\to B}^{\mathrm {path} \,P_{0},\,\mathrm {reversible} }+Q_{A\to B}^{\mathrm {path} \,P_{0},\,\mathrm {reversible} }=\Delta U\,.} 10886:, G. Reimer (publisher), Berlin, read on 23 July in a session of the Physikalischen Gesellschaft zu Berlin. Reprinted in Helmholtz, H. von (1882), 4974: 4872: 3622:

Another way to deal with it is to allow that experiments with processes of heat transfer to or from the system may be used to justify the formula (

1632: 10896:(1853), volume 7, edited by J. Tyndall, W. Francis, published by Taylor and Francis, London, pp. 114–162, reprinted as volume 7 of Series 7, 2998:

conserved quantity. For the latter, another step of evidence is needed, which may be related to the concept of reversibility, as mentioned below.

2426:." This definition may be regarded as expressing a conceptual revision, as follows. This reinterpretation was systematically expounded in 1909 by 7091:

denote the changes in mole number of a component substance of the system and of its surroundings respectively. This is a statement of the law of

6747:{\displaystyle E=E_{1}^{\mathrm {kin} }+E_{1}^{\mathrm {pot} }+U_{1}+E_{2}^{\mathrm {kin} }+E_{2}^{\mathrm {pot} }+U_{2}+E_{12}^{\mathrm {pot} }} 5802:. It is only in the reversible case or for a quasistatic process without composition change that the work done and heat transferred are given by 4492: 4396: 10337:"Equations of motion of viscoelastic systems as derived from the conservation laws and the phenomenological theory of non-equilibrium processes" 5666:

While this has been shown here for reversible changes, it is valid more generally in the absence of chemical reactions or phase transitions, as

2352:. He expressed it in terms of a differential equation for the increments of a thermodynamic process. This equation may be described as follows: 8793:

number 1, according to the first law of thermodynamics. This usage is also followed by workers in the kinetic theory of gases. This is not the

5397:

integral of an exact differential is always zero. The path taken by a thermodynamic system through a chemical or physical change is known as a

2149:. Internal energy is a property of the system, while work and heat describe the process, not the system. Thus, a given internal energy change, 1333: 2310:. Also in 1842, Mayer measured a temperature rise caused by friction in a body of paper pulp. This was near the time of the 1842–1845 work of 2125:

is the quantity of energy added or removed as heat in the thermodynamic sense, not referring to a form of energy within the system. Likewise,

6167: 1221: 9878: 9000: 2337:

The original 19th-century statements of the first law appeared in a conceptual framework in which transfer of energy as heat was taken as a

10294:

Aston, J. G., Fritz, J. J. (1959), Chapter 9. This is an unusually explicit account of some of the physical meaning of the Gibbs formalism.

8559:{\displaystyle \mathrm {d} U=T\,dS-\,p\Delta V\,+\sum _{j}\,\Xi _{j}\,\Delta \xi _{j}+\sum _{\alpha }\,\mu _{\alpha }\,\Delta n_{\alpha },} 9796: 5965: 455: 2888:

is evaluated for bodies in states of thermodynamic equilibrium, which possess well-defined temperatures, relative to a reference state.

8871: 2546:, such a distinction is beyond the scope of the present article, but some limited comments are made on it in the section below headed 1311: 2446:

Bailyn) refrains from labelling as 'heat' such non-adiabatic, unaccompanied transfer of energy. It rests on the primitive notion of

2438:

work and heat transfers can be distinguished only when they pass through walls physically separate from those for matter transfer.

11266: 4309: 8357:{\displaystyle \mathrm {d} S={\frac {\Delta E}{T}},\quad \Delta E=\Delta Q+\sum _{\alpha }\,\eta _{\alpha }\,\Delta N_{\alpha }.} 2249: 1344: 10894:

Scientific Memoirs, Selected from the Transactions of Foreign Academies of Science and from Foreign Journals. Natural Philosophy

8056:{\displaystyle \mathrm {\Delta } U\,=\,\Delta Q\,-\,p\Delta V\,+\,\sum _{j=1}^{n}h_{j}\,\mathrm {\Delta } N_{j}\,\,\,\,\,\,\,.} 6371: 10696: 6535:

A compound system consisting of two interacting closed homogeneous component subsystems has a potential energy of interaction

3393:{\displaystyle U(A)=U(O)-W_{O\to A}^{\mathrm {adiabatic} }\,\,\mathrm {or} \,\,U(O)=U(A)-W_{A\to O}^{\mathrm {adiabatic} }\,.} 11250: 11230: 10996: 10630: 10572: 9732: 9711: 8970: 8946: 8886: 914: 10056: 6509:

denote respectively the total kinetic energy and the total potential energy of the component closed homogeneous system, and

1625: 1212: 881: 448: 326: 10700: 7452:{\displaystyle \mathrm {d} U_{0}\,=\,T\,\mathrm {d} S\,-\,P\,\mathrm {d} V\,+\,\sum _{j=1}^{n}\mu _{j}\,\mathrm {d} N_{j}} 4612:, through the space of thermodynamic states. Then the work and heat transfers can occur and be calculated simultaneously. 5837: 5556: 4390: 264: 2903:(1921). The earlier traditional versions of the law for closed systems are nowadays often considered to be out of date. 2806: 11016: 8960: 8820: 6999: 5769: 4815:

This combined statement is the expression the first law of thermodynamics for reversible processes for closed systems.

3465: 2600:

total energy. The first two quantities are specifiable in terms of appropriate mechanical variables, and by definition

1396: 1370: 891: 345: 11202: 11175: 11160: 11142: 11034: 10981: 10913: 10848: 10808: 10655: 10587: 10543: 9894: 9871: 9809: 9548: 9524: 9503: 9078: 2873:

are heat and work added, with no restrictions as to whether the process is reversible, quasistatic, or irreversible.

2240:

Empirical developments of the early ideas, in the century following, wrestled with contravening concepts such as the

297: 7015: 6850: 2348:

in 1850, referred to cyclic thermodynamic processes, and to the existence of a function of state of the system, the

10716:"Ueber die bewegende Kraft der Wärme und die Gesetze, welche sich daraus für die Wärmelehre selbst ableiten lassen" 3406: 2930:

addition and removal of heat do not alter its temperature. A current student text on chemistry defines heat thus: "

1449: 920: 319: 5372:

When the heat and work transfers in the equations above are infinitesimal in magnitude, they are often denoted by

3403:

Except under the special, and strictly speaking, fictional, condition of reversibility, only one of the processes

1777:, supplied or withdrawn from the system. The historical sign convention for the terms has been that heat supplied 11312: 4615:

Putting the two complementary aspects together, the first law for a particular reversible process can be written

1618: 6806:. This is a serious difficulty for attempts to define entropy for time-varying spatially inhomogeneous systems. 2522:

The constant of proportionality is universal and independent of the system and in 1845 and 1847 was measured by

10784: 8383: 7946:

The first law of thermodynamics for any process on the specification of equation (3) can be defined as

7292:

denotes the internal energy transferred as heat from the heat reservoir of the surroundings to the system, and

6803: 1549: 81: 4216:

This kind of empirical evidence, coupled with theory of this kind, largely justifies the following statement:

2254: 1444: 11307: 11153:

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

9748: 7279:

surrounding subsystems that are in open contact with the system, due to transfer between the system and that

6760: 6538: 2527: 1524: 1297: 274: 3527:

The fact of such irreversibility may be dealt with in two main ways, according to different points of view:

2011: 10755:

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

10611:

Thermodynamics. An Introductory Treatise dealing mainly with First Principles and their Direct Applications

8831: 8089:

denotes the internal energy transferred as heat from the heat reservoir of the surroundings to the system,

3598:{\displaystyle W_{A\to O}^{\text{adiabatic, quasi-static}}=-W_{O\to A}^{\text{adiabatic, quasi-static}}\,.} 2891:

The history of statements of the law for closed systems has two main periods, before and after the work of

2790:{\displaystyle \Delta E^{\mathrm {tot} }=\Delta E^{\mathrm {kin} }+\Delta E^{\mathrm {pot} }+\Delta U\,\,.} 2105:

is a mathematical abstraction that keeps account of the changes of energy that befall the system. The term

909: 112: 102: 10254: 10186: 11289: 11283: 9095: 5739:{\displaystyle dU=TdS-PdV\,\,\,\,\,{\text{(closed system, general process without composition change).}}} 5656:{\displaystyle dU=TdS-PdV\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{(closed system, reversible process).}}} 1713:

of energy transfer without transfer of matter, the first law of thermodynamics is often expressed by the

1698: 117: 6477: 6442: 2543: 1694: 1401: 1365: 143: 77: 10662: 9983:

Denbigh, K. G. (1951), p. 56. Denbigh states in a footnote that he is indebted to correspondence with

9541:

Generalized Thermodynamics, the Thermodynamics of Irreversible Processes and Generalized Hydrodynamics

9337: 8236:{\displaystyle \mathrm {d} U=T\,dS-\,p\Delta V\,+\sum _{\alpha }\,\mu _{\alpha }\,\Delta N_{\alpha },} 2896: 2494: 2427: 1439: 1685: 1194: 942: 388: 201: 191: 11273: 2085:

Work and heat express physical processes of supply or removal of energy, while the internal energy

6844:

as closed systems as above, can be measured. Then the law of conservation of energy requires that

4824: 1818: 10830:

Nonequilibrium Thermodynamics. Phenomenological Theory of Irreversible Processes in Fluid Systems

9875: 7512:

For a general natural process, there is no immediate term-wise correspondence between equations (

6840: 4251: 2299: 2218: 1972: 1710: 1606: 1434: 1231: 1112: 1057: 1002: 934: 873: 409: 398: 64: 10900:, edited by H. Woolf, (1966), Johnson Reprint Corporation, New York, and again in Brush, S. G., 10762: 2800:

The first law in a form that involves the principle of conservation of energy more generally is

2183: 1900: 836: 789: 704: 657: 569: 522: 10858:, translated from the 1967 Hungarian by E. Gyarmati and W. F. Heinz, Springer-Verlag, New York. 10801:

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

8810: 6836: 1650: 1539: 1256: 340: 94: 69: 7479:

chemical constituents of the system and permeably connected surrounding subsystems, and where

5335: 4275: 2486:

temperature that are presupposed by the original statements. Largely through the influence of

2152: 1949: 1792: 1459: 740: 605: 10879: 9599: 9310:

Born, M. (1921). "Kritische Betrachtungen zur traditionellen Darstellung der Thermodynamik".

7105: 5772:

for a closed system in the energy representation, for which the defining state variables are

5560: 5398: 2960: 2457: 2146: 1870: 1662: 1654: 1474: 1051: 364: 210: 59: 7668: 7098: 7006:

recognized as a fourth law of thermodynamics, though this is not repeated by other authors.

962: 11082: 11008: 10955: 10929: 10727: 10423: 10351: 9984: 9611: 9560: 9536: 9398: 9199: 9090: 9012: 8098: 7890: 7718: 7092: 5393: 5076: 5073:, which belong to the same particular process defined by its particular irreversible path, 4588: 2523: 2311: 2172:, can be achieved by different combinations of heat and work. Heat and work are said to be 1666: 1554: 1479: 1469: 269: 131: 10715: 9910:

Helmholtz, H. (1869/1871). Zur Theorie der stationären Ströme in reibenden Flüssigkeiten,

4393:. For a particular reversible process in general, the work done reversibly on the system, 3144: 3095: 2469:

given states, of a reference process that occurs purely through stages of adiabatic work.

8: 11068: 9656: 9056:

Mayer, Robert (1841). "Remarks on the Forces of Nature". Quoted in Lehninger, A. (1971).

7220:(suitably defined surrounding subsystems, general process, quasi-static or irreversible), 2447: 2314:, measuring the mechanical equivalent of heat. In 1845, Joule published a paper entitled 2263:

Reciprocally, wherever there is destruction of heat, there is production of motive power.

1499: 1261: 283: 249: 244: 157: 11086: 10933: 10887: 10731: 10597: 10427: 10355: 9615: 9016: 1494: 473: 11191: 11148: 11130: 10686: 10367: 8826: 8142:, coming into the system from the surrounding that is in contact with the system. 8125: 7917: 7698: 6512: 6348: 6083: 5938: 5379: 5315: 4224: 3681: 3661: 3641: 3193: 3173: 3124: 3075: 3072:

In an adiabatic process, adiabatic work takes the system either from a reference state

3045: 3025: 3004: 2463: 2303: 2128: 2108: 2088: 2061: 1929: 1876: 1760: 1740: 1720: 1674: 1588: 1251: 1246: 1199: 815: 768: 683: 636: 548: 501: 431: 415: 302: 254: 239: 229: 38: 32: 10902:

The Kinetic Theory of Gases. An Anthology of Classic Papers with Historical Commentary

9498:, (first edition by Kittel alone 1969), second edition, W. H. Freeman, San Francisco, 9220:(1921). "Kritische Betrachtungen zur traditionellen Darstellungen der Thermodynamik", 6100:

are independent of the size of the system and are called intensive parameters and the

11246: 11226: 11208: 11198: 11171: 11156: 11138: 11120: 11030: 11012: 10992: 10977: 10909: 10844: 10804: 10780: 10754: 10690: 10651: 10626: 10583: 10568: 10539: 10371: 9897:(1852 b). On a universal tendency in nature to the dissipation of mechanical energy, 9805: 9728: 9707: 9544: 9520: 9499: 9074: 8966: 8942: 3638:) above allows that to go by processes of quasi-static adiabatic work from the state 2972: 2956: 2442: 2177: 1583: 1544: 1534: 1106: 904: 732: 234: 224: 166: 11061:, original publication 1957, reprint 1966, Cambridge University Press, Cambridge UK. 5672:

can be considered as a thermodynamic state function of the defining state variables

2418:

wrote about systems between which there is no transfer of matter (closed systems): "

10937: 10743: 10735: 10678: 10398: 10359: 9619: 9171:(1850), page 373, translation here taken from Truesdell, C. A. (1980), pp. 188–189. 9107: 9028: 9020: 8962:

Seduced by logic: Émilie du Châtelet, Mary Somerville, and the Newtonian revolution

8920: 8815: 2338: 2329:. Some scholars consider Rankine's statement less distinct than that of Clausius. 1866: 1714: 1504: 1489: 1429: 1424: 1241: 1236: 886: 354: 219: 10561:

From Microphysics to Macrophysics: Methods and Applications of Statistical Physics

10305: 2945: 2217:

In the first half of the eighteenth century, French philosopher and mathematician

11040: 10791: 10779:, North-Holland, Amsterdam. Reprinted (1984), Dover Publications Inc., New York, 10711: 10605: 10336: 10261: 10193: 10060: 10046: 9882: 9744: 9431: 9189: 9168: 9156: 8893: 7125:

An open system can be in contact equilibrium with several other systems at once.

3064: 2983: 2892: 2415: 2349: 2345: 2326: 2322: 2307: 2005:

the system by the surroundings. The change in internal energy of the system is:

1786: 1678: 1670: 1454: 1302: 956: 597: 420: 181: 148: 10876:, ed. H. Eyring, D. Henderson, W. Jost, Academic Press, New York, lcn 73–117081. 10618: 9706:, (first edition 1978), ninth edition 2010, Oxford University Press, Oxford UK, 4818:

In particular, if no work is done on a thermally isolated closed system we have

2922:

Sometimes the concept of internal energy is not made explicit in the statement.

2247:

In the few years of his life (1796–1832) after the 1824 publication of his book

11103: 11093: 10836: 10748: 10643: 10282: 10146: 9841: 9782: 9482: 9294: 6135:

can be viewed as a force (and in fact has units of force per unit area) while d

2684:{\displaystyle E^{\mathrm {tot} }=E^{\mathrm {kin} }+E^{\mathrm {pot} }+U\,\,.} 2276: 2268: 2241: 1509: 1279: 379: 259: 196: 186: 54: 24: 10650:, (first edition 1960), second edition 1985, John Wiley & Sons, New York, 8924: 2332: 11301: 11054: 10739: 10609: 10564: 9452: 9290: 9233: 9024: 6930:

For the thermodynamic operation of adding two systems with internal energies

5410:

may then be expressed as a function of the system's defining state variables

5066:{\displaystyle Q_{A\to B}^{\mathrm {path} \,P_{1},\,\mathrm {irreversible} }} 4964:{\displaystyle W_{A\to B}^{\mathrm {path} \,P_{1},\,\mathrm {irreversible} }} 4261: 4257: 2935: 2287: 1578: 896: 465: 426: 138: 11212: 10556: 10083: 9699: 9112: 9033: 8763:

and a conduction flow. This conduction flow is by definition the heat flow

7645:(suitably defined surrounding subsystems, quasi-static transfers of energy) 6111:

only of its initial and final states, as noted in the section below headed

5930:

is the (small) increase in number of type-i particles in the reaction, and

5367: 4855:

This is one aspect of the law of conservation of energy and can be stated:

4578:{\displaystyle Q_{A\to B}^{\mathrm {path} \,P_{0},\,\mathrm {reversible} }} 4482:{\displaystyle W_{A\to B}^{\mathrm {path} \,P_{0},\,\mathrm {reversible} }} 2511:

internal state of the system, and did not expect the process to be cyclic.

2409: 2283: 1529: 1514: 1464: 947: 10403: 10386: 9876:

On a Universal Tendency in Nature to the Dissipation of Mechanical Energy

7099:

Process of transfer of matter between an open system and its surroundings

5949: 4265: 2272: 1484: 292: 10892:, Band 1, J. A. Barth, Leipzig. Translated and edited by J. Tyndall, in 10538:, (first edition 1968), third edition 1983, Cambridge University Press, 9058:

Bioenergetics – the Molecular Basis of Biological Energy Transformations

2361:

Reflecting the experimental work of Mayer and of Joule, Clausius wrote:

11064: 10856:

Non-equilibrium Thermodynamics. Field Theory and Variational Principles

10682: 10363: 2557: 1855: 1573: 1519: 10941: 10387:"A derivation of the main relations of non-equilibrium thermodynamics" 8887:

Quantities, Units and Symbols in Physical Chemistry (IUPAC Green Book)

8430:

have been introduced, which allows to formulate for the general case

11059:

Elements of Classical Thermodynamics for Advanced Students of Physics

9912:

Verhandlungen des naturhistorisch-medizinischen Vereins zu Heidelberg

7524:), because they describe the process in different conceptual frames. 171: 10666: 9624: 8823:– includes microscopic definitions of internal energy, heat and work 6575:

between the subsystems. Thus, in an obvious notation, one may write

6065:{\displaystyle dU=TdS-\sum _{i}X_{i}dx_{i}+\sum _{j}\mu _{j}dN_{j}.} 2464:

Conceptually revised statement, according to the mechanical approach

2344:

The first explicit statement of the first law of thermodynamics, by

2221:

made notable contributions to the emerging theoretical framework of

10593: 10250: 9971: 9885:" Proceedings of the Royal Society of Edinburgh for April 19, 1852 9751:

calls the curves representing changes without performance of work,

9244: 9217: 6829: 6140:

this term negative then this would be the work done on the system.

3698:, since the quasi-static adiabatic work is independent of the path 2900: 2573:

An example of a mathematical statement is that of Crawford (1963):

2533: 2487: 2431: 1287: 1204: 996: 404: 176: 7307:

If the system is described by the energetic fundamental equation,

11217:

Chpts. 2 and 3 contain a nontechnical treatment of the first law.

10814:

Eckart, C. (1940). The thermodynamics of irreversible processes.

9565:

Thermodynamics. An Advanced Treatment for Chemists and Physicists

7855:(suitably defined surrounding subsystems, quasi-static transfers) 6365:

denotes the total energy of that component system, one may write

6112: 5358: 2547: 1669:

containing a constant amount of matter. The law also defines the

393: 11007:(2nd ed.). Chichester·New York·Brisbane·Toronto·Singapore: 9925:"Helmholtz, Hermann von - Wissenschaftliche Abhandlungen, Bd. 1" 5555:

can be written in terms of exact differentials. One may imagine

2938:, specific heat capacity, molar heat capacity, and temperature. 1657:. The law distinguishes two principal forms of energy transfer, 11029:, translated by E. S. Halberstadt, Wiley–Interscience, London, 6809: 5532:(closed system, general process, quasi-static or irreversible). 3001:

That important state variable was first recognized and denoted

2946:

Evidence for the first law of thermodynamics for closed systems

2222: 11079:

Thermodynamics of Complex Systems: Principles and applications

10772:, Rupert Hart-Davis, London, Harcourt, Brace & World, Inc. 10420:

Thermodynamics of Complex Systems: Principles and applications

6107:

are proportional to the size and called extensive parameters.

10865:, English translation, Addison-Wesley Publishing, Reading MA. 10841:

Thermodynamic Theory of Structure, Stability and Fluctuations

7109:

between the system and its contiguous surrounding subsystem.

1859: 16:

Law of thermodynamics establishing the conservation of energy

10884:

Ueber die Erhaltung der Kraft. Eine physikalische Abhandlung

10803:, fourth edition, Cambridge University Press, Cambridge UK, 5733:(closed system, general process without composition change). 4373:{\displaystyle Q_{A\to B}^{\mathrm {adynamic} }=\Delta U\,.} 4256:

A complementary observable aspect of the first law is about

2694:

For any finite process, whether reversible or irreversible,

11168:

Fundamentals of Equilibrium and Steady-State Thermodynamics

10868:

Haase, R. (1971). Survey of Fundamental Laws, chapter 1 of

9060:, 2nd ed. London: The Benjamin/Cummings Publishing Company. 5332:

is a function of state and that the internal energy change

4859:

The internal energy of an isolated system remains constant.

2079: 1658: 369: 11072:, translated by A. Ogg, Longmans, Green & Co., London. 10070: 10068: 8875:, translated by A. Ogg, Longmans, Green & Co., London. 4863: 11277: 10045:

Smith, D. A. (1980). Definition of heat in open systems,

9922:, volume 1, Johann Ambrosius Barth, Leipzig, pp. 223–230 9100:

Philosophical Transactions of the Royal Society of London

7256:

denotes the change of internal energy of the system, and

6429:{\displaystyle E=E^{\mathrm {kin} }+E^{\mathrm {pot} }+U} 6172:

In fluid dynamics, the first law of thermodynamics reads

5355:

between two states is a function only of the two states.

3678:

we can take a path that goes through the reference state

2899:(1909), and the approval of Carathéodory's work given by 11188: 11108:

Introduction to Thermodynamics of Irreversible Processes

10908:, edited by N. S. Hall, Imperial College Press, London, 9192:(1907), p. 47. Also Bryan had written about this in the 9127: 9125: 9123: 8906: 8904: 8902: 5368:

State functional formulation for infinitesimal processes

4383: 10065: 9488: 9240: 9238: 9236: 7302: 5388:, as a reminder that heat and work do not describe the 4971:, and the heat transferred irreversibly to the system, 2321:

The first full statements of the law came in 1850 from

10667:"Untersuchungen über die Grundlagen der Thermodynamik" 10648:

Thermodynamics and an Introduction to Thermostatistics

7571: 2145:

denotes the quantity of energy gained or lost through

1757:, done on or by the system, and the quantity of heat, 11135:

The Tragicomical History of Thermodynamics, 1822–1854

10967:

Thermodynamics with Quantum Statistical Illustrations

9120: 8899: 8590: 8441: 8386: 8267: 8156: 8128: 8101: 8083:

denotes the change of internal energy of the system,

7957: 7920: 7893: 7756: 7721: 7701: 7671: 7541: 7347: 7144: 7120: 7018: 6853: 6822: 6763: 6584: 6541: 6515: 6480: 6445: 6374: 6351: 6178: 5968: 5840: 5695: 5600: 5483: 5338: 5318: 5109: 5079: 4977: 4875: 4827: 4624: 4591: 4495: 4489:, and the heat transferred reversibly to the system, 4399: 4312: 4278: 4227: 3707: 3684: 3664: 3644: 3542: 3468: 3409: 3219: 3196: 3176: 3147: 3127: 3098: 3078: 3048: 3028: 3007: 2809: 2703: 2609: 2186: 2155: 2131: 2111: 2091: 2064: 2014: 1975: 1952: 1932: 1903: 1879: 1821: 1795: 1785:

the system is subtracted. This was the convention of

1763: 1743: 1723: 1115: 1060: 1005: 965: 839: 818: 792: 771: 743: 707: 686: 660: 639: 608: 572: 551: 525: 504: 476: 11220: 10467:

Lebon, G., Jou, D., Casas-Vázquez, J. (2008), p. 45.

9333: 9331: 9329: 9327: 9325: 5548:

Then, for the fictive case of a reversible process,

2225:, for example by emphasising Leibniz's concept of ' 11110:, third edition, Interscience Publishers, New York. 10288: 5913:{\displaystyle dU=TdS-PdV+\sum _{i}\mu _{i}dN_{i}.} 5577:and the quantity of heat added can be expressed as 4270:

measurement of masses of material that change phase

11190: 11098:Étude Thermodynamique des Phénomènes irréversibles 10920:Kestin, J. (1961). "On intersecting isentropics". 10325:Callen, J. B. (1960/1985), Section 2-1, pp. 35–37. 8965:(US ed.). New York: Oxford University Press. 8717: 8558: 8418: 8356: 8235: 8134: 8114: 8055: 7926: 7906: 7863: 7734: 7707: 7687: 7654: 7451: 7225: 7060: 6895: 6789: 6746: 6567: 6521: 6501: 6466: 6428: 6357: 6339: 6328: 6064: 5912: 5738: 5655: 5537: 5347: 5324: 5301: 5092: 5065: 4963: 4843: 4804: 4604: 4577: 4481: 4372: 4287: 4233: 4205: 3690: 3670: 3650: 3597: 3516: 3454: 3392: 3202: 3182: 3162: 3133: 3113: 3084: 3054: 3034: 3013: 2851:{\displaystyle \Delta E^{\mathrm {tot} }=Q+W\,\,.} 2850: 2789: 2683: 2201: 2164: 2137: 2117: 2097: 2070: 2047: 1993: 1961: 1938: 1918: 1885: 1842: 1804: 1769: 1749: 1729: 1151: 1096: 1041: 986: 848: 824: 801: 777: 752: 716: 692: 669: 645: 620: 581: 557: 534: 510: 485: 10582:, American Institute of Physics Press, New York, 9322: 8797:definition of "reduced heat flux" of Rolf Haase. 3517:{\displaystyle \mathrm {adiabatic} ,\,{A\to O}\,} 2333:Original statements: the "thermodynamic approach" 11299: 10707:, Dowden, Hutchinson & Ross, Stroudsburg PA. 10316:Buchdahl, H. A. (1966), Section 66, pp. 121–125. 9519:, Pearson/Prentice Hall, Upper Saddle River NJ, 9350: 9348: 9346: 2534:Various statements of the law for closed systems 11115:Fundamentals of Statistical and Thermal Physics 11049:Fundamental Principles. The Properties of Gases 10623:Statistical Dynamics; Matter out of Equilibrium 9418: 9416: 8861:Equation IIa on page 384 of Clausius, R. (1850) 6948:, to produce a new system with internal energy 1897:the system on the surroundings is the product, 10987:Lebon, G., Jou, D., Casas-Vázquez, J. (2008). 9953:Münster A. (1970), Sections 14, 15, pp. 45–51. 9575: 9573: 9195:Enzyklopädie der Mathematischen Wissenschaften 7061:{\displaystyle \Delta N_{s}+\Delta N_{o}=0\,,} 6896:{\displaystyle \Delta U_{s}+\Delta U_{o}=0\,,} 5359:Overview of the weight of evidence for the law 2556:An example of a physical statement is that of 2548:'First law of thermodynamics for open systems' 2410:Conceptual revision: the "mechanical approach" 2082:supplied to the system from its surroundings. 10770:Heat, Thermodynamics, and Statistical Physics 10551:Thermodynamics and Statistical Thermodynamics 10494:Truesdell, C., Muncaster, R. G. (1980), p. 3. 10205:Aston, J. G., Fritz, J. J. (1959), Chapter 9. 10041: 10039: 9949: 9947: 9945: 9376: 9374: 9372: 9343: 9286: 9284: 8939:Émilie du Chatelet between Leibniz and Newton 8910: 7266:denotes the change of internal energy of the 6168:First law of thermodynamics (fluid mechanics) 5100:, through the space of thermodynamic states. 3455:{\displaystyle \mathrm {adiabatic} ,\,O\to A} 2209:, which is not a form of thermodynamic work. 1689:sustain the work of the system continuously. 1626: 10989:Understanding Non-equilibrium Thermodynamics 10710: 10661: 10124: 10122: 10112: 10110: 9888: 9865: 9413: 9305: 9303: 9203: 9193: 9143: 9141: 9139: 9137: 7937: 6810:First law of thermodynamics for open systems 6113:First law of thermodynamics for open systems 4391:reversible in the strict thermodynamic sense 2959:(in which there is no transfer as heat) and 1681:the sum of all forms of energy is constant. 10952:, Blaisdell Publishing Company, Waltham MA. 9663:, Longmans, Green, and Co., London, p. 150. 9570: 9362: 9360: 9205:Bull. de la société français de philosophie 8896:See Sec. 2.11 Chemical Thermodynamics p. 56 5941:of the type-i particles in the system. If d 5453:, its pressure, are partial derivatives of 1789:, so that a change in the internal energy, 1693:thermodynamics also defines the concept of 11076: 11045:An Advanced Treatise on Physical Chemistry 10872:, pages 1–97 of volume 1, ed. W. Jost, of 10485:de Groot, S. R., Mazur, P. (1962), p. 169. 10458:Glansdorff, P, Prigogine, I, (1971), p. 9. 10417: 10384: 10334: 10036: 9942: 9918:: 1–7. Reprinted in Helmholtz, H. (1882), 9672:Planck, M. (1897/1903), Section 71, p. 52. 9425: 9369: 9281: 2430:, whose attention had been drawn to it by 2279:of heat, being unaware of Carnot's notes. 2001:is said to be the thermodynamic work done 1633: 1619: 31: 11240: 10747: 10476:de Groot, S. R., Mazur, P. (1962), p. 18. 10402: 10119: 10107: 9623: 9600:"Rudolf Clausius and the road to entropy" 9543:, Kluwer Academic Publishers, Dordrecht, 9300: 9134: 9111: 9032: 8958: 8698: 8687: 8660: 8649: 8539: 8528: 8501: 8490: 8476: 8466: 8456: 8419:{\displaystyle \xi _{1},\xi _{2},\ldots } 8337: 8326: 8216: 8205: 8191: 8181: 8171: 8049: 8048: 8047: 8046: 8045: 8044: 8043: 8027: 7995: 7991: 7981: 7977: 7970: 7966: 7852: 7851: 7850: 7849: 7848: 7847: 7846: 7830: 7798: 7794: 7787: 7783: 7776: 7772: 7642: 7641: 7640: 7639: 7638: 7637: 7628: 7624: 7620: 7608: 7594: 7556: 7552: 7548: 7433: 7401: 7397: 7388: 7384: 7380: 7371: 7367: 7363: 7217: 7216: 7215: 7214: 7213: 7178: 7174: 7170: 7166: 7162: 7158: 7054: 6889: 6828:is not in general possible. According to 5730: 5729: 5728: 5727: 5726: 5647: 5646: 5645: 5644: 5643: 5642: 5641: 5640: 5639: 5638: 5637: 5636: 5635: 5634: 5633: 5632: 5631: 5529: 5528: 5527: 5526: 5525: 5524: 5523: 5522: 5521: 5520: 5519: 5518: 5517: 5516: 5515: 5514: 5513: 5512: 5511: 5510: 5509: 5508: 5295: 5245: 5231: 5157: 5143: 5022: 5008: 4920: 4906: 4840: 4798: 4754: 4740: 4672: 4658: 4540: 4526: 4444: 4430: 4366: 4121: 4031: 3941: 3851: 3758: 3591: 3513: 3501: 3442: 3386: 3308: 3307: 3298: 3297: 2963:(in which there is no transfer as work). 2844: 2843: 2783: 2782: 2677: 2676: 1717:of contributions to the internal energy, 10974:Thermodynamics and Statistical Mechanics 10874:Physical Chemistry. An Advanced Treatise 10863:Thermodynamics of Irreversible Processes 10638:The Concepts of Classical Thermodynamics 9357: 6086:corresponding to the external variables 11223:Thermodynamics: an engineering approach 9597: 8987:Reflections on the Motive Power of Fire 6790:{\displaystyle E_{12}^{\mathrm {pot} }} 6568:{\displaystyle E_{12}^{\mathrm {pot} }} 4864:General case for irreversible processes 2460:, but also in the work of many others. 2250:Reflections on the Motive Power of Fire 11300: 10976:, Oxford University Press, Oxford UK, 10919: 10793:The Thermodynamics of the Steady State 10599:Natural Philosophy of Cause and Chance 10158:Landsberg, P. T. (1961), pp. 142, 387. 9988:existence of the 'heat of transport'." 9096:"On the Mechanical Equivalent of Heat" 9069:Blundell, S.J., Blundell, K.M., 2006, 3062:"energy". In 1882 it was named as the 2966: 2302:made a statement that was rendered by 2233:, as distinct from Newton's momentum, 2048:{\displaystyle \Delta U=Q-P~\Delta V,} 1781:the system is positive, but work done 11291:Unified Thermodynamics and Propulsion 11117:, McGraw-Hill Book Company, New York. 11002: 10962:, McGraw-Hill Book Company, New York. 10640:, Cambridge University Press, London. 10223:Landsberg, P. T. (1961), pp. 128–142. 10167:Landsberg, P. T. (1978), pp. 79, 102. 9794: 9725:Introduction to Modern Thermodynamics 9638:Truesdell, C. A. (1980), pp. 161–162. 9094: 9047:Truesdell, C. A. (1980), pp. 157–158. 8850: 4384:General case for reversible processes 4245: 9804:. McGraw-Hill, Inc. pp. 69–72. 9422:Crawford, F. H. (1963), pp. 106–107. 9309: 8998: 8581: 8432: 8258: 8147: 7948: 7747: 7742:is the corresponding molar entropy. 7338: 7303:Combination of first and second laws 7135: 5686: 5650:(closed system, reversible process). 5312:This means that the internal energy 3533: 11189:Goldstein, Martin; Inge F. (1993). 11100:, Dunod, Paris, and Desoers, Liège. 10906:History of Modern Physical Sciences 10796:, Methuen, London, Wiley, New York. 10775:de Groot, S. R., Mazur, P. (1962). 10761:, 1–21, 102–119. Also available on 10549:Aston, J. G., Fritz, J. J. (1959). 10006:Denbigh, K. (1954/1971), pp. 81–82. 8095:denotes the work of the system and 2505: 2180:', at constant system volume, with 13: 11182: 11051:, Longmans, Green and Co., London. 10625:, Imperial College Press, London, 10602:, Oxford University Press, London. 10553:, John Wiley & Sons, New York. 9401:, Oppenheim, I. (1961), pp. 31–33. 8937:Hagengruber, Ruth, editor (2011). 8821:Microstate (statistical mechanics) 8699: 8661: 8651: 8630: 8621: 8605: 8592: 8540: 8502: 8492: 8470: 8443: 8338: 8307: 8298: 8282: 8269: 8217: 8185: 8158: 8029: 7985: 7971: 7959: 7832: 7758: 7630: 7558: 7435: 7390: 7373: 7349: 7200: 7145: 7121:Open system with multiple contacts 7035: 7019: 6870: 6854: 6823:Internal energy for an open system 6781: 6778: 6775: 6738: 6735: 6732: 6699: 6696: 6693: 6673: 6670: 6667: 6634: 6631: 6628: 6608: 6605: 6602: 6559: 6556: 6553: 6502:{\displaystyle E^{\mathrm {pot} }} 6493: 6490: 6487: 6467:{\displaystyle E^{\mathrm {kin} }} 6458: 6455: 6452: 6414: 6411: 6408: 6393: 6390: 6387: 6313: 6285: 5770:fundamental thermodynamic relation 5392:of any system. The integral of an 5339: 5289: 5280: 5277: 5274: 5271: 5268: 5265: 5262: 5259: 5256: 5253: 5250: 5247: 5227: 5224: 5221: 5218: 5192: 5189: 5186: 5183: 5180: 5177: 5174: 5171: 5168: 5165: 5162: 5159: 5139: 5136: 5133: 5130: 5057: 5054: 5051: 5048: 5045: 5042: 5039: 5036: 5033: 5030: 5027: 5024: 5004: 5001: 4998: 4995: 4955: 4952: 4949: 4946: 4943: 4940: 4937: 4934: 4931: 4928: 4925: 4922: 4902: 4899: 4896: 4893: 4828: 4792: 4783: 4780: 4777: 4774: 4771: 4768: 4765: 4762: 4759: 4756: 4736: 4733: 4730: 4727: 4701: 4698: 4695: 4692: 4689: 4686: 4683: 4680: 4677: 4674: 4654: 4651: 4648: 4645: 4569: 4566: 4563: 4560: 4557: 4554: 4551: 4548: 4545: 4542: 4522: 4519: 4516: 4513: 4473: 4470: 4467: 4464: 4461: 4458: 4455: 4452: 4449: 4446: 4426: 4423: 4420: 4417: 4360: 4351: 4348: 4345: 4342: 4339: 4336: 4333: 4330: 4279: 4197: 4155: 4152: 4149: 4146: 4143: 4140: 4134: 4131: 4128: 4125: 4122: 4115: 4112: 4109: 4106: 4103: 4100: 4097: 4094: 4091: 4065: 4062: 4059: 4056: 4053: 4050: 4044: 4041: 4038: 4035: 4032: 4025: 4022: 4019: 4016: 4013: 4010: 4007: 4004: 4001: 3975: 3972: 3969: 3966: 3963: 3960: 3954: 3951: 3948: 3945: 3942: 3935: 3932: 3929: 3926: 3923: 3920: 3917: 3914: 3911: 3885: 3882: 3879: 3876: 3873: 3870: 3864: 3861: 3858: 3855: 3852: 3845: 3842: 3839: 3836: 3833: 3830: 3827: 3824: 3821: 3792: 3789: 3786: 3783: 3780: 3777: 3771: 3768: 3765: 3762: 3759: 3752: 3749: 3746: 3743: 3740: 3737: 3734: 3731: 3728: 3494: 3491: 3488: 3485: 3482: 3479: 3476: 3473: 3470: 3435: 3432: 3429: 3426: 3423: 3420: 3417: 3414: 3411: 3380: 3377: 3374: 3371: 3368: 3365: 3362: 3359: 3356: 3303: 3300: 3291: 3288: 3285: 3282: 3279: 3276: 3273: 3270: 3267: 2825: 2822: 2819: 2810: 2776: 2767: 2764: 2761: 2752: 2743: 2740: 2737: 2728: 2719: 2716: 2713: 2704: 2664: 2661: 2658: 2643: 2640: 2637: 2622: 2619: 2616: 2592:large-scale potential energy, and 2187: 2156: 2036: 2015: 1985: 1953: 1910: 1822: 1796: 840: 793: 708: 661: 573: 526: 346:Intensive and extensive properties 14: 11324: 11260: 11243:Four Laws that drive the Universe 11193:The Refrigerator and the Universe 10440:Prigogine, I., (1947), pp. 48–49. 9773:Adkins, C. J. (1968/1983), p. 75. 9690:Adkins, C. J. (1968/1983), p. 35. 9473:Adkins, C. J. (1968/1983), p. 31. 9293:(1957/1966), p. 15. According to 8122:is the molar enthalpy of species 7914:is the molar enthalpy of species 6161: 2316:The Mechanical Equivalent of Heat 11225:. McGraw-Hill Higher Education. 10705:The Second Law of Thermodynamics 10567:, J.F. Gregg, Springer, Berlin, 10528: 10515: 10506: 10497: 10488: 10479: 10470: 10461: 10452: 10443: 10434: 10411: 10378: 10328: 10319: 10310: 10116:Callen H. B. (1960/1985), p. 54. 9198:, volume 3, p. 81. Also in 1906 9159:(1850), p. 384, equation (IIa.). 9001:"Thermochemische Untersuchungen" 6321: 5447:, the system's temperature, and 2876:This statement by Crawford, for 1854:Modern formulations, such as by 1684:An equivalent statement is that 1602: 1601: 921:Table of thermodynamic equations 11269:The First Law of Thermodynamics 11221:Çengel Y. A.; Boles M. (2007). 11081:. IOP Publishing, Bristol, UK. 10757:. Phil. Mag. (1851), series 4, 10422:. IOP Publishing, Bristol, UK. 10297: 10276: 10267: 10244: 10241:Tschoegl, N. W. (2000), p. 201. 10235: 10226: 10217: 10208: 10199: 10179: 10170: 10161: 10152: 10140: 10131: 10098: 10089: 10077: 10027: 10018: 10009: 10000: 9991: 9977: 9965: 9962:Landsberg, P. T. (1978), p. 78. 9956: 9931:from the original on 2012-03-11 9904: 9856: 9847: 9834: 9825: 9788: 9776: 9767: 9764:Denbigh, K. (1954/1981), p. 45. 9758: 9738: 9717: 9693: 9684: 9675: 9666: 9650: 9641: 9632: 9591: 9582: 9554: 9530: 9517:Chemistry. A Molecular Approach 9509: 9494:Kittel, C. Kroemer, H. (1980). 9476: 9467: 9458: 9446: 9437: 9404: 9392: 9383: 9272: 9263: 9254: 9211: 9183: 9174: 9162: 9150: 9084: 9063: 9050: 9041: 8620: 8297: 7695:is the added amount of species 6340:Spatially inhomogeneous systems 2584:large-scale mechanical energy, 1649:is a formulation of the law of 1397:Maxwell's thermodynamic surface 10889:Wissenschaftliche Abhandlungen 10777:Non-equilibrium Thermodynamics 9920:Wissenschaftliche Abhandlungen 9647:Buchdahl, H. A. (1966), p. 43. 9443:Buchdahl, H. A. (1966), p. 34. 9410:Planck, M. (1897/1903), p. 86. 9354:Münster, A. (1970), pp. 23–24. 9260:Bailyn, M. (1994), pp. 65, 79. 8992: 8979: 8952: 8931: 8880: 8864: 8855: 8844: 6804:non-equilibrium thermodynamics 6307: 6291: 6252: 5209: 5121: 4986: 4884: 4718: 4636: 4504: 4408: 4321: 4191: 4185: 4176: 4170: 4082: 3992: 3902: 3812: 3719: 3578: 3551: 3506: 3446: 3347: 3333: 3327: 3318: 3312: 3258: 3244: 3238: 3229: 3223: 3157: 3151: 3108: 3102: 2500: 2472:The revised statement is then 1131: 1119: 1076: 1064: 1021: 1009: 981: 969: 1: 11127:, M.I.T. Press, Cambridge MA. 11077:Pokrovskii, Vladimir (2020). 10512:Haase, R. (1963/1969), p. 18. 10418:Pokrovskii, Vladimir (2020). 10385:Pokrovskii, Vladimir (2013). 10185:Born, M. (1949), Appendix 8, 10024:Haase, R. (1963/1969), p. 15. 9862:Denbigh, K. G. (1951), p. 50. 9005:Annalen der Physik und Chemie 8837: 6529:denotes its internal energy. 5474:The first law requires that: 2528:mechanical equivalent of heat 2267:At that time, the concept of 1704: 1298:Mechanical equivalent of heat 11197:. Harvard University Press. 11155:, Academic Press, New York, 10176:Prigogine, I. (1947), p. 48. 9785:(1960/1985), pp. 36, 41, 63. 9702:, de Paula, J. (1978/2010). 9380:Haase, R. (1971), pp. 24–25. 8985:Carnot, N.L.S. (1890/1960). 8832:Relativistic heat conduction 8731: 4844:{\displaystyle \Delta U=0\,} 1946:, and system volume change, 1865:When a system expands in an 1843:{\displaystyle \Delta U=Q-W} 910:Onsager reciprocal relations 7: 11294:from Prof. Z. S. Spakovszky 11285:First law of thermodynamics 11151:, Muncaster, R. G. (1980). 10753:. See English Translation: 10695:A translation may be found 10534:Adkins, C. J. (1968/1983). 10449:Gyarmati, I. (1970), p. 68. 9997:Fitts, D. D. (1962), p. 28. 9831:Bailyn, M. (1994), 254–256. 9604:American Journal of Physics 9073:, Oxford University Press, 9071:Concepts in Thermal Physics 8804: 8572: 8370: 8249: 8069: 7877: 7520: 7514: 7465: 7286:surrounding subsystem, and 7239: 6974:; the reference states for 5796:are partial derivatives of 5764: 5752: 3634: 3624: 3611: 2286:stated a conservation law ( 1994:{\displaystyle -P~\Delta V} 1647:first law of thermodynamics 1402:Entropy as energy dispersal 1213:"Perpetual motion" machines 1152:{\displaystyle G(T,p)=H-TS} 1097:{\displaystyle A(T,V)=U-TS} 1042:{\displaystyle H(S,p)=U+pV} 10: 11329: 11276:) by Jerzy Borysowicz for 11125:Generalized Thermodynamics 11070:Treatise on Thermodynamics 10950:A Course in Thermodynamics 10854:Gyarmati, I. (1967/1970). 10701:translation is to be found 10580:A Survey of Thermodynamics 10563:, volume 1, translated by 10536:Equilibrium Thermodynamics 10095:Münster, A. (1970), p. 46. 10074:Bailyn, M. (1994), p. 308. 10015:Münster, A. (1970), p. 50. 9588:Kestin, J. (1966), p. 156. 8873:Treatise on Thermodynamics 6165: 4297:adiabatic bomb calorimeter 4249: 2970: 2576:For a given system we let 2526:, who described it as the 2212: 2202:{\displaystyle \Delta V=0} 1919:{\displaystyle P~\Delta V} 849:{\displaystyle \partial T} 802:{\displaystyle \partial V} 717:{\displaystyle \partial p} 670:{\displaystyle \partial V} 582:{\displaystyle \partial T} 535:{\displaystyle \partial S} 10972:Landsberg, P. T. (1978). 10969:, Interscience, New York. 10965:Landsberg, P. T. (1961). 10799:Denbigh, K. (1954/1981). 10699:. Also a mostly reliable 10503:Balescu, R. (1997), p. 9. 10335:Pokrovskii, V.N. (1970). 10232:Tisza, L. (1966), p. 108. 10137:Tisza, L. (1966), p. 111. 10128:Tisza, L. (1966), p. 110. 10059:October 12, 2014, at the 9681:Bailyn, M. (1994), p. 95. 9180:Bailyn, M. (1994), p. 80. 9147:Bailyn, M. (1994), p. 79. 8959:Arianrhod, Robyn (2012). 8925:10.1016/j.jct.2004.12.012 8892:October 27, 2016, at the 7938:Non-equilibrium transfers 6143:It is useful to view the 1686:perpetual motion machines 1323:An Inquiry Concerning the 11166:Tschoegl, N. W. (2000). 11027:Classical Thermodynamics 10958:, Oppenheim, I. (1961). 10832:, McGraw-Hill, New York. 10768:Crawford, F. H. (1963). 10740:10.1002/andp.18501550403 10636:Buchdahl, H. A. (1966), 10613:, B. G. Teubner, Leipzig 10273:Haase, R. (1971), p. 35. 10104:Tisza, L. (1966), p. 41. 10033:Haase, R. (1971), p. 20. 9853:Tisza, L. (1966), p. 91. 9795:White, Frank M. (1991). 9485:(1960/1985), pp. 13, 17. 9366:Reif, F. (1965), p. 122. 9131:Truesdell, C. A. (1980). 9025:10.1002/andp.18401260620 8870:Planck, M. (1897/1903). 7509:, are defined as above. 7113:volume and temperature. 5784:, with respect to which 5348:{\displaystyle \Delta U} 4288:{\displaystyle \Delta U} 2165:{\displaystyle \Delta U} 2078:denotes the quantity of 1962:{\displaystyle \Delta V} 1805:{\displaystyle \Delta U} 1336:Heterogeneous Substances 753:{\displaystyle \alpha =} 621:{\displaystyle \beta =-} 11170:, Elsevier, Amsterdam, 10960:Chemical Thermodynamics 10861:Haase, R. (1963/1969). 10790:Denbigh, K. G. (1951). 10726:(4): 368–397, 500–524, 9598:Cropper, W. H. (1986). 9579:Planck, M. (1897/1903). 9464:Reif, F. (1965), p. 82. 8913:J. Chem. Thermodynamics 6841:thermodynamic operation 5591:. For these conditions 4252:Thermodynamic processes 3587:adiabatic, quasi-static 3560:adiabatic, quasi-static 2495:Constantin Carathéodory 2428:Constantin Carathéodory 2300:Julius Robert von Mayer 1711:thermodynamic processes 1655:thermodynamic processes 11313:Laws of thermodynamics 11137:, Springer, New York, 10898:The Sources of Science 10703:at Kestin, J. (1976). 10260:April 7, 2016, at the 10192:April 7, 2016, at the 9899:Philosophical Magazine 9881:April 1, 2016, at the 9723:Kondepudi, D. (2008). 9269:Bailyn, (1994), p. 82. 9204: 9194: 9113:10.1098/rstl.1850.0004 8811:Laws of thermodynamics 8719: 8560: 8420: 8358: 8237: 8136: 8116: 8057: 8016: 7928: 7908: 7865: 7819: 7736: 7709: 7689: 7688:{\displaystyle dN_{i}} 7656: 7453: 7422: 7227: 7199: 7062: 6897: 6837:conservation of energy 6791: 6748: 6569: 6523: 6503: 6468: 6430: 6359: 6330: 6066: 5914: 5740: 5657: 5539: 5349: 5326: 5303: 5094: 5067: 4965: 4845: 4806: 4606: 4579: 4483: 4374: 4289: 4235: 4207: 3692: 3672: 3652: 3599: 3518: 3456: 3394: 3204: 3184: 3164: 3135: 3115: 3086: 3056: 3036: 3015: 2852: 2791: 2685: 2368: 2359: 2265: 2203: 2166: 2139: 2119: 2099: 2072: 2049: 1995: 1963: 1940: 1926:, of system pressure, 1920: 1887: 1844: 1806: 1771: 1751: 1731: 1651:conservation of energy 1153: 1098: 1043: 988: 987:{\displaystyle U(S,V)} 850: 826: 803: 779: 754: 718: 694: 671: 647: 622: 583: 559: 536: 512: 487: 466:Specific heat capacity 70:Quantum thermodynamics 11009:John Wiley & Sons 10828:Fitts, D. D. (1962). 10671:Mathematische Annalen 10285:, (1960/1985), p. 35. 10149:, (1955/1967), p. 12. 9727:, Wiley, Chichester, 9278:Helmholtz, H. (1847). 8720: 8561: 8421: 8359: 8238: 8137: 8117: 8115:{\displaystyle h_{i}} 8058: 7996: 7929: 7909: 7907:{\displaystyle h_{i}} 7866: 7799: 7737: 7735:{\displaystyle s_{i}} 7710: 7690: 7657: 7454: 7402: 7228: 7179: 7106:thermodynamic process 7063: 6898: 6792: 6749: 6570: 6524: 6504: 6469: 6431: 6360: 6331: 6067: 5915: 5741: 5658: 5540: 5399:thermodynamic process 5350: 5327: 5304: 5095: 5093:{\displaystyle P_{1}} 5068: 4966: 4846: 4807: 4607: 4605:{\displaystyle P_{0}} 4580: 4484: 4375: 4290: 4236: 4208: 3693: 3673: 3653: 3600: 3519: 3457: 3395: 3205: 3185: 3165: 3141:with internal energy 3136: 3116: 3092:with internal energy 3087: 3057: 3037: 3016: 2853: 2792: 2686: 2458:Hermann von Helmholtz 2363: 2354: 2260: 2204: 2167: 2140: 2120: 2100: 2073: 2050: 1996: 1964: 1941: 1921: 1888: 1845: 1807: 1772: 1752: 1732: 1334:On the Equilibrium of 1154: 1099: 1052:Helmholtz free energy 1044: 989: 851: 827: 804: 780: 755: 719: 695: 672: 648: 623: 584: 560: 537: 513: 488: 11308:Equations of physics 11025:Münster, A. (1970), 10991:, Springer, Berlin, 9200:Jean Baptiste Perrin 8588: 8439: 8384: 8265: 8154: 8126: 8099: 7955: 7918: 7891: 7754: 7719: 7699: 7669: 7539: 7345: 7142: 7093:conservation of mass 7016: 6851: 6761: 6582: 6539: 6513: 6478: 6443: 6372: 6349: 6176: 5966: 5838: 5693: 5598: 5481: 5394:inexact differential 5336: 5316: 5107: 5077: 4975: 4873: 4825: 4622: 4589: 4493: 4397: 4310: 4276: 4225: 3705: 3682: 3662: 3642: 3540: 3466: 3407: 3217: 3194: 3174: 3170:, or from the state 3163:{\displaystyle U(A)} 3145: 3125: 3121:to an arbitrary one 3114:{\displaystyle U(O)} 3096: 3076: 3046: 3026: 3005: 2807: 2701: 2607: 2312:James Prescott Joule 2184: 2153: 2129: 2109: 2089: 2062: 2012: 1973: 1950: 1930: 1901: 1877: 1819: 1793: 1761: 1741: 1721: 1667:thermodynamic system 1347:Motive Power of Fire 1113: 1058: 1003: 963: 915:Bridgman's equations 892:Fundamental relation 837: 816: 790: 769: 741: 705: 684: 658: 637: 606: 570: 549: 523: 502: 474: 11087:2020tcsp.book.....P 11005:Statistical Physics 11003:Mandl, F. (1988) . 10948:Kestin, J. (1966). 10934:1961AmJPh..29..329K 10732:1850AnP...155..500C 10578:Bailyn, M. (1994). 10428:2020tcsp.book.....P 10404:10.1155/2013/906136 10391:ISRN Thermodynamics 10356:1970PoMec...6..693P 10086:(1991/2007), p. 217 9616:1986AmJPh..54.1068C 9515:Tro, N. J. (2008). 9455:(1957/1966), p. 14. 9389:Münster, A. (1970). 9230:, Supp pp. 218—224. 9017:1840AnP...126..385H 7000:extensive variables 6786: 6743: 6704: 6678: 6639: 6613: 6564: 5380:exact differentials 5285: 5197: 5062: 4960: 4788: 4706: 4574: 4478: 4356: 4160: 4070: 3980: 3890: 3797: 3590: 3563: 3385: 3296: 2967:Adiabatic processes 2957:adiabatic processes 1701:, and other types. 1325:Source ... Friction 1257:Loschmidt's paradox 449:Material properties 327:Conjugate variables 11288:in the MIT Course 11241:Atkins P. (2007). 10916:, pp. 89–110. 10818:The simple fluid, 10749:2027/uc1.$ b242250 10720:Annalen der Physik 10683:10.1007/BF01450409 10521:Eckart, C. (1940). 10364:10.1007/BF00856197 10214:Kestin, J. (1961). 9798:Viscous Fluid Flow 9704:Physical Chemistry 9208:, volume 6, p. 81. 9202:wrote about it in 8827:Entropy production 8715: 8686: 8648: 8556: 8527: 8489: 8428:internal variables 8416: 8354: 8325: 8233: 8204: 8132: 8112: 8053: 7924: 7904: 7861: 7732: 7705: 7685: 7652: 7651: 7582: 7449: 7223: 7058: 6893: 6787: 6764: 6744: 6721: 6682: 6656: 6617: 6591: 6565: 6542: 6519: 6499: 6464: 6426: 6355: 6326: 6084:generalized forces 6062: 6035: 5999: 5939:chemical potential 5910: 5883: 5768:) is known as the 5736: 5653: 5535: 5441:. In these terms, 5345: 5322: 5299: 5201: 5113: 5090: 5063: 4978: 4961: 4876: 4841: 4802: 4710: 4628: 4602: 4575: 4496: 4479: 4400: 4370: 4313: 4285: 4246:Adynamic processes 4231: 4203: 4074: 3984: 3894: 3804: 3711: 3688: 3668: 3648: 3595: 3570: 3543: 3514: 3452: 3390: 3339: 3250: 3200: 3180: 3160: 3131: 3111: 3082: 3052: 3032: 3011: 2961:adynamic processes 2848: 2787: 2681: 2304:Clifford Truesdell 2219:Émilie du Châtelet 2199: 2162: 2147:thermodynamic work 2135: 2115: 2095: 2068: 2045: 1991: 1959: 1936: 1916: 1883: 1871:thermodynamic work 1840: 1802: 1767: 1747: 1727: 1675:extensive property 1663:thermodynamic work 1653:in the context of 1589:Order and disorder 1345:Reflections on the 1252:Heat death paradox 1149: 1094: 1039: 984: 846: 822: 799: 775: 750: 714: 690: 667: 643: 618: 579: 555: 532: 508: 486:{\displaystyle c=} 483: 456:Property databases 432:Reduced properties 416:Chemical potential 380:Functions of state 303:Thermal efficiency 39:Carnot heat engine 11252:978-0-19-923236-9 11232:978-0-07-125771-8 11113:Reif, F. (1965). 10997:978-3-540-74251-7 10942:10.1119/1.1937763 10843:, Wiley, London, 10631:978-1-86094-045-3 10573:978-3-540-45469-4 10344:Polymer Mechanics 9747:(1949), p. 183: " 9733:978-0-470-01598-8 9712:978-0-19-954337-3 9610:(12): 1068–1074. 9561:Guggenheim, E. A. 9551:, pp. 18, 29, 66. 8999:Hess, H. (1840). 8972:978-0-19-993161-3 8947:978-94-007-2074-9 8739: 8738: 8677: 8639: 8615: 8580: 8579: 8518: 8480: 8378: 8377: 8316: 8292: 8257: 8256: 8195: 8135:{\displaystyle i} 8077: 8076: 7927:{\displaystyle i} 7885: 7884: 7856: 7708:{\displaystyle i} 7646: 7612: 7573: 7473: 7472: 7247: 7246: 7221: 6522:{\displaystyle U} 6358:{\displaystyle E} 6280: 6250: 6227: 6204: 6093:. The parameters 6026: 5990: 5874: 5760: 5759: 5734: 5651: 5533: 5325:{\displaystyle U} 4389:process is to be 4234:{\displaystyle U} 3691:{\displaystyle O} 3671:{\displaystyle B} 3651:{\displaystyle A} 3619: 3618: 3588: 3561: 3203:{\displaystyle O} 3183:{\displaystyle A} 3134:{\displaystyle A} 3085:{\displaystyle O} 3055:{\displaystyle U} 3035:{\displaystyle U} 3014:{\displaystyle U} 2973:Adiabatic process 2138:{\displaystyle W} 2118:{\displaystyle Q} 2098:{\displaystyle U} 2071:{\displaystyle Q} 2035: 1984: 1939:{\displaystyle P} 1909: 1886:{\displaystyle W} 1770:{\displaystyle Q} 1750:{\displaystyle W} 1737:, from all work, 1730:{\displaystyle U} 1643: 1642: 1584:Self-organization 1409: 1408: 1107:Gibbs free energy 905:Maxwell relations 863: 862: 859: 858: 825:{\displaystyle V} 778:{\displaystyle 1} 733:Thermal expansion 727: 726: 693:{\displaystyle V} 646:{\displaystyle 1} 592: 591: 558:{\displaystyle N} 511:{\displaystyle T} 439: 438: 355:Process functions 341:Property diagrams 320:System properties 310: 309: 275:Endoreversibility 167:Equation of state 11320: 11256: 11236: 11216: 11196: 11149:Truesdell, C. A. 11131:Truesdell, C. A. 11090: 11041:Partington, J.R. 11022: 10945: 10835:Glansdorff, P., 10817: 10752: 10751: 10694: 10663:Carathéodory, C. 10522: 10519: 10513: 10510: 10504: 10501: 10495: 10492: 10486: 10483: 10477: 10474: 10468: 10465: 10459: 10456: 10450: 10447: 10441: 10438: 10432: 10431: 10415: 10409: 10408: 10406: 10397:(ID 906136): 9. 10382: 10376: 10375: 10341: 10332: 10326: 10323: 10317: 10314: 10308: 10301: 10295: 10292: 10286: 10280: 10274: 10271: 10265: 10248: 10242: 10239: 10233: 10230: 10224: 10221: 10215: 10212: 10206: 10203: 10197: 10183: 10177: 10174: 10168: 10165: 10159: 10156: 10150: 10144: 10138: 10135: 10129: 10126: 10117: 10114: 10105: 10102: 10096: 10093: 10087: 10081: 10075: 10072: 10063: 10043: 10034: 10031: 10025: 10022: 10016: 10013: 10007: 10004: 9998: 9995: 9989: 9985:E. A. Guggenheim 9981: 9975: 9969: 9963: 9960: 9954: 9951: 9940: 9939: 9937: 9936: 9908: 9902: 9892: 9886: 9869: 9863: 9860: 9854: 9851: 9845: 9840:Glansdorff, P., 9838: 9832: 9829: 9823: 9822: 9820: 9818: 9803: 9792: 9786: 9780: 9774: 9771: 9765: 9762: 9756: 9745:Partington, J.R. 9742: 9736: 9721: 9715: 9697: 9691: 9688: 9682: 9679: 9673: 9670: 9664: 9654: 9648: 9645: 9639: 9636: 9630: 9629: 9627: 9595: 9589: 9586: 9580: 9577: 9568: 9558: 9552: 9534: 9528: 9513: 9507: 9492: 9486: 9480: 9474: 9471: 9465: 9462: 9456: 9450: 9444: 9441: 9435: 9429: 9423: 9420: 9411: 9408: 9402: 9396: 9390: 9387: 9381: 9378: 9367: 9364: 9355: 9352: 9341: 9335: 9320: 9319: 9307: 9298: 9288: 9279: 9276: 9270: 9267: 9261: 9258: 9252: 9250: 9247:(1949), Lecture 9242: 9231: 9215: 9209: 9207: 9197: 9187: 9181: 9178: 9172: 9166: 9160: 9154: 9148: 9145: 9132: 9129: 9118: 9117: 9115: 9088: 9082: 9067: 9061: 9054: 9048: 9045: 9039: 9038: 9036: 8996: 8990: 8983: 8977: 8976: 8956: 8950: 8935: 8929: 8928: 8908: 8897: 8884: 8878: 8868: 8862: 8859: 8853: 8848: 8816:Perpetual motion 8791: 8785: 8768: 8762: 8733: 8724: 8722: 8721: 8716: 8711: 8710: 8697: 8696: 8685: 8673: 8672: 8659: 8658: 8647: 8616: 8611: 8603: 8595: 8582: 8574: 8565: 8563: 8562: 8557: 8552: 8551: 8538: 8537: 8526: 8514: 8513: 8500: 8499: 8488: 8446: 8433: 8426:that are called 8425: 8423: 8422: 8417: 8409: 8408: 8396: 8395: 8372: 8363: 8361: 8360: 8355: 8350: 8349: 8336: 8335: 8324: 8293: 8288: 8280: 8272: 8259: 8251: 8242: 8240: 8239: 8234: 8229: 8228: 8215: 8214: 8203: 8161: 8148: 8141: 8139: 8138: 8133: 8121: 8119: 8118: 8113: 8111: 8110: 8094: 8088: 8071: 8062: 8060: 8059: 8054: 8042: 8041: 8032: 8026: 8025: 8015: 8010: 7962: 7949: 7933: 7931: 7930: 7925: 7913: 7911: 7910: 7905: 7903: 7902: 7879: 7870: 7868: 7867: 7862: 7857: 7854: 7845: 7844: 7835: 7829: 7828: 7818: 7813: 7771: 7770: 7761: 7748: 7741: 7739: 7738: 7733: 7731: 7730: 7714: 7712: 7711: 7706: 7694: 7692: 7691: 7686: 7684: 7683: 7661: 7659: 7658: 7653: 7647: 7644: 7633: 7613: 7610: 7607: 7606: 7593: 7592: 7583: 7581: 7561: 7475:where there are 7467: 7458: 7456: 7455: 7450: 7448: 7447: 7438: 7432: 7431: 7421: 7416: 7393: 7376: 7362: 7361: 7352: 7339: 7297: 7291: 7285: 7278: 7272: 7265: 7241: 7232: 7230: 7229: 7224: 7222: 7219: 7212: 7211: 7198: 7193: 7157: 7156: 7136: 7090: 7080: 7067: 7065: 7064: 7059: 7047: 7046: 7031: 7030: 6997: 6988: 6979: 6973: 6954:, one may write 6953: 6947: 6938: 6925: 6915: 6902: 6900: 6899: 6894: 6882: 6881: 6866: 6865: 6796: 6794: 6793: 6788: 6785: 6784: 6772: 6753: 6751: 6750: 6745: 6742: 6741: 6729: 6717: 6716: 6703: 6702: 6690: 6677: 6676: 6664: 6652: 6651: 6638: 6637: 6625: 6612: 6611: 6599: 6574: 6572: 6571: 6566: 6563: 6562: 6550: 6528: 6526: 6525: 6520: 6508: 6506: 6505: 6500: 6498: 6497: 6496: 6473: 6471: 6470: 6465: 6463: 6462: 6461: 6435: 6433: 6432: 6427: 6419: 6418: 6417: 6398: 6397: 6396: 6364: 6362: 6361: 6356: 6335: 6333: 6332: 6327: 6325: 6324: 6306: 6299: 6281: 6279: 6271: 6270: 6269: 6256: 6251: 6249: 6241: 6233: 6228: 6226: 6218: 6210: 6205: 6203: 6195: 6194: 6193: 6180: 6071: 6069: 6068: 6063: 6058: 6057: 6045: 6044: 6034: 6022: 6021: 6009: 6008: 5998: 5948:is expressed in 5937:is known as the 5919: 5917: 5916: 5911: 5906: 5905: 5893: 5892: 5882: 5822: 5812: 5801: 5795: 5789: 5783: 5777: 5754: 5745: 5743: 5742: 5737: 5735: 5732: 5687: 5683: 5677: 5671: 5662: 5660: 5659: 5654: 5652: 5649: 5590: 5576: 5554: 5544: 5542: 5541: 5536: 5534: 5531: 5470: 5464: 5459:with respect to 5458: 5452: 5446: 5440: 5421: 5415: 5409: 5387: 5377: 5354: 5352: 5351: 5346: 5331: 5329: 5328: 5323: 5308: 5306: 5305: 5300: 5284: 5283: 5241: 5240: 5230: 5215: 5196: 5195: 5153: 5152: 5142: 5127: 5099: 5097: 5096: 5091: 5089: 5088: 5072: 5070: 5069: 5064: 5061: 5060: 5018: 5017: 5007: 4992: 4970: 4968: 4967: 4962: 4959: 4958: 4916: 4915: 4905: 4890: 4850: 4848: 4847: 4842: 4811: 4809: 4808: 4803: 4787: 4786: 4750: 4749: 4739: 4724: 4705: 4704: 4668: 4667: 4657: 4642: 4611: 4609: 4608: 4603: 4601: 4600: 4584: 4582: 4581: 4576: 4573: 4572: 4536: 4535: 4525: 4510: 4488: 4486: 4485: 4480: 4477: 4476: 4440: 4439: 4429: 4414: 4379: 4377: 4376: 4371: 4355: 4354: 4327: 4294: 4292: 4291: 4286: 4240: 4238: 4237: 4232: 4212: 4210: 4209: 4204: 4159: 4158: 4088: 4069: 4068: 3998: 3979: 3978: 3908: 3889: 3888: 3818: 3796: 3795: 3725: 3697: 3695: 3694: 3689: 3677: 3675: 3674: 3669: 3657: 3655: 3654: 3649: 3613: 3604: 3602: 3601: 3596: 3589: 3586: 3584: 3562: 3559: 3557: 3534: 3523: 3521: 3520: 3515: 3512: 3497: 3461: 3459: 3458: 3453: 3438: 3399: 3397: 3396: 3391: 3384: 3383: 3353: 3306: 3295: 3294: 3264: 3209: 3207: 3206: 3201: 3189: 3187: 3186: 3181: 3169: 3167: 3166: 3161: 3140: 3138: 3137: 3132: 3120: 3118: 3117: 3112: 3091: 3089: 3088: 3083: 3061: 3059: 3058: 3053: 3041: 3039: 3038: 3033: 3020: 3018: 3017: 3012: 2887: 2881: 2872: 2866: 2857: 2855: 2854: 2849: 2830: 2829: 2828: 2796: 2794: 2793: 2788: 2772: 2771: 2770: 2748: 2747: 2746: 2724: 2723: 2722: 2690: 2688: 2687: 2682: 2669: 2668: 2667: 2648: 2647: 2646: 2627: 2626: 2625: 2599: 2591: 2583: 2506:Cyclic processes 2405: 2403: 2339:primitive notion 2292:heat of reaction 2275:believed in the 2208: 2206: 2205: 2200: 2171: 2169: 2168: 2163: 2144: 2142: 2141: 2136: 2124: 2122: 2121: 2116: 2104: 2102: 2101: 2096: 2077: 2075: 2074: 2069: 2054: 2052: 2051: 2046: 2033: 2000: 1998: 1997: 1992: 1982: 1968: 1966: 1965: 1960: 1945: 1943: 1942: 1937: 1925: 1923: 1922: 1917: 1907: 1892: 1890: 1889: 1884: 1867:isobaric process 1849: 1847: 1846: 1841: 1811: 1809: 1808: 1803: 1776: 1774: 1773: 1768: 1756: 1754: 1753: 1748: 1736: 1734: 1733: 1728: 1673:of a system, an 1665:, that modify a 1635: 1628: 1621: 1605: 1604: 1312:Key publications 1293: 1292:("living force") 1242:Brownian ratchet 1237:Entropy and life 1232:Entropy and time 1183: 1182: 1158: 1156: 1155: 1150: 1103: 1101: 1100: 1095: 1048: 1046: 1045: 1040: 993: 991: 990: 985: 887:Clausius theorem 882:Carnot's theorem 855: 853: 852: 847: 831: 829: 828: 823: 808: 806: 805: 800: 784: 782: 781: 776: 763: 762: 759: 757: 756: 751: 723: 721: 720: 715: 699: 697: 696: 691: 676: 674: 673: 668: 652: 650: 649: 644: 631: 630: 627: 625: 624: 619: 588: 586: 585: 580: 564: 562: 561: 556: 541: 539: 538: 533: 517: 515: 514: 509: 496: 495: 492: 490: 489: 484: 462: 461: 335: 334: 154: 153: 35: 21: 20: 11328: 11327: 11323: 11322: 11321: 11319: 11318: 11317: 11298: 11297: 11278:Project PHYSNET 11263: 11253: 11233: 11205: 11185: 11183:Further reading 11106:, (1955/1967). 11019: 10956:Kirkwood, J. G. 10815: 10531: 10526: 10525: 10520: 10516: 10511: 10507: 10502: 10498: 10493: 10489: 10484: 10480: 10475: 10471: 10466: 10462: 10457: 10453: 10448: 10444: 10439: 10435: 10416: 10412: 10383: 10379: 10339: 10333: 10329: 10324: 10320: 10315: 10311: 10302: 10298: 10293: 10289: 10281: 10277: 10272: 10268: 10262:Wayback Machine 10249: 10245: 10240: 10236: 10231: 10227: 10222: 10218: 10213: 10209: 10204: 10200: 10194:Wayback Machine 10184: 10180: 10175: 10171: 10166: 10162: 10157: 10153: 10145: 10141: 10136: 10132: 10127: 10120: 10115: 10108: 10103: 10099: 10094: 10090: 10082: 10078: 10073: 10066: 10061:Wayback Machine 10044: 10037: 10032: 10028: 10023: 10019: 10014: 10010: 10005: 10001: 9996: 9992: 9982: 9978: 9970: 9966: 9961: 9957: 9952: 9943: 9934: 9932: 9923: 9909: 9905: 9893: 9889: 9883:Wayback Machine 9870: 9866: 9861: 9857: 9852: 9848: 9839: 9835: 9830: 9826: 9816: 9814: 9812: 9801: 9793: 9789: 9781: 9777: 9772: 9768: 9763: 9759: 9743: 9739: 9722: 9718: 9698: 9694: 9689: 9685: 9680: 9676: 9671: 9667: 9655: 9651: 9646: 9642: 9637: 9633: 9625:10.1119/1.14740 9596: 9592: 9587: 9583: 9578: 9571: 9559: 9555: 9537:Kirkwood, J. G. 9535: 9531: 9514: 9510: 9496:Thermal Physics 9493: 9489: 9481: 9477: 9472: 9468: 9463: 9459: 9451: 9447: 9442: 9438: 9430: 9426: 9421: 9414: 9409: 9405: 9399:Kirkwood, J. G. 9397: 9393: 9388: 9384: 9379: 9370: 9365: 9358: 9353: 9344: 9336: 9323: 9308: 9301: 9289: 9282: 9277: 9273: 9268: 9264: 9259: 9255: 9248: 9243: 9234: 9216: 9212: 9188: 9184: 9179: 9175: 9167: 9163: 9155: 9151: 9146: 9135: 9130: 9121: 9106:: 61–82. 1850. 9089: 9085: 9068: 9064: 9055: 9051: 9046: 9042: 9034:2027/hvd.hxdhbq 8997: 8993: 8984: 8980: 8973: 8957: 8953: 8936: 8932: 8909: 8900: 8894:Wayback Machine 8885: 8881: 8869: 8865: 8860: 8856: 8849: 8845: 8840: 8807: 8787: 8770: 8764: 8755: 8706: 8702: 8692: 8688: 8681: 8668: 8664: 8654: 8650: 8643: 8604: 8602: 8591: 8589: 8586: 8585: 8547: 8543: 8533: 8529: 8522: 8509: 8505: 8495: 8491: 8484: 8442: 8440: 8437: 8436: 8404: 8400: 8391: 8387: 8385: 8382: 8381: 8345: 8341: 8331: 8327: 8320: 8281: 8279: 8268: 8266: 8263: 8262: 8224: 8220: 8210: 8206: 8199: 8157: 8155: 8152: 8151: 8127: 8124: 8123: 8106: 8102: 8100: 8097: 8096: 8090: 8084: 8037: 8033: 8028: 8021: 8017: 8011: 8000: 7958: 7956: 7953: 7952: 7940: 7919: 7916: 7915: 7898: 7894: 7892: 7889: 7888: 7853: 7840: 7836: 7831: 7824: 7820: 7814: 7803: 7766: 7762: 7757: 7755: 7752: 7751: 7726: 7722: 7720: 7717: 7716: 7700: 7697: 7696: 7679: 7675: 7670: 7667: 7666: 7643: 7629: 7611: and 7609: 7602: 7598: 7588: 7584: 7577: 7572: 7557: 7540: 7537: 7536: 7507: 7500: 7443: 7439: 7434: 7427: 7423: 7417: 7406: 7389: 7372: 7357: 7353: 7348: 7346: 7343: 7342: 7334: 7320: 7313: 7305: 7293: 7287: 7280: 7274: 7267: 7263: 7257: 7255: 7218: 7207: 7203: 7194: 7183: 7152: 7148: 7143: 7140: 7139: 7123: 7101: 7089: 7082: 7079: 7072: 7042: 7038: 7026: 7022: 7017: 7014: 7013: 7009:Also of course 6996: 6990: 6987: 6981: 6975: 6972: 6965: 6955: 6949: 6946: 6940: 6937: 6931: 6924: 6917: 6914: 6907: 6877: 6873: 6861: 6857: 6852: 6849: 6848: 6825: 6812: 6774: 6773: 6768: 6762: 6759: 6758: 6731: 6730: 6725: 6712: 6708: 6692: 6691: 6686: 6666: 6665: 6660: 6647: 6643: 6627: 6626: 6621: 6601: 6600: 6595: 6583: 6580: 6579: 6552: 6551: 6546: 6540: 6537: 6536: 6514: 6511: 6510: 6486: 6485: 6481: 6479: 6476: 6475: 6451: 6450: 6446: 6444: 6441: 6440: 6407: 6406: 6402: 6386: 6385: 6381: 6373: 6370: 6369: 6350: 6347: 6346: 6342: 6320: 6319: 6295: 6294: 6272: 6265: 6261: 6257: 6255: 6242: 6234: 6232: 6219: 6211: 6209: 6196: 6189: 6185: 6181: 6179: 6177: 6174: 6173: 6170: 6164: 6131:. The pressure 6106: 6099: 6092: 6081: 6053: 6049: 6040: 6036: 6030: 6017: 6013: 6004: 6000: 5994: 5967: 5964: 5963: 5958: 5947: 5936: 5929: 5901: 5897: 5888: 5884: 5878: 5839: 5836: 5835: 5814: 5803: 5797: 5791: 5785: 5779: 5773: 5731: 5694: 5691: 5690: 5679: 5673: 5667: 5648: 5599: 5596: 5595: 5578: 5564: 5549: 5530: 5482: 5479: 5478: 5466: 5460: 5454: 5448: 5442: 5423: 5417: 5416:, entropy, and 5411: 5405: 5383: 5373: 5370: 5361: 5337: 5334: 5333: 5317: 5314: 5313: 5246: 5236: 5232: 5217: 5216: 5205: 5158: 5148: 5144: 5129: 5128: 5117: 5108: 5105: 5104: 5084: 5080: 5078: 5075: 5074: 5023: 5013: 5009: 4994: 4993: 4982: 4976: 4973: 4972: 4921: 4911: 4907: 4892: 4891: 4880: 4874: 4871: 4870: 4866: 4826: 4823: 4822: 4755: 4745: 4741: 4726: 4725: 4714: 4673: 4663: 4659: 4644: 4643: 4632: 4623: 4620: 4619: 4596: 4592: 4590: 4587: 4586: 4541: 4531: 4527: 4512: 4511: 4500: 4494: 4491: 4490: 4445: 4435: 4431: 4416: 4415: 4404: 4398: 4395: 4394: 4386: 4329: 4328: 4317: 4311: 4308: 4307: 4277: 4274: 4273: 4254: 4248: 4226: 4223: 4222: 4090: 4089: 4078: 4000: 3999: 3988: 3910: 3909: 3898: 3820: 3819: 3808: 3727: 3726: 3715: 3706: 3703: 3702: 3683: 3680: 3679: 3663: 3660: 3659: 3643: 3640: 3639: 3585: 3574: 3558: 3547: 3541: 3538: 3537: 3502: 3469: 3467: 3464: 3463: 3410: 3408: 3405: 3404: 3355: 3354: 3343: 3299: 3266: 3265: 3254: 3218: 3215: 3214: 3195: 3192: 3191: 3175: 3172: 3171: 3146: 3143: 3142: 3126: 3123: 3122: 3097: 3094: 3093: 3077: 3074: 3073: 3065:internal energy 3047: 3044: 3043: 3027: 3024: 3023: 3006: 3003: 3002: 2975: 2969: 2948: 2893:George H. Bryan 2883: 2877: 2868: 2862: 2818: 2817: 2813: 2808: 2805: 2804: 2760: 2759: 2755: 2736: 2735: 2731: 2712: 2711: 2707: 2702: 2699: 2698: 2657: 2656: 2652: 2636: 2635: 2631: 2615: 2614: 2610: 2608: 2605: 2604: 2593: 2585: 2577: 2536: 2508: 2503: 2466: 2416:George H. Bryan 2412: 2404: 2401: 2400: 2396: 2392: 2390: 2386: 2382: 2379: 2376: 2350:internal energy 2346:Rudolf Clausius 2335: 2327:William Rankine 2323:Rudolf Clausius 2308:internal energy 2269:mechanical work 2215: 2185: 2182: 2181: 2154: 2151: 2150: 2130: 2127: 2126: 2110: 2107: 2106: 2090: 2087: 2086: 2063: 2060: 2059: 2013: 2010: 2009: 1974: 1971: 1970: 1951: 1948: 1947: 1931: 1928: 1927: 1902: 1899: 1898: 1878: 1875: 1874: 1820: 1817: 1816: 1794: 1791: 1790: 1787:Rudolf Clausius 1762: 1759: 1758: 1742: 1739: 1738: 1722: 1719: 1718: 1707: 1679:isolated system 1671:internal energy 1639: 1594: 1593: 1569: 1561: 1560: 1559: 1419: 1411: 1410: 1389: 1375: 1350: 1346: 1339: 1335: 1328: 1324: 1291: 1284: 1266: 1247:Maxwell's demon 1209: 1180: 1179: 1163: 1162: 1161: 1114: 1111: 1110: 1109: 1059: 1056: 1055: 1054: 1004: 1001: 1000: 999: 964: 961: 960: 959: 957:Internal energy 952: 937: 927: 926: 901: 876: 866: 865: 864: 838: 835: 834: 817: 814: 813: 791: 788: 787: 770: 767: 766: 742: 739: 738: 706: 703: 702: 685: 682: 681: 659: 656: 655: 638: 635: 634: 607: 604: 603: 598:Compressibility 571: 568: 567: 550: 547: 546: 524: 521: 520: 503: 500: 499: 475: 472: 471: 451: 441: 440: 421:Particle number 374: 333: 322: 312: 311: 270:Irreversibility 182:State of matter 149:Isolated system 134: 124: 123: 122: 97: 87: 86: 82:Non-equilibrium 74: 49: 41: 17: 12: 11: 5: 11326: 11316: 11315: 11310: 11296: 11295: 11281: 11262: 11261:External links 11259: 11258: 11257: 11251: 11245:. OUP Oxford. 11238: 11231: 11218: 11203: 11184: 11181: 11180: 11179: 11164: 11146: 11128: 11118: 11111: 11101: 11091: 11074: 11062: 11055:Pippard, A. B. 11052: 11038: 11023: 11018:978-0471915331 11017: 11000: 10985: 10970: 10963: 10953: 10946: 10928:(5): 329–331. 10917: 10904:, volume 1 of 10877: 10870:Thermodynamics 10866: 10859: 10852: 10833: 10826: 10812: 10797: 10788: 10773: 10766: 10708: 10677:(3): 355–386. 10659: 10641: 10634: 10616: 10603: 10591: 10576: 10554: 10547: 10530: 10527: 10524: 10523: 10514: 10505: 10496: 10487: 10478: 10469: 10460: 10451: 10442: 10433: 10410: 10377: 10350:(5): 693–702. 10327: 10318: 10309: 10296: 10287: 10275: 10266: 10243: 10234: 10225: 10216: 10207: 10198: 10178: 10169: 10160: 10151: 10139: 10130: 10118: 10106: 10097: 10088: 10076: 10064: 10048:Aust. J. Phys. 10035: 10026: 10017: 10008: 9999: 9990: 9976: 9974:(1949), p. 44. 9964: 9955: 9941: 9903: 9887: 9864: 9855: 9846: 9833: 9824: 9810: 9787: 9775: 9766: 9757: 9737: 9716: 9692: 9683: 9674: 9665: 9661:Theory of Heat 9657:Maxwell, J. C. 9649: 9640: 9631: 9590: 9581: 9569: 9553: 9529: 9508: 9506:, pp. 49, 227. 9487: 9475: 9466: 9457: 9453:Pippard, A. B. 9445: 9436: 9434:(1907), p. 47. 9424: 9412: 9403: 9391: 9382: 9368: 9356: 9342: 9321: 9299: 9295:Herbert Callen 9291:Pippard, A. B. 9280: 9271: 9262: 9253: 9232: 9210: 9182: 9173: 9161: 9149: 9133: 9119: 9083: 9062: 9049: 9040: 9011:(6): 385–404. 8991: 8978: 8971: 8951: 8930: 8919:(9): 954–966. 8898: 8879: 8863: 8854: 8842: 8841: 8839: 8836: 8835: 8834: 8829: 8824: 8818: 8813: 8806: 8803: 8737: 8736: 8727: 8725: 8714: 8709: 8705: 8701: 8695: 8691: 8684: 8680: 8676: 8671: 8667: 8663: 8657: 8653: 8646: 8642: 8638: 8635: 8632: 8629: 8626: 8623: 8619: 8614: 8610: 8607: 8601: 8598: 8594: 8578: 8577: 8568: 8566: 8555: 8550: 8546: 8542: 8536: 8532: 8525: 8521: 8517: 8512: 8508: 8504: 8498: 8494: 8487: 8483: 8479: 8475: 8472: 8469: 8465: 8462: 8459: 8455: 8452: 8449: 8445: 8415: 8412: 8407: 8403: 8399: 8394: 8390: 8376: 8375: 8366: 8364: 8353: 8348: 8344: 8340: 8334: 8330: 8323: 8319: 8315: 8312: 8309: 8306: 8303: 8300: 8296: 8291: 8287: 8284: 8278: 8275: 8271: 8255: 8254: 8245: 8243: 8232: 8227: 8223: 8219: 8213: 8209: 8202: 8198: 8194: 8190: 8187: 8184: 8180: 8177: 8174: 8170: 8167: 8164: 8160: 8131: 8109: 8105: 8075: 8074: 8065: 8063: 8052: 8040: 8036: 8031: 8024: 8020: 8014: 8009: 8006: 8003: 7999: 7994: 7990: 7987: 7984: 7980: 7976: 7973: 7969: 7965: 7961: 7939: 7936: 7923: 7901: 7897: 7883: 7882: 7873: 7871: 7860: 7843: 7839: 7834: 7827: 7823: 7817: 7812: 7809: 7806: 7802: 7797: 7793: 7790: 7786: 7782: 7779: 7775: 7769: 7765: 7760: 7729: 7725: 7704: 7682: 7678: 7674: 7663: 7662: 7650: 7636: 7632: 7627: 7623: 7619: 7616: 7605: 7601: 7597: 7591: 7587: 7580: 7576: 7570: 7567: 7564: 7560: 7555: 7551: 7547: 7544: 7505: 7498: 7471: 7470: 7461: 7459: 7446: 7442: 7437: 7430: 7426: 7420: 7415: 7412: 7409: 7405: 7400: 7396: 7392: 7387: 7383: 7379: 7375: 7370: 7366: 7360: 7356: 7351: 7332: 7318: 7311: 7304: 7301: 7261: 7253: 7245: 7244: 7235: 7233: 7210: 7206: 7202: 7197: 7192: 7189: 7186: 7182: 7177: 7173: 7169: 7165: 7161: 7155: 7151: 7147: 7122: 7119: 7100: 7097: 7087: 7077: 7069: 7068: 7057: 7053: 7050: 7045: 7041: 7037: 7034: 7029: 7025: 7021: 6994: 6985: 6970: 6963: 6944: 6935: 6922: 6912: 6904: 6903: 6892: 6888: 6885: 6880: 6876: 6872: 6869: 6864: 6860: 6856: 6824: 6821: 6811: 6808: 6783: 6780: 6777: 6771: 6767: 6755: 6754: 6740: 6737: 6734: 6728: 6724: 6720: 6715: 6711: 6707: 6701: 6698: 6695: 6689: 6685: 6681: 6675: 6672: 6669: 6663: 6659: 6655: 6650: 6646: 6642: 6636: 6633: 6630: 6624: 6620: 6616: 6610: 6607: 6604: 6598: 6594: 6590: 6587: 6561: 6558: 6555: 6549: 6545: 6518: 6495: 6492: 6489: 6484: 6460: 6457: 6454: 6449: 6437: 6436: 6425: 6422: 6416: 6413: 6410: 6405: 6401: 6395: 6392: 6389: 6384: 6380: 6377: 6354: 6341: 6338: 6323: 6318: 6315: 6312: 6309: 6305: 6302: 6298: 6293: 6290: 6287: 6284: 6278: 6275: 6268: 6264: 6260: 6254: 6248: 6245: 6240: 6237: 6231: 6225: 6222: 6217: 6214: 6208: 6202: 6199: 6192: 6188: 6184: 6166:Main article: 6163: 6162:Fluid dynamics 6160: 6104: 6097: 6090: 6079: 6073: 6072: 6061: 6056: 6052: 6048: 6043: 6039: 6033: 6029: 6025: 6020: 6016: 6012: 6007: 6003: 5997: 5993: 5989: 5986: 5983: 5980: 5977: 5974: 5971: 5956: 5945: 5934: 5927: 5921: 5920: 5909: 5904: 5900: 5896: 5891: 5887: 5881: 5877: 5873: 5870: 5867: 5864: 5861: 5858: 5855: 5852: 5849: 5846: 5843: 5758: 5757: 5748: 5746: 5725: 5722: 5719: 5716: 5713: 5710: 5707: 5704: 5701: 5698: 5664: 5663: 5630: 5627: 5624: 5621: 5618: 5615: 5612: 5609: 5606: 5603: 5546: 5545: 5507: 5504: 5501: 5498: 5495: 5492: 5489: 5486: 5378:, rather than 5369: 5366: 5360: 5357: 5344: 5341: 5321: 5310: 5309: 5298: 5294: 5291: 5288: 5282: 5279: 5276: 5273: 5270: 5267: 5264: 5261: 5258: 5255: 5252: 5249: 5244: 5239: 5235: 5229: 5226: 5223: 5220: 5214: 5211: 5208: 5204: 5200: 5194: 5191: 5188: 5185: 5182: 5179: 5176: 5173: 5170: 5167: 5164: 5161: 5156: 5151: 5147: 5141: 5138: 5135: 5132: 5126: 5123: 5120: 5116: 5112: 5087: 5083: 5059: 5056: 5053: 5050: 5047: 5044: 5041: 5038: 5035: 5032: 5029: 5026: 5021: 5016: 5012: 5006: 5003: 5000: 4997: 4991: 4988: 4985: 4981: 4957: 4954: 4951: 4948: 4945: 4942: 4939: 4936: 4933: 4930: 4927: 4924: 4919: 4914: 4910: 4904: 4901: 4898: 4895: 4889: 4886: 4883: 4879: 4865: 4862: 4861: 4860: 4853: 4852: 4839: 4836: 4833: 4830: 4813: 4812: 4801: 4797: 4794: 4791: 4785: 4782: 4779: 4776: 4773: 4770: 4767: 4764: 4761: 4758: 4753: 4748: 4744: 4738: 4735: 4732: 4729: 4723: 4720: 4717: 4713: 4709: 4703: 4700: 4697: 4694: 4691: 4688: 4685: 4682: 4679: 4676: 4671: 4666: 4662: 4656: 4653: 4650: 4647: 4641: 4638: 4635: 4631: 4627: 4599: 4595: 4571: 4568: 4565: 4562: 4559: 4556: 4553: 4550: 4547: 4544: 4539: 4534: 4530: 4524: 4521: 4518: 4515: 4509: 4506: 4503: 4499: 4475: 4472: 4469: 4466: 4463: 4460: 4457: 4454: 4451: 4448: 4443: 4438: 4434: 4428: 4425: 4422: 4419: 4413: 4410: 4407: 4403: 4385: 4382: 4381: 4380: 4369: 4365: 4362: 4359: 4353: 4350: 4347: 4344: 4341: 4338: 4335: 4332: 4326: 4323: 4320: 4316: 4284: 4281: 4247: 4244: 4243: 4242: 4230: 4214: 4213: 4202: 4199: 4196: 4193: 4190: 4187: 4184: 4181: 4178: 4175: 4172: 4169: 4166: 4163: 4157: 4154: 4151: 4148: 4145: 4142: 4139: 4136: 4133: 4130: 4127: 4124: 4120: 4117: 4114: 4111: 4108: 4105: 4102: 4099: 4096: 4093: 4087: 4084: 4081: 4077: 4073: 4067: 4064: 4061: 4058: 4055: 4052: 4049: 4046: 4043: 4040: 4037: 4034: 4030: 4027: 4024: 4021: 4018: 4015: 4012: 4009: 4006: 4003: 3997: 3994: 3991: 3987: 3983: 3977: 3974: 3971: 3968: 3965: 3962: 3959: 3956: 3953: 3950: 3947: 3944: 3940: 3937: 3934: 3931: 3928: 3925: 3922: 3919: 3916: 3913: 3907: 3904: 3901: 3897: 3893: 3887: 3884: 3881: 3878: 3875: 3872: 3869: 3866: 3863: 3860: 3857: 3854: 3850: 3847: 3844: 3841: 3838: 3835: 3832: 3829: 3826: 3823: 3817: 3814: 3811: 3807: 3803: 3800: 3794: 3791: 3788: 3785: 3782: 3779: 3776: 3773: 3770: 3767: 3764: 3761: 3757: 3754: 3751: 3748: 3745: 3742: 3739: 3736: 3733: 3730: 3724: 3721: 3718: 3714: 3710: 3687: 3667: 3647: 3630: 3629: 3620: 3617: 3616: 3607: 3605: 3594: 3583: 3580: 3577: 3573: 3569: 3566: 3556: 3553: 3550: 3546: 3511: 3508: 3505: 3500: 3496: 3493: 3490: 3487: 3484: 3481: 3478: 3475: 3472: 3451: 3448: 3445: 3441: 3437: 3434: 3431: 3428: 3425: 3422: 3419: 3416: 3413: 3401: 3400: 3389: 3382: 3379: 3376: 3373: 3370: 3367: 3364: 3361: 3358: 3352: 3349: 3346: 3342: 3338: 3335: 3332: 3329: 3326: 3323: 3320: 3317: 3314: 3311: 3305: 3302: 3293: 3290: 3287: 3284: 3281: 3278: 3275: 3272: 3269: 3263: 3260: 3257: 3253: 3249: 3246: 3243: 3240: 3237: 3234: 3231: 3228: 3225: 3222: 3199: 3179: 3159: 3156: 3153: 3150: 3130: 3110: 3107: 3104: 3101: 3081: 3051: 3031: 3010: 2971:Main article: 2968: 2965: 2947: 2944: 2859: 2858: 2847: 2842: 2839: 2836: 2833: 2827: 2824: 2821: 2816: 2812: 2798: 2797: 2786: 2781: 2778: 2775: 2769: 2766: 2763: 2758: 2754: 2751: 2745: 2742: 2739: 2734: 2730: 2727: 2721: 2718: 2715: 2710: 2706: 2692: 2691: 2680: 2675: 2672: 2666: 2663: 2660: 2655: 2651: 2645: 2642: 2639: 2634: 2630: 2624: 2621: 2618: 2613: 2567: 2566: 2535: 2532: 2507: 2504: 2502: 2499: 2483: 2482: 2481: 2480: 2465: 2462: 2411: 2408: 2398: 2397: 2394: 2388: 2387: 2384: 2380: 2377: 2334: 2331: 2277:caloric theory 2242:caloric theory 2214: 2211: 2198: 2195: 2192: 2189: 2178:isochoric work 2174:path dependent 2161: 2158: 2134: 2114: 2094: 2067: 2056: 2055: 2044: 2041: 2038: 2032: 2029: 2026: 2023: 2020: 2017: 1990: 1987: 1981: 1978: 1958: 1955: 1935: 1915: 1912: 1906: 1882: 1852: 1851: 1839: 1836: 1833: 1830: 1827: 1824: 1801: 1798: 1766: 1746: 1726: 1706: 1703: 1699:closed systems 1641: 1640: 1638: 1637: 1630: 1623: 1615: 1612: 1611: 1610: 1609: 1596: 1595: 1592: 1591: 1586: 1581: 1576: 1570: 1567: 1566: 1563: 1562: 1558: 1557: 1552: 1547: 1542: 1537: 1532: 1527: 1522: 1517: 1512: 1507: 1502: 1497: 1492: 1487: 1482: 1477: 1472: 1467: 1462: 1457: 1452: 1447: 1442: 1437: 1432: 1427: 1421: 1420: 1417: 1416: 1413: 1412: 1407: 1406: 1405: 1404: 1399: 1391: 1390: 1388: 1387: 1384: 1380: 1377: 1376: 1374: 1373: 1368: 1366:Thermodynamics 1362: 1359: 1358: 1354: 1353: 1352: 1351: 1342: 1340: 1331: 1329: 1320: 1315: 1314: 1308: 1307: 1306: 1305: 1300: 1295: 1283: 1282: 1280:Caloric theory 1276: 1273: 1272: 1268: 1267: 1265: 1264: 1259: 1254: 1249: 1244: 1239: 1234: 1228: 1225: 1224: 1218: 1217: 1216: 1215: 1208: 1207: 1202: 1197: 1191: 1188: 1187: 1181: 1178: 1177: 1174: 1170: 1169: 1168: 1165: 1164: 1160: 1159: 1148: 1145: 1142: 1139: 1136: 1133: 1130: 1127: 1124: 1121: 1118: 1104: 1093: 1090: 1087: 1084: 1081: 1078: 1075: 1072: 1069: 1066: 1063: 1049: 1038: 1035: 1032: 1029: 1026: 1023: 1020: 1017: 1014: 1011: 1008: 994: 983: 980: 977: 974: 971: 968: 953: 951: 950: 945: 939: 938: 933: 932: 929: 928: 925: 924: 917: 912: 907: 900: 899: 894: 889: 884: 878: 877: 872: 871: 868: 867: 861: 860: 857: 856: 845: 842: 832: 821: 810: 809: 798: 795: 785: 774: 760: 749: 746: 736: 729: 728: 725: 724: 713: 710: 700: 689: 678: 677: 666: 663: 653: 642: 628: 617: 614: 611: 601: 594: 593: 590: 589: 578: 575: 565: 554: 543: 542: 531: 528: 518: 507: 493: 482: 479: 469: 460: 459: 458: 452: 447: 446: 443: 442: 437: 436: 435: 434: 429: 424: 413: 402: 383: 382: 376: 375: 373: 372: 367: 361: 358: 357: 351: 350: 349: 348: 343: 324: 323: 318: 317: 314: 313: 308: 307: 306: 305: 300: 295: 287: 286: 280: 279: 278: 277: 272: 267: 262: 260:Free expansion 257: 252: 247: 242: 237: 232: 227: 222: 214: 213: 207: 206: 205: 204: 199: 197:Control volume 194: 189: 187:Phase (matter) 184: 179: 174: 169: 161: 160: 152: 151: 146: 141: 135: 130: 129: 126: 125: 121: 120: 115: 110: 105: 99: 98: 93: 92: 89: 88: 85: 84: 73: 72: 67: 62: 57: 51: 50: 47: 46: 43: 42: 37:The classical 36: 28: 27: 25:Thermodynamics 15: 9: 6: 4: 3: 2: 11325: 11314: 11311: 11309: 11306: 11305: 11303: 11293: 11292: 11287: 11286: 11282: 11279: 11275: 11271: 11270: 11265: 11264: 11254: 11248: 11244: 11239: 11234: 11228: 11224: 11219: 11214: 11210: 11206: 11204:0-674-75325-9 11200: 11195: 11194: 11187: 11186: 11177: 11176:0-444-50426-5 11173: 11169: 11165: 11162: 11161:0-12-701350-4 11158: 11154: 11150: 11147: 11144: 11143:0-387-90403-4 11140: 11136: 11132: 11129: 11126: 11122: 11119: 11116: 11112: 11109: 11105: 11104:Prigogine, I. 11102: 11099: 11095: 11094:Prigogine, I. 11092: 11088: 11084: 11080: 11075: 11073: 11071: 11067:(1897/1903). 11066: 11063: 11060: 11057:(1957/1966). 11056: 11053: 11050: 11046: 11042: 11039: 11036: 11035:0-471-62430-6 11032: 11028: 11024: 11020: 11014: 11010: 11006: 11001: 10998: 10994: 10990: 10986: 10983: 10982:0-19-851142-6 10979: 10975: 10971: 10968: 10964: 10961: 10957: 10954: 10951: 10947: 10943: 10939: 10935: 10931: 10927: 10923: 10918: 10915: 10914:1-86094-347-0 10911: 10907: 10903: 10899: 10895: 10891: 10890: 10885: 10881: 10880:Helmholtz, H. 10878: 10875: 10871: 10867: 10864: 10860: 10857: 10853: 10850: 10849:0-471-30280-5 10846: 10842: 10838: 10837:Prigogine, I. 10834: 10831: 10827: 10824: 10821: 10813: 10810: 10809:0-521-23682-7 10806: 10802: 10798: 10795: 10794: 10789: 10786: 10782: 10778: 10774: 10771: 10767: 10764: 10760: 10756: 10750: 10745: 10741: 10737: 10733: 10729: 10725: 10721: 10717: 10713: 10709: 10706: 10702: 10698: 10692: 10688: 10684: 10680: 10676: 10672: 10668: 10664: 10660: 10657: 10656:0-471-86256-8 10653: 10649: 10646:(1960/1985), 10645: 10644:Callen, H. B. 10642: 10639: 10635: 10632: 10628: 10624: 10620: 10617: 10614: 10612: 10607: 10604: 10601: 10600: 10595: 10592: 10589: 10588:0-88318-797-3 10585: 10581: 10577: 10574: 10570: 10566: 10562: 10559:(1991/2007). 10558: 10555: 10552: 10548: 10545: 10544:0-521-25445-0 10541: 10537: 10533: 10532: 10529:Cited sources 10518: 10509: 10500: 10491: 10482: 10473: 10464: 10455: 10446: 10437: 10429: 10425: 10421: 10414: 10405: 10400: 10396: 10392: 10388: 10381: 10373: 10369: 10365: 10361: 10357: 10353: 10349: 10345: 10338: 10331: 10322: 10313: 10306: 10300: 10291: 10284: 10283:Callen, H. B. 10279: 10270: 10263: 10259: 10256: 10252: 10247: 10238: 10229: 10220: 10211: 10202: 10195: 10191: 10188: 10182: 10173: 10164: 10155: 10148: 10147:Prigogine, I. 10143: 10134: 10125: 10123: 10113: 10111: 10101: 10092: 10085: 10080: 10071: 10069: 10062: 10058: 10055: 10053: 10049: 10042: 10040: 10030: 10021: 10012: 10003: 9994: 9986: 9980: 9973: 9968: 9959: 9950: 9948: 9946: 9930: 9926: 9921: 9917: 9913: 9907: 9900: 9896: 9891: 9884: 9880: 9877: 9873: 9868: 9859: 9850: 9844:(1971), p. 8. 9843: 9842:Prigogine, I. 9837: 9828: 9813: 9811:0-07-069712-4 9807: 9800: 9799: 9791: 9784: 9783:Callen, H. B. 9779: 9770: 9761: 9754: 9750: 9746: 9741: 9734: 9730: 9726: 9720: 9713: 9709: 9705: 9701: 9696: 9687: 9678: 9669: 9662: 9658: 9653: 9644: 9635: 9626: 9621: 9617: 9613: 9609: 9605: 9601: 9594: 9585: 9576: 9574: 9566: 9563:(1949/1967). 9562: 9557: 9550: 9549:1-4020-0788-4 9546: 9542: 9538: 9533: 9526: 9525:0-13-100065-9 9522: 9518: 9512: 9505: 9504:0-7167-1088-9 9501: 9497: 9491: 9484: 9483:Callen, H. B. 9479: 9470: 9461: 9454: 9449: 9440: 9433: 9428: 9419: 9417: 9407: 9400: 9395: 9386: 9377: 9375: 9373: 9363: 9361: 9351: 9349: 9347: 9339: 9334: 9332: 9330: 9328: 9326: 9317: 9313: 9306: 9304: 9296: 9292: 9287: 9285: 9275: 9266: 9257: 9246: 9241: 9239: 9237: 9229: 9226: 9223: 9219: 9214: 9206: 9201: 9196: 9191: 9186: 9177: 9170: 9165: 9158: 9153: 9144: 9142: 9140: 9138: 9128: 9126: 9124: 9114: 9109: 9105: 9101: 9097: 9092: 9087: 9080: 9079:9780198567691 9076: 9072: 9066: 9059: 9053: 9044: 9035: 9030: 9026: 9022: 9018: 9014: 9010: 9006: 9002: 8995: 8988: 8982: 8974: 8968: 8964: 8963: 8955: 8948: 8944: 8940: 8934: 8926: 8922: 8918: 8914: 8907: 8905: 8903: 8895: 8891: 8888: 8883: 8876: 8874: 8867: 8858: 8852: 8847: 8843: 8833: 8830: 8828: 8825: 8822: 8819: 8817: 8814: 8812: 8809: 8808: 8802: 8798: 8796: 8790: 8784: 8780: 8777: 8773: 8769:. Therefore: 8767: 8761: 8758: 8751: 8747: 8743: 8735: 8728: 8726: 8712: 8707: 8703: 8693: 8689: 8682: 8678: 8674: 8669: 8665: 8655: 8644: 8640: 8636: 8633: 8627: 8624: 8617: 8612: 8608: 8599: 8596: 8584: 8583: 8576: 8569: 8567: 8553: 8548: 8544: 8534: 8530: 8523: 8519: 8515: 8510: 8506: 8496: 8485: 8481: 8477: 8473: 8467: 8463: 8460: 8457: 8453: 8450: 8447: 8435: 8434: 8431: 8429: 8413: 8410: 8405: 8401: 8397: 8392: 8388: 8374: 8367: 8365: 8351: 8346: 8342: 8332: 8328: 8321: 8317: 8313: 8310: 8304: 8301: 8294: 8289: 8285: 8276: 8273: 8261: 8260: 8253: 8246: 8244: 8230: 8225: 8221: 8211: 8207: 8200: 8196: 8192: 8188: 8182: 8178: 8175: 8172: 8168: 8165: 8162: 8150: 8149: 8146: 8143: 8129: 8107: 8103: 8093: 8087: 8082: 8073: 8066: 8064: 8050: 8038: 8034: 8022: 8018: 8012: 8007: 8004: 8001: 7997: 7992: 7988: 7982: 7978: 7974: 7967: 7963: 7951: 7950: 7947: 7944: 7935: 7921: 7899: 7895: 7881: 7874: 7872: 7858: 7841: 7837: 7825: 7821: 7815: 7810: 7807: 7804: 7800: 7795: 7791: 7788: 7784: 7780: 7777: 7773: 7767: 7763: 7750: 7749: 7746: 7743: 7727: 7723: 7702: 7680: 7676: 7672: 7648: 7634: 7625: 7621: 7617: 7614: 7603: 7599: 7595: 7589: 7585: 7578: 7574: 7568: 7565: 7562: 7553: 7549: 7545: 7542: 7535: 7534: 7533: 7529: 7525: 7523: 7522: 7517: 7516: 7510: 7508: 7501: 7494: 7490: 7486: 7482: 7478: 7469: 7462: 7460: 7444: 7440: 7428: 7424: 7418: 7413: 7410: 7407: 7403: 7398: 7394: 7385: 7381: 7377: 7368: 7364: 7358: 7354: 7341: 7340: 7337: 7335: 7328: 7324: 7317: 7310: 7300: 7296: 7290: 7283: 7277: 7270: 7264: 7252: 7243: 7236: 7234: 7208: 7204: 7195: 7190: 7187: 7184: 7180: 7175: 7171: 7167: 7163: 7159: 7153: 7149: 7138: 7137: 7134: 7130: 7126: 7118: 7114: 7110: 7107: 7096: 7094: 7086: 7076: 7055: 7051: 7048: 7043: 7039: 7032: 7027: 7023: 7012: 7011: 7010: 7007: 7003: 7001: 6993: 6984: 6978: 6969: 6962: 6958: 6952: 6943: 6934: 6928: 6921: 6911: 6890: 6886: 6883: 6878: 6874: 6867: 6862: 6858: 6847: 6846: 6845: 6842: 6838: 6833: 6831: 6820: 6816: 6807: 6805: 6799: 6769: 6765: 6757:The quantity 6726: 6722: 6718: 6713: 6709: 6705: 6687: 6683: 6679: 6661: 6657: 6653: 6648: 6644: 6640: 6622: 6618: 6614: 6596: 6592: 6588: 6585: 6578: 6577: 6576: 6547: 6543: 6533: 6530: 6516: 6482: 6447: 6423: 6420: 6403: 6399: 6382: 6378: 6375: 6368: 6367: 6366: 6352: 6337: 6316: 6310: 6303: 6300: 6296: 6288: 6282: 6276: 6273: 6266: 6262: 6258: 6246: 6243: 6238: 6235: 6229: 6223: 6220: 6215: 6212: 6206: 6200: 6197: 6190: 6186: 6182: 6169: 6159: 6156: 6152: 6150: 6146: 6141: 6138: 6134: 6130: 6126: 6122: 6116: 6114: 6108: 6103: 6096: 6089: 6085: 6078: 6059: 6054: 6050: 6046: 6041: 6037: 6031: 6027: 6023: 6018: 6014: 6010: 6005: 6001: 5995: 5991: 5987: 5984: 5981: 5978: 5975: 5972: 5969: 5962: 5961: 5960: 5955: 5951: 5944: 5940: 5933: 5926: 5907: 5902: 5898: 5894: 5889: 5885: 5879: 5875: 5871: 5868: 5865: 5862: 5859: 5856: 5853: 5850: 5847: 5844: 5841: 5834: 5833: 5832: 5830: 5824: 5821: 5817: 5811: 5807: 5800: 5794: 5788: 5782: 5776: 5771: 5767: 5766: 5756: 5749: 5747: 5723: 5720: 5717: 5714: 5711: 5708: 5705: 5702: 5699: 5696: 5689: 5688: 5685: 5682: 5676: 5670: 5628: 5625: 5622: 5619: 5616: 5613: 5610: 5607: 5604: 5601: 5594: 5593: 5592: 5589: 5585: 5581: 5575: 5571: 5567: 5562: 5558: 5553: 5505: 5502: 5499: 5496: 5493: 5490: 5487: 5484: 5477: 5476: 5475: 5472: 5469: 5463: 5457: 5451: 5445: 5438: 5434: 5430: 5426: 5420: 5414: 5408: 5402: 5400: 5395: 5391: 5386: 5381: 5376: 5365: 5356: 5342: 5319: 5296: 5292: 5286: 5242: 5237: 5233: 5212: 5206: 5202: 5198: 5154: 5149: 5145: 5124: 5118: 5114: 5110: 5103: 5102: 5101: 5085: 5081: 5019: 5014: 5010: 4989: 4983: 4979: 4917: 4912: 4908: 4887: 4881: 4877: 4858: 4857: 4856: 4837: 4834: 4831: 4821: 4820: 4819: 4816: 4799: 4795: 4789: 4751: 4746: 4742: 4721: 4715: 4711: 4707: 4669: 4664: 4660: 4639: 4633: 4629: 4625: 4618: 4617: 4616: 4613: 4597: 4593: 4537: 4532: 4528: 4507: 4501: 4497: 4441: 4436: 4432: 4411: 4405: 4401: 4392: 4367: 4363: 4357: 4324: 4318: 4314: 4306: 4305: 4304: 4300: 4298: 4282: 4271: 4267: 4263: 4262:sensible heat 4259: 4258:heat transfer 4253: 4228: 4219: 4218: 4217: 4200: 4194: 4188: 4182: 4179: 4173: 4167: 4164: 4161: 4137: 4118: 4085: 4079: 4075: 4071: 4047: 4028: 3995: 3989: 3985: 3981: 3957: 3938: 3905: 3899: 3895: 3891: 3867: 3848: 3815: 3809: 3805: 3801: 3798: 3774: 3755: 3722: 3716: 3712: 3708: 3701: 3700: 3699: 3685: 3665: 3658:to the state 3645: 3637: 3636: 3632:The formula ( 3627: 3626: 3621: 3615: 3608: 3606: 3592: 3581: 3575: 3571: 3567: 3564: 3554: 3548: 3544: 3536: 3535: 3530: 3529: 3528: 3525: 3509: 3503: 3498: 3449: 3443: 3439: 3387: 3350: 3344: 3340: 3336: 3330: 3324: 3321: 3315: 3309: 3261: 3255: 3251: 3247: 3241: 3235: 3232: 3226: 3220: 3213: 3212: 3211: 3197: 3190:to the state 3177: 3154: 3148: 3128: 3105: 3099: 3079: 3070: 3067: 3066: 3049: 3029: 3008: 2999: 2995: 2991: 2987: 2985: 2979: 2974: 2964: 2962: 2958: 2952: 2943: 2939: 2937: 2936:heat capacity 2933: 2927: 2923: 2920: 2916: 2912: 2908: 2904: 2902: 2898: 2894: 2889: 2886: 2880: 2874: 2871: 2865: 2845: 2840: 2837: 2834: 2831: 2814: 2803: 2802: 2801: 2784: 2779: 2773: 2756: 2749: 2732: 2725: 2708: 2697: 2696: 2695: 2678: 2673: 2670: 2653: 2649: 2632: 2628: 2611: 2603: 2602: 2601: 2597: 2589: 2581: 2574: 2571: 2563: 2562: 2561: 2560:(1897/1903): 2559: 2554: 2551: 2549: 2545: 2540: 2531: 2529: 2525: 2520: 2516: 2512: 2498: 2496: 2491: 2489: 2477: 2476: 2475: 2474: 2473: 2470: 2461: 2459: 2453: 2451: 2450: 2444: 2443:adiabatically 2439: 2435: 2433: 2429: 2425: 2421: 2417: 2407: 2372: 2367: 2362: 2358: 2353: 2351: 2347: 2342: 2340: 2330: 2328: 2324: 2319: 2317: 2313: 2309: 2305: 2301: 2296: 2293: 2289: 2285: 2280: 2278: 2274: 2270: 2264: 2259: 2256: 2252: 2251: 2245: 2243: 2238: 2236: 2232: 2228: 2224: 2220: 2210: 2196: 2193: 2190: 2179: 2175: 2159: 2148: 2132: 2112: 2092: 2083: 2081: 2065: 2042: 2039: 2030: 2027: 2024: 2021: 2018: 2008: 2007: 2006: 2004: 1988: 1979: 1976: 1956: 1933: 1913: 1904: 1896: 1880: 1872: 1868: 1863: 1861: 1857: 1837: 1834: 1831: 1828: 1825: 1815: 1814: 1813: 1812:, is written 1799: 1788: 1784: 1780: 1764: 1744: 1724: 1716: 1715:algebraic sum 1712: 1702: 1700: 1696: 1690: 1687: 1682: 1680: 1676: 1672: 1668: 1664: 1660: 1656: 1652: 1648: 1636: 1631: 1629: 1624: 1622: 1617: 1616: 1614: 1613: 1608: 1600: 1599: 1598: 1597: 1590: 1587: 1585: 1582: 1580: 1579:Self-assembly 1577: 1575: 1572: 1571: 1565: 1564: 1556: 1553: 1551: 1550:van der Waals 1548: 1546: 1543: 1541: 1538: 1536: 1533: 1531: 1528: 1526: 1523: 1521: 1518: 1516: 1513: 1511: 1508: 1506: 1503: 1501: 1498: 1496: 1493: 1491: 1488: 1486: 1483: 1481: 1478: 1476: 1475:von Helmholtz 1473: 1471: 1468: 1466: 1463: 1461: 1458: 1456: 1453: 1451: 1448: 1446: 1443: 1441: 1438: 1436: 1433: 1431: 1428: 1426: 1423: 1422: 1415: 1414: 1403: 1400: 1398: 1395: 1394: 1393: 1392: 1385: 1382: 1381: 1379: 1378: 1372: 1369: 1367: 1364: 1363: 1361: 1360: 1356: 1355: 1349: 1348: 1341: 1338: 1337: 1330: 1327: 1326: 1319: 1318: 1317: 1316: 1313: 1310: 1309: 1304: 1301: 1299: 1296: 1294: 1290: 1286: 1285: 1281: 1278: 1277: 1275: 1274: 1270: 1269: 1263: 1260: 1258: 1255: 1253: 1250: 1248: 1245: 1243: 1240: 1238: 1235: 1233: 1230: 1229: 1227: 1226: 1223: 1220: 1219: 1214: 1211: 1210: 1206: 1203: 1201: 1198: 1196: 1193: 1192: 1190: 1189: 1185: 1184: 1175: 1172: 1171: 1167: 1166: 1146: 1143: 1140: 1137: 1134: 1128: 1125: 1122: 1116: 1108: 1105: 1091: 1088: 1085: 1082: 1079: 1073: 1070: 1067: 1061: 1053: 1050: 1036: 1033: 1030: 1027: 1024: 1018: 1015: 1012: 1006: 998: 995: 978: 975: 972: 966: 958: 955: 954: 949: 946: 944: 941: 940: 936: 931: 930: 923: 922: 918: 916: 913: 911: 908: 906: 903: 902: 898: 897:Ideal gas law 895: 893: 890: 888: 885: 883: 880: 879: 875: 870: 869: 843: 833: 819: 812: 811: 796: 786: 772: 765: 764: 761: 747: 744: 737: 734: 731: 730: 711: 701: 687: 680: 679: 664: 654: 640: 633: 632: 629: 615: 612: 609: 602: 599: 596: 595: 576: 566: 552: 545: 544: 529: 519: 505: 498: 497: 494: 480: 477: 470: 467: 464: 463: 457: 454: 453: 450: 445: 444: 433: 430: 428: 427:Vapor quality 425: 423: 422: 417: 414: 412: 411: 406: 403: 400: 396: 395: 390: 387: 386: 385: 384: 381: 378: 377: 371: 368: 366: 363: 362: 360: 359: 356: 353: 352: 347: 344: 342: 339: 338: 337: 336: 332: 328: 321: 316: 315: 304: 301: 299: 296: 294: 291: 290: 289: 288: 285: 282: 281: 276: 273: 271: 268: 266: 265:Reversibility 263: 261: 258: 256: 253: 251: 248: 246: 243: 241: 238: 236: 233: 231: 228: 226: 223: 221: 218: 217: 216: 215: 212: 209: 208: 203: 200: 198: 195: 193: 190: 188: 185: 183: 180: 178: 175: 173: 170: 168: 165: 164: 163: 162: 159: 156: 155: 150: 147: 145: 142: 140: 139:Closed system 137: 136: 133: 128: 127: 119: 116: 114: 111: 109: 106: 104: 101: 100: 96: 91: 90: 83: 79: 76: 75: 71: 68: 66: 63: 61: 58: 56: 53: 52: 45: 44: 40: 34: 30: 29: 26: 23: 22: 19: 11290: 11284: 11268: 11267:MISN-0-158, 11242: 11222: 11192: 11167: 11152: 11134: 11124: 11114: 11107: 11097: 11078: 11069: 11058: 11048: 11047:, volume 1, 11044: 11026: 11004: 10988: 10973: 10966: 10959: 10949: 10925: 10921: 10905: 10901: 10897: 10893: 10888: 10883: 10873: 10869: 10862: 10855: 10840: 10829: 10822: 10819: 10800: 10792: 10776: 10769: 10763:Google Books 10758: 10723: 10719: 10712:Clausius, R. 10704: 10674: 10670: 10647: 10637: 10622: 10610: 10606:Bryan, G. H. 10598: 10579: 10560: 10550: 10535: 10517: 10508: 10499: 10490: 10481: 10472: 10463: 10454: 10445: 10436: 10419: 10413: 10394: 10390: 10380: 10347: 10343: 10330: 10321: 10312: 10299: 10290: 10278: 10269: 10246: 10237: 10228: 10219: 10210: 10201: 10181: 10172: 10163: 10154: 10142: 10133: 10100: 10091: 10079: 10051: 10047: 10029: 10020: 10011: 10002: 9993: 9979: 9967: 9958: 9933:. Retrieved 9919: 9915: 9911: 9906: 9898: 9890: 9867: 9858: 9849: 9836: 9827: 9815:. Retrieved 9797: 9790: 9778: 9769: 9760: 9752: 9740: 9724: 9719: 9703: 9695: 9686: 9677: 9668: 9660: 9652: 9643: 9634: 9607: 9603: 9593: 9584: 9564: 9556: 9540: 9532: 9516: 9511: 9495: 9490: 9478: 9469: 9460: 9448: 9439: 9432:Bryan, G. H. 9427: 9406: 9394: 9385: 9340:, C. (1909). 9338:Carathéodory 9315: 9311: 9274: 9265: 9256: 9251:, pp. 31–45. 9227: 9224: 9221: 9213: 9190:Bryan, G. H. 9185: 9176: 9169:Clausius, R. 9164: 9157:Clausius, R. 9152: 9103: 9099: 9086: 9070: 9065: 9057: 9052: 9043: 9008: 9004: 8994: 8986: 8981: 8961: 8954: 8941:. Springer. 8938: 8933: 8916: 8912: 8882: 8872: 8866: 8857: 8846: 8799: 8794: 8788: 8782: 8778: 8775: 8771: 8765: 8759: 8756: 8752: 8748: 8744: 8740: 8729: 8570: 8427: 8379: 8368: 8247: 8144: 8091: 8085: 8080: 8078: 8067: 7945: 7941: 7886: 7875: 7744: 7664: 7530: 7526: 7519: 7513: 7511: 7503: 7496: 7492: 7488: 7484: 7480: 7476: 7474: 7463: 7330: 7326: 7322: 7315: 7308: 7306: 7294: 7288: 7281: 7275: 7268: 7259: 7250: 7248: 7237: 7131: 7127: 7124: 7115: 7111: 7102: 7084: 7074: 7070: 7008: 7004: 6991: 6982: 6976: 6967: 6960: 6956: 6950: 6941: 6932: 6929: 6919: 6909: 6905: 6834: 6826: 6817: 6813: 6800: 6756: 6534: 6531: 6438: 6343: 6171: 6157: 6153: 6148: 6144: 6142: 6136: 6132: 6128: 6124: 6120: 6117: 6109: 6101: 6094: 6087: 6076: 6074: 5953: 5942: 5931: 5924: 5922: 5828: 5825: 5819: 5815: 5809: 5805: 5798: 5792: 5786: 5780: 5774: 5763: 5761: 5750: 5680: 5674: 5668: 5665: 5587: 5583: 5579: 5573: 5569: 5565: 5563:is given by 5551: 5547: 5473: 5467: 5461: 5455: 5449: 5443: 5436: 5432: 5428: 5424: 5418: 5412: 5406: 5403: 5389: 5384: 5374: 5371: 5362: 5311: 4867: 4854: 4817: 4814: 4614: 4387: 4301: 4296: 4255: 4215: 3633: 3631: 3623: 3609: 3526: 3402: 3071: 3063: 3000: 2996: 2992: 2988: 2980: 2976: 2953: 2949: 2940: 2931: 2928: 2924: 2921: 2917: 2913: 2909: 2905: 2897:Carathéodory 2890: 2884: 2878: 2875: 2869: 2863: 2860: 2799: 2693: 2595: 2587: 2579: 2575: 2572: 2568: 2555: 2552: 2544:open systems 2541: 2537: 2521: 2517: 2513: 2509: 2492: 2484: 2471: 2467: 2454: 2448: 2440: 2436: 2423: 2419: 2413: 2373: 2369: 2364: 2360: 2355: 2343: 2336: 2320: 2315: 2297: 2291: 2284:Germain Hess 2281: 2266: 2261: 2248: 2246: 2239: 2234: 2230: 2226: 2216: 2173: 2084: 2057: 2002: 1894: 1864: 1853: 1782: 1778: 1708: 1695:open systems 1691: 1683: 1646: 1644: 1440:Carathéodory 1371:Heat engines 1343: 1332: 1321: 1303:Motive power 1288: 948:Free entropy 919: 419: 418: / 408: 407: / 399:introduction 392: 391: / 330: 293:Heat engines 107: 80: / 18: 10922:Am. J. Phys 10619:Balescu, R. 10565:D. ter Haar 10255:pp. 146–147 10187:pp. 146–149 9901:4: 304–306. 9895:Thomson, W. 9874:(1852 a). " 9872:Thomson, W. 9091:Joule, J.P. 9081:, page 106. 5382:denoted by 4266:latent heat 2895:(1907), of 2524:James Joule 2501:Description 2420:Definition. 2325:, and from 2273:Lord Kelvin 2255:Sadi Carnot 1262:Synergetics 943:Free energy 389:Temperature 250:Quasistatic 245:Isenthalpic 202:Instruments 192:Equilibrium 144:Open system 78:Equilibrium 60:Statistical 11302:Categories 11237:Chapter 2. 11065:Planck, M. 10839:, (1971). 10825:: 267–269. 10820:Phys. Rev. 10785:0486647412 10557:Balian, R. 10084:Balian, R. 9935:2011-06-03 9700:Atkins, P. 9318:: 218–224. 8851:Mandl 1988 8838:References 5762:Equation ( 5557:reversible 5422:, volume: 4268:, through 4250:See also: 2984:electrical 2290:) for the 2288:Hess's Law 1969:, whereas 1856:Max Planck 1705:Definition 1574:Nucleation 1418:Scientists 1222:Philosophy 935:Potentials 298:Heat pumps 255:Polytropic 240:Isentropic 230:Isothermal 11121:Tisza, L. 10691:118230148 10372:119766602 10054:: 95–105. 9753:adynamics 9527:, p. 246. 9222:Physik Z. 8708:α 8700:Δ 8694:α 8690:η 8683:α 8679:∑ 8666:ξ 8662:Δ 8652:Ξ 8641:∑ 8637:− 8631:Δ 8622:Δ 8606:Δ 8549:α 8541:Δ 8535:α 8531:μ 8524:α 8520:∑ 8507:ξ 8503:Δ 8493:Ξ 8482:∑ 8471:Δ 8464:− 8414:… 8402:ξ 8389:ξ 8347:α 8339:Δ 8333:α 8329:η 8322:α 8318:∑ 8308:Δ 8299:Δ 8283:Δ 8226:α 8218:Δ 8212:α 8208:μ 8201:α 8197:∑ 8186:Δ 8179:− 8030:Δ 7998:∑ 7986:Δ 7979:− 7972:Δ 7960:Δ 7801:∑ 7789:δ 7785:− 7778:δ 7615:δ 7575:∑ 7566:− 7543:δ 7425:μ 7404:∑ 7382:− 7201:Δ 7181:∑ 7176:− 7168:− 7146:Δ 7036:Δ 7020:Δ 6871:Δ 6855:Δ 6317:⋅ 6314:∇ 6311:− 6301:⋅ 6297:σ 6289:⋅ 6286:∇ 6253:→ 6075:Here the 6038:μ 6028:∑ 5992:∑ 5988:− 5886:μ 5876:∑ 5860:− 5831:becomes: 5715:− 5620:− 5503:δ 5500:− 5494:δ 5340:Δ 5290:Δ 5210:→ 5122:→ 5111:− 4987:→ 4885:→ 4829:Δ 4793:Δ 4719:→ 4637:→ 4626:− 4505:→ 4409:→ 4361:Δ 4322:→ 4280:Δ 4198:Δ 4165:− 4138:− 4083:→ 4072:− 4048:− 3993:→ 3958:− 3903:→ 3892:− 3868:− 3813:→ 3802:− 3775:− 3720:→ 3709:− 3579:→ 3568:− 3552:→ 3507:→ 3447:→ 3348:→ 3337:− 3259:→ 3248:− 2811:Δ 2777:Δ 2753:Δ 2729:Δ 2705:Δ 2414:In 1907, 2366:produced. 2298:In 1842, 2282:In 1840, 2244:of heat. 2188:Δ 2157:Δ 2037:Δ 2028:− 2016:Δ 1986:Δ 1977:− 1954:Δ 1911:Δ 1858:, and by 1835:− 1823:Δ 1797:Δ 1555:Waterston 1505:von Mayer 1460:de Donder 1450:Clapeyron 1430:Boltzmann 1425:Bernoulli 1386:Education 1357:Timelines 1141:− 1086:− 874:Equations 841:∂ 794:∂ 745:α 709:∂ 662:∂ 616:− 610:β 574:∂ 527:∂ 235:Adiabatic 225:Isochoric 211:Processes 172:Ideal gas 55:Classical 11274:PDF file 11213:32826343 11133:(1980). 11123:(1966). 11096:(1947). 11043:(1949). 10882:(1847). 10714:(1850), 10665:(1909). 10621:(1997). 10608:(1907). 10596:(1949). 10594:Born, M. 10258:Archived 10253:(1949), 10251:Born, M. 10190:Archived 10057:Archived 9972:Born, M. 9929:Archived 9879:Archived 9735:, p. 63. 9714:, p. 54. 9659:(1871). 9245:Born, M. 9218:Born, M. 8890:Archived 8805:See also 6830:Max Born 6082:are the 2565:nothing. 2488:Max Born 2432:Max Born 2227:vis viva 1607:Category 1545:Thompson 1455:Clausius 1435:Bridgman 1289:Vis viva 1271:Theories 1205:Gas laws 997:Enthalpy 405:Pressure 220:Isobaric 177:Real gas 65:Chemical 48:Branches 11083:Bibcode 10930:Bibcode 10728:Bibcode 10424:Bibcode 10352:Bibcode 9914:, Band 9817:18 June 9749:Rankine 9612:Bibcode 9312:Phys. Z 9093:(1845). 9013:Bibcode 8877:, p. 43 8079:where Δ 7518:) and ( 7273:of the 7249:where Δ 5923:where d 2213:History 1893:, done 1530:Smeaton 1525:Rankine 1515:Onsager 1500:Maxwell 1495:Massieu 1200:Entropy 1195:General 1186:History 1176:Culture 1173:History 397: ( 394:Entropy 331:italics 132:Systems 11249: 11229: 11211: 11201: 11174: 11159: 11141: 11033: 11015: 10995: 10980: 10912: 10847: 10807: 10783: 10689: 10654: 10629: 10586: 10571: 10542: 10370: 9808: 9731: 9710: 9547: 9523: 9502: 9077: 8969: 8945: 8795:ad hoc 8786:where 8092:p Δ V 7887:where 7665:where 7502:, and 7071:where 6906:where 6439:where 4295:is an 2558:Planck 2223:energy 2058:where 2034: 1983: 1908: 1869:, the 1520:Planck 1510:Nernst 1485:Kelvin 1445:Carnot 735: 600: 468: 410:Volume 325:Note: 284:Cycles 113:Second 103:Zeroth 10687:S2CID 10368:S2CID 10340:(PDF) 9802:(PDF) 5952:then 5390:state 2861:Here 2449:walls 1860:IUPAC 1568:Other 1535:Stahl 1490:Lewis 1480:Joule 1470:Gibbs 1465:Duhem 158:State 118:Third 108:First 11247:ISBN 11227:ISBN 11209:OCLC 11199:ISBN 11172:ISBN 11157:ISBN 11139:ISBN 11031:ISBN 11013:ISBN 10993:ISBN 10978:ISBN 10910:ISBN 10845:ISBN 10805:ISBN 10781:ISBN 10697:here 10652:ISBN 10627:ISBN 10584:ISBN 10569:ISBN 10540:ISBN 10395:2013 9819:2021 9806:ISBN 9729:ISBN 9708:ISBN 9545:ISBN 9521:ISBN 9500:ISBN 9075:ISBN 8967:ISBN 8943:ISBN 7715:and 7081:and 6989:and 6939:and 6916:and 6474:and 5813:and 5790:and 5778:and 5678:and 5561:work 5465:and 2932:heat 2901:Born 2867:and 2424:heat 2080:heat 1709:For 1661:and 1659:heat 1645:The 1540:Tait 370:Heat 365:Work 95:Laws 10938:doi 10744:hdl 10736:doi 10679:doi 10399:doi 10360:doi 9620:doi 9108:doi 9104:140 9029:hdl 9021:doi 9009:126 8921:doi 8086:Δ Q 6123:= − 5950:mol 5568:= − 3462:or 2357:it. 2229:', 1383:Art 329:in 11304:: 11207:. 11011:. 10936:. 10926:29 10924:. 10823:58 10816:I. 10742:, 10734:, 10724:79 10722:, 10718:, 10685:. 10675:67 10673:. 10669:. 10393:. 10389:. 10366:. 10358:. 10346:. 10342:. 10121:^ 10109:^ 10067:^ 10052:33 10050:, 10038:^ 9944:^ 9927:. 9755:." 9618:. 9608:54 9606:. 9602:. 9572:^ 9415:^ 9371:^ 9359:^ 9345:^ 9324:^ 9316:22 9314:. 9302:^ 9283:^ 9235:^ 9225:22 9136:^ 9122:^ 9102:. 9098:. 9027:. 9019:. 9007:. 9003:. 8917:37 8915:. 8901:^ 8781:+ 8776:ρu 8774:= 8757:ρu 8732:10 7934:. 7495:, 7491:, 7487:, 7483:, 7329:, 7325:, 7314:= 7284:th 7271:th 7095:. 7002:. 6980:, 6966:+ 6959:= 6770:12 6727:12 6548:12 6336:. 6115:. 5823:. 5684:: 5582:= 5580:δQ 5566:δW 5435:, 5427:= 5401:. 3210:: 2550:. 2530:. 2393:− 2383:= 2253:, 2237:. 2235:mv 2231:mv 2003:on 1895:by 1873:, 1783:by 1779:to 1697:, 11280:. 11272:( 11255:. 11235:. 11215:. 11178:. 11163:. 11145:. 11089:. 11085:: 11037:. 11021:. 10999:. 10984:. 10944:. 10940:: 10932:: 10851:. 10811:. 10787:. 10765:. 10759:2 10746:: 10738:: 10730:: 10693:. 10681:: 10658:. 10633:. 10615:. 10590:. 10575:. 10546:. 10430:. 10426:: 10407:. 10401:: 10374:. 10362:: 10354:: 10348:6 10307:. 10264:. 10196:. 9938:. 9916:V 9821:. 9628:. 9622:: 9614:: 9249:V 9228:i 9116:. 9110:: 9037:. 9031:: 9023:: 9015:: 8975:. 8949:. 8927:. 8923:: 8789:u 8783:W 8779:v 8772:j 8766:W 8760:v 8734:) 8730:( 8713:. 8704:n 8675:+ 8670:j 8656:j 8645:j 8634:Q 8628:= 8625:E 8618:, 8613:T 8609:E 8600:= 8597:S 8593:d 8575:) 8573:9 8571:( 8554:, 8545:n 8516:+ 8511:j 8497:j 8486:j 8478:+ 8474:V 8468:p 8461:S 8458:d 8454:T 8451:= 8448:U 8444:d 8411:, 8406:2 8398:, 8393:1 8373:) 8371:8 8369:( 8352:. 8343:N 8314:+ 8311:Q 8305:= 8302:E 8295:, 8290:T 8286:E 8277:= 8274:S 8270:d 8252:) 8250:7 8248:( 8231:, 8222:N 8193:+ 8189:V 8183:p 8176:S 8173:d 8169:T 8166:= 8163:U 8159:d 8130:i 8108:i 8104:h 8081:U 8072:) 8070:6 8068:( 8051:. 8039:j 8035:N 8023:j 8019:h 8013:n 8008:1 8005:= 8002:j 7993:+ 7989:V 7983:p 7975:Q 7968:= 7964:U 7922:i 7900:i 7896:h 7880:) 7878:5 7876:( 7859:. 7842:j 7838:N 7833:d 7826:j 7822:h 7816:n 7811:1 7808:= 7805:j 7796:+ 7792:W 7781:Q 7774:= 7768:0 7764:U 7759:d 7728:i 7724:s 7703:i 7681:i 7677:N 7673:d 7649:, 7635:V 7631:d 7626:P 7622:= 7618:W 7604:i 7600:N 7596:d 7590:i 7586:s 7579:i 7569:T 7563:S 7559:d 7554:T 7550:= 7546:Q 7521:4 7515:3 7506:j 7504:μ 7499:j 7497:N 7493:V 7489:P 7485:S 7481:T 7477:n 7468:) 7466:4 7464:( 7445:j 7441:N 7436:d 7429:j 7419:n 7414:1 7411:= 7408:j 7399:+ 7395:V 7391:d 7386:P 7378:S 7374:d 7369:T 7365:= 7359:0 7355:U 7350:d 7333:j 7331:N 7327:V 7323:S 7321:( 7319:0 7316:U 7312:0 7309:U 7295:W 7289:Q 7282:i 7276:m 7269:i 7262:i 7260:U 7258:Δ 7254:0 7251:U 7242:) 7240:3 7238:( 7209:i 7205:U 7196:m 7191:1 7188:= 7185:i 7172:W 7164:Q 7160:= 7154:0 7150:U 7088:o 7085:N 7083:Δ 7078:s 7075:N 7073:Δ 7056:, 7052:0 7049:= 7044:o 7040:N 7033:+ 7028:s 7024:N 6995:2 6992:U 6986:1 6983:U 6977:U 6971:2 6968:U 6964:1 6961:U 6957:U 6951:U 6945:2 6942:U 6936:1 6933:U 6923:o 6920:U 6918:Δ 6913:s 6910:U 6908:Δ 6891:, 6887:0 6884:= 6879:o 6875:U 6868:+ 6863:s 6859:U 6782:t 6779:o 6776:p 6766:E 6739:t 6736:o 6733:p 6723:E 6719:+ 6714:2 6710:U 6706:+ 6700:t 6697:o 6694:p 6688:2 6684:E 6680:+ 6674:n 6671:i 6668:k 6662:2 6658:E 6654:+ 6649:1 6645:U 6641:+ 6635:t 6632:o 6629:p 6623:1 6619:E 6615:+ 6609:n 6606:i 6603:k 6597:1 6593:E 6589:= 6586:E 6560:t 6557:o 6554:p 6544:E 6517:U 6494:t 6491:o 6488:p 6483:E 6459:n 6456:i 6453:k 6448:E 6424:U 6421:+ 6415:t 6412:o 6409:p 6404:E 6400:+ 6394:n 6391:i 6388:k 6383:E 6379:= 6376:E 6353:E 6322:q 6308:) 6304:v 6292:( 6283:= 6277:t 6274:D 6267:t 6263:E 6259:D 6247:t 6244:D 6239:Q 6236:D 6230:+ 6224:t 6221:D 6216:W 6213:D 6207:= 6201:t 6198:D 6191:t 6187:E 6183:D 6149:S 6147:d 6145:T 6137:V 6133:P 6129:V 6127:d 6125:P 6121:U 6119:d 6105:i 6102:x 6098:i 6095:X 6091:i 6088:x 6080:i 6077:X 6060:. 6055:j 6051:N 6047:d 6042:j 6032:j 6024:+ 6019:i 6015:x 6011:d 6006:i 6002:X 5996:i 5985:S 5982:d 5979:T 5976:= 5973:U 5970:d 5957:i 5954:μ 5946:i 5943:N 5935:i 5932:μ 5928:i 5925:N 5908:. 5903:i 5899:N 5895:d 5890:i 5880:i 5872:+ 5869:V 5866:d 5863:P 5857:S 5854:d 5851:T 5848:= 5845:U 5842:d 5829:U 5827:d 5820:S 5818:d 5816:T 5810:V 5808:d 5806:P 5804:− 5799:U 5793:P 5787:T 5781:V 5775:S 5765:2 5755:) 5753:2 5751:( 5724:V 5721:d 5718:P 5712:S 5709:d 5706:T 5703:= 5700:U 5697:d 5681:V 5675:S 5669:U 5629:V 5626:d 5623:P 5617:S 5614:d 5611:T 5608:= 5605:U 5602:d 5588:S 5586:d 5584:T 5574:V 5572:d 5570:P 5552:U 5550:d 5506:W 5497:Q 5491:= 5488:U 5485:d 5468:V 5462:S 5456:U 5450:P 5444:T 5439:) 5437:V 5433:S 5431:( 5429:U 5425:U 5419:V 5413:S 5407:U 5385:d 5375:δ 5343:U 5320:U 5297:. 5293:U 5287:= 5281:e 5278:l 5275:b 5272:i 5269:s 5266:r 5263:e 5260:v 5257:e 5254:r 5251:r 5248:i 5243:, 5238:1 5234:P 5228:h 5225:t 5222:a 5219:p 5213:B 5207:A 5203:Q 5199:+ 5193:e 5190:l 5187:b 5184:i 5181:s 5178:r 5175:e 5172:v 5169:e 5166:r 5163:r 5160:i 5155:, 5150:1 5146:P 5140:h 5137:t 5134:a 5131:p 5125:B 5119:A 5115:W 5086:1 5082:P 5058:e 5055:l 5052:b 5049:i 5046:s 5043:r 5040:e 5037:v 5034:e 5031:r 5028:r 5025:i 5020:, 5015:1 5011:P 5005:h 5002:t 4999:a 4996:p 4990:B 4984:A 4980:Q 4956:e 4953:l 4950:b 4947:i 4944:s 4941:r 4938:e 4935:v 4932:e 4929:r 4926:r 4923:i 4918:, 4913:1 4909:P 4903:h 4900:t 4897:a 4894:p 4888:B 4882:A 4878:W 4851:. 4838:0 4835:= 4832:U 4800:. 4796:U 4790:= 4784:e 4781:l 4778:b 4775:i 4772:s 4769:r 4766:e 4763:v 4760:e 4757:r 4752:, 4747:0 4743:P 4737:h 4734:t 4731:a 4728:p 4722:B 4716:A 4712:Q 4708:+ 4702:e 4699:l 4696:b 4693:i 4690:s 4687:r 4684:e 4681:v 4678:e 4675:r 4670:, 4665:0 4661:P 4655:h 4652:t 4649:a 4646:p 4640:B 4634:A 4630:W 4598:0 4594:P 4570:e 4567:l 4564:b 4561:i 4558:s 4555:r 4552:e 4549:v 4546:e 4543:r 4538:, 4533:0 4529:P 4523:h 4520:t 4517:a 4514:p 4508:B 4502:A 4498:Q 4474:e 4471:l 4468:b 4465:i 4462:s 4459:r 4456:e 4453:v 4450:e 4447:r 4442:, 4437:0 4433:P 4427:h 4424:t 4421:a 4418:p 4412:B 4406:A 4402:W 4368:. 4364:U 4358:= 4352:c 4349:i 4346:m 4343:a 4340:n 4337:y 4334:d 4331:a 4325:B 4319:A 4315:Q 4283:U 4241:. 4229:U 4201:U 4195:= 4192:) 4189:B 4186:( 4183:U 4180:+ 4177:) 4174:A 4171:( 4168:U 4162:= 4156:c 4153:i 4150:t 4147:a 4144:t 4141:s 4135:i 4132:s 4129:a 4126:u 4123:q 4119:, 4116:c 4113:i 4110:t 4107:a 4104:b 4101:a 4098:i 4095:d 4092:a 4086:B 4080:O 4076:W 4066:c 4063:i 4060:t 4057:a 4054:t 4051:s 4045:i 4042:s 4039:a 4036:u 4033:q 4029:, 4026:c 4023:i 4020:t 4017:a 4014:b 4011:a 4008:i 4005:d 4002:a 3996:A 3990:O 3986:W 3982:= 3976:c 3973:i 3970:t 3967:a 3964:t 3961:s 3955:i 3952:s 3949:a 3946:u 3943:q 3939:, 3936:c 3933:i 3930:t 3927:a 3924:b 3921:a 3918:i 3915:d 3912:a 3906:B 3900:O 3896:W 3886:c 3883:i 3880:t 3877:a 3874:t 3871:s 3865:i 3862:s 3859:a 3856:u 3853:q 3849:, 3846:c 3843:i 3840:t 3837:a 3834:b 3831:a 3828:i 3825:d 3822:a 3816:O 3810:A 3806:W 3799:= 3793:c 3790:i 3787:t 3784:a 3781:t 3778:s 3772:i 3769:s 3766:a 3763:u 3760:q 3756:, 3753:c 3750:i 3747:t 3744:a 3741:b 3738:a 3735:i 3732:d 3729:a 3723:B 3717:A 3713:W 3686:O 3666:B 3646:A 3635:1 3625:1 3614:) 3612:1 3610:( 3593:. 3582:A 3576:O 3572:W 3565:= 3555:O 3549:A 3545:W 3510:O 3504:A 3499:, 3495:c 3492:i 3489:t 3486:a 3483:b 3480:a 3477:i 3474:d 3471:a 3450:A 3444:O 3440:, 3436:c 3433:i 3430:t 3427:a 3424:b 3421:a 3418:i 3415:d 3412:a 3388:. 3381:c 3378:i 3375:t 3372:a 3369:b 3366:a 3363:i 3360:d 3357:a 3351:O 3345:A 3341:W 3334:) 3331:A 3328:( 3325:U 3322:= 3319:) 3316:O 3313:( 3310:U 3304:r 3301:o 3292:c 3289:i 3286:t 3283:a 3280:b 3277:a 3274:i 3271:d 3268:a 3262:A 3256:O 3252:W 3245:) 3242:O 3239:( 3236:U 3233:= 3230:) 3227:A 3224:( 3221:U 3198:O 3178:A 3158:) 3155:A 3152:( 3149:U 3129:A 3109:) 3106:O 3103:( 3100:U 3080:O 3050:U 3030:U 3009:U 2885:U 2879:W 2870:W 2864:Q 2846:. 2841:W 2838:+ 2835:Q 2832:= 2826:t 2823:o 2820:t 2815:E 2785:. 2780:U 2774:+ 2768:t 2765:o 2762:p 2757:E 2750:+ 2744:n 2741:i 2738:k 2733:E 2726:= 2720:t 2717:o 2714:t 2709:E 2679:. 2674:U 2671:+ 2665:t 2662:o 2659:p 2654:E 2650:+ 2644:n 2641:i 2638:k 2633:E 2629:= 2623:t 2620:o 2617:t 2612:E 2598:= 2596:E 2594:Δ 2590:= 2588:E 2586:Δ 2582:= 2580:E 2578:Δ 2402:′ 2399:n 2395:E 2391:″ 2389:n 2385:E 2381:ν 2378:h 2197:0 2194:= 2191:V 2160:U 2133:W 2113:Q 2093:U 2066:Q 2043:, 2040:V 2031:P 2025:Q 2022:= 2019:U 1989:V 1980:P 1957:V 1934:P 1914:V 1905:P 1881:W 1850:. 1838:W 1832:Q 1829:= 1826:U 1800:U 1765:Q 1745:W 1725:U 1634:e 1627:t 1620:v 1147:S 1144:T 1138:H 1135:= 1132:) 1129:p 1126:, 1123:T 1120:( 1117:G 1092:S 1089:T 1083:U 1080:= 1077:) 1074:V 1071:, 1068:T 1065:( 1062:A 1037:V 1034:p 1031:+ 1028:U 1025:= 1022:) 1019:p 1016:, 1013:S 1010:( 1007:H 982:) 979:V 976:, 973:S 970:( 967:U 844:T 820:V 797:V 773:1 748:= 712:p 688:V 665:V 641:1 613:= 577:T 553:N 530:S 506:T 481:= 478:c 401:)

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Knowledge

First law of thermodynamics

Index