1740:, by which bodies pass from one equilibrium state to another by transfer of matter and energy between them. The term 'thermodynamic system' is used to refer to bodies of matter and energy in the special context of thermodynamics. The possible equilibria between bodies are determined by the physical properties of the walls that separate the bodies. Equilibrium thermodynamics in general does not measure time. Equilibrium thermodynamics is a relatively simple and well settled subject. One reason for this is the existence of a well defined physical quantity called 'the entropy of a body'.
3465:, who investigated a system of chemically reacting substances. In this case the internal variables appear to be measures of incompleteness of chemical reactions, that is measures of how much the considered system with chemical reactions is out of equilibrium. The theory can be generalized, to consider any deviations from the equilibrium state, such as structure of the system, gradients of temperature, difference of concentrations of substances and so on, to say nothing of degrees of completeness of all chemical reactions, to be internal variables.
1748:. It is characterized by presence of flows of matter and energy. For this topic, very often the bodies considered have smooth spatial inhomogeneities, so that spatial gradients, for example a temperature gradient, are well enough defined. Thus the description of non-equilibrium thermodynamic systems is a field theory, more complicated than the theory of equilibrium thermodynamics. Non-equilibrium thermodynamics is a growing subject, not an established edifice. Example theories and modeling approaches include the
3077:
117:
1687:
94:
33:
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1985:
1960:
1950:
1902:
2112:. The properties of the walls determine what transfers can occur. A wall that allows transfer of a quantity is said to be permeable to it, and a thermodynamic system is classified by the permeabilities of its several walls. A transfer between system and surroundings can arise by contact, such as conduction of heat, or by long-range forces such as an electric field in the surroundings.
2068:
2058:
2048:
2023:
2013:
1995:
1975:
1940:
1922:
1912:
1830:, each step in the process must be reversible. For a step in a process to be reversible, the system must be in equilibrium throughout the step. That ideal cannot be accomplished in practice because no step can be taken without perturbing the system from equilibrium, but the ideal can be approached by making changes slowly.
3000:
Isolated systems are not equivalent to closed systems. Closed systems cannot exchange matter with the surroundings, but can exchange energy. Isolated systems can exchange neither matter nor energy with their surroundings, and as such are only theoretical and do not exist in reality (except, possibly,
2914:
Truly isolated physical systems do not exist in reality (except perhaps for the universe as a whole), because, for example, there is always gravity between a system with mass and masses elsewhere. However, real systems may behave nearly as an isolated system for finite (possibly very long) times. The
1789:
If there is a temperature difference inside the thermodynamic system, for example in a rod, one end of which is warmer than the other, then thermal energy transfer processes occur in it, in which the temperature of the colder part rises and the warmer part decreases. As a result, after some time, the
1743:
Non-equilibrium thermodynamics, as a subject in physics, considers bodies of matter and energy that are not in states of internal thermodynamic equilibrium, but are usually participating in processes of transfer that are slow enough to allow description in terms of quantities that are closely related
2083:
A wall can be fixed (e.g. a constant volume reactor) or moveable (e.g. a piston). For example, in a reciprocating engine, a fixed wall means the piston is locked at its position; then, a constant volume process may occur. In that same engine, a piston may be unlocked and allowed to move in and out.
2906:
An isolated system is more restrictive than a closed system as it does not interact with its surroundings in any way. Mass and energy remains constant within the system, and no energy or mass transfer takes place across the boundary. As time passes in an isolated system, internal differences in the
2079:
A system is enclosed by walls that bound it and connect it to its surroundings. Often a wall restricts passage across it by some form of matter or energy, making the connection indirect. Sometimes a wall is no more than an imaginary two-dimensional closed surface through which the connection to the
1838:
is a consequence of this fundamental postulate. In reality, practically nothing in nature is in strict thermodynamic equilibrium, but the postulate of thermodynamic equilibrium often provides very useful idealizations or approximations, both theoretically and experimentally; experiments can provide
1798:
If the process of converting one type of energy into another takes place inside a thermodynamic system, for example, in chemical reactions, in electric or pneumatic motors, when one solid body rubs against another, then the processes of energy release or absorption will occur, and the thermodynamic
2211:
In a closed system, no mass may be transferred in or out of the system boundaries. The system always contains the same amount of matter, but (sensible) heat and (boundary) work can be exchanged across the boundary of the system. Whether a system can exchange heat, work, or both is dependent on the
1756:
Another kind of thermodynamic system is considered in most engineering. It takes part in a flow process. The account is in terms that approximate, well enough in practice in many cases, equilibrium thermodynamical concepts. This is mostly beyond the scope of the present article, and is set out in
1842:
In equilibrium thermodynamics the state variables do not include fluxes because in a state of thermodynamic equilibrium all fluxes have zero values by definition. Equilibrium thermodynamic processes may involve fluxes but these must have ceased by the time a thermodynamic process or operation is
3031:
A thermodynamic operation can render impermeable to matter all system walls other than the contact equilibrium wall for that substance. This allows the definition of an intensive state variable, with respect to a reference state of the surroundings, for that substance. The intensive variable is
59:
Thermodynamic systems can be passive and active according to internal processes. According to internal processes, passive systems and active systems are distinguished: passive, in which there is a redistribution of available energy, active, in which one type of energy is converted into another.
1752:
for complex fluids, viscoelasticity, and soft materials. In general, it is not possible to find an exactly defined entropy for non-equilibrium problems. For many non-equilibrium thermodynamical problems, an approximately defined quantity called 'time rate of entropy production' is very useful.
2638:, there may be all sorts of molecules being generated and destroyed by the reaction process. In this case, the fact that the system is closed is expressed by stating that the total number of each elemental atom is conserved, no matter what kind of molecule it may be a part of. Mathematically:
3023:
A wall selectively permeable only to a pure substance can put the system in diffusive contact with a reservoir of that pure substance in the surroundings. Then a process is possible in which that pure substance is transferred between system and surroundings. Also, across that wall a contact
2992:
The second law of thermodynamics for isolated systems states that the entropy of an isolated system not in equilibrium tends to increase over time, approaching maximum value at equilibrium. Overall, in an isolated system, the internal energy is constant and the entropy can never decrease. A
1772:
Theoretical studies of thermodynamic processes in the period from the first theory of heat engines (Saadi Carnot, France, 1824) to the theory of dissipative structures (Ilya
Prigozhin, Belgium, 1971) mainly concerned the patterns of interaction of thermodynamic systems with the environment.
1833:
The very existence of thermodynamic equilibrium, defining states of thermodynamic systems, is the essential, characteristic, and most fundamental postulate of thermodynamics, though it is only rarely cited as a numbered law. According to Bailyn, the commonly rehearsed statement of the
3063:
For a contact equilibrium across a wall permeable to a substance, the chemical potentials of the substance must be same on either side of the wall. This is part of the nature of thermodynamic equilibrium, and may be regarded as related to the zeroth law of thermodynamics.
3839:
3107:
In an open system, there is an exchange of energy and matter between the system and the surroundings. The presence of reactants in an open beaker is an example of an open system. Here the boundary is an imaginary surface enclosing the beaker and reactants. It is named
75:. An isolated system does not exchange matter or energy with its surroundings. A closed system may exchange heat, experience forces, and exert forces, but does not exchange matter. An open system can interact with its surroundings by exchanging both matter and energy.
3310:
2099:
The system is delimited by walls or boundaries, either actual or notional, across which conserved (such as matter and energy) or unconserved (such as entropy) quantities can pass into and out of the system. The space outside the thermodynamic system is known as the
3116:, if there is no exchange of heat and substances. The open system cannot exist in the equilibrium state. To describe deviation of the thermodynamic system from equilibrium, in addition to constitutive variables that was described above, a set of internal variables
1807:
In isolated systems it is consistently observed that as time goes on internal rearrangements diminish and stable conditions are approached. Pressures and temperatures tend to equalize, and matter arranges itself into one or a few relatively homogeneous
3695:
1776:
At the same time, thermodynamic systems were mainly classified as isolated, closed and open, with corresponding properties in various thermodynamic states, for example, in states close to equilibrium, nonequilibrium and strongly nonequilibrium.
2237:
of a particular reaction. Electrical energy travels across the boundary to produce a spark between the electrodes and initiates combustion. Heat transfer occurs across the boundary after combustion but no mass transfer takes place either way.
3015:
An open system has one or several walls that allow transfer of matter. To account for the internal energy of the open system, this requires energy transfer terms in addition to those for heat and work. It also leads to the idea of the
2138:
Anything that passes across the boundary and effects a change in the contents of the system must be accounted for in an appropriate balance equation. The volume can be the region surrounding a single atom resonating energy, such as
2134:
allow transfer both of matter and of energy. This scheme of definition of terms is not uniformly used, though it is convenient for some purposes. In particular, some writers use 'closed system' where 'isolated system' is here used.
1816:. The thermodynamic properties of a system in equilibrium are unchanging in time. Equilibrium system states are much easier to describe in a deterministic manner than non-equilibrium states. In some cases, when analyzing a
1780:
In 2010, Boris
Dobroborsky (Israel, Russia) proposed a classification of thermodynamic systems according to internal processes consisting in energy redistribution (passive systems) and energy conversion (active systems).
2119:. This is an idealized conception, because in practice some transfer is always possible, for example by gravitational forces. It is an axiom of thermodynamics that an isolated system eventually reaches internal
3420:
4784:
Dobroborsky B.S. Machine safety and the human factor / Edited by Doctor of
Technical Sciences, prof. S.A. Volkov. — St. Petersburg: SPbGASU, 2011. — pp. 33–35. — 114 p. — ISBN 978-5-9227-0276-8. (Ru)
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system tend to even out and pressures and temperatures tend to equalize, as do density differences. A system in which all equalizing processes have gone practically to completion is in a state of
2718:
3174:
2389:
4514:
3160:
3028:, the pure substance reservoir can be dealt with as a closed system. Its internal energy and its entropy can be determined as functions of its temperature, pressure, and mole number.
2480:
4614:
Pokrovskii V.N. (2013) A derivation of the main relations of non-equilibrium thermodynamics. Hindawi
Publishing Corporation: ISRN Thermodynamics, vol. 2013, article ID 906136, 9 p.
2523:
3598:
3004:'Closed system' is often used in thermodynamics discussions when 'isolated system' would be correct – i.e. there is an assumption that energy does not enter or leave the system.
2955:
1843:
complete bringing a system to its eventual thermodynamic state. Non-equilibrium thermodynamics allows its state variables to include non-zero fluxes, which describe transfers of
3919:
3885:
1736:
Equilibrium thermodynamics, as a subject in physics, considers macroscopic bodies of matter and energy in states of internal thermodynamic equilibrium. It uses the concept of
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1131:
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For a thermodynamic process, the precise physical properties of the walls and surroundings of the system are important, because they determine the possible processes.
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For a simple system, with only one type of particle (atom or molecule), a closed system amounts to a constant number of particles. For systems undergoing a
4522:
1716:
4877:
1417:
4465:
3166:
of the system, is their trending to disappear; the local law of disappearing can be written as relaxation equation for each internal variable
1305:
3891:. The sum of the last terms in the equations presents the total energy coming into the system with the stream of particles of substances
539:
3162:
have been introduced. The equilibrium state is considered to be stable and the main property of the internal variables, as measures of
3331:
4544:
4123:
1395:
4651:
Zotin, Alexei; Pokrovskii, Vladimir (2018). "The growth and development of living organisms from the thermodynamic point of view".
17:
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5039:
1428:
3834:{\displaystyle T\,dS=\Delta Q-\sum _{j}\,\Xi _{j}\,\Delta \xi _{j}+\sum _{\alpha =1}^{k}\,\eta _{\alpha }\,\Delta N_{\alpha }.}
2892:
in the system, which remains constant, since the system is closed. There is one such equation for each element in the system.
4815:
4449:
1729:
Thermodynamic equilibrium is characterized not only by the absence of any flow of mass or energy, but by “the absence of any
998:
3305:{\displaystyle {\frac {d\xi _{i}}{dt}}=-{\frac {1}{\tau _{i}}}\,\left(\xi _{i}-\xi _{i}^{(0)}\right),\quad i=1,\,2,\ldots ,}
1709:
1296:
965:
532:
410:
2644:
2185:. Depending on the type of system, it may interact with the system by exchanging mass, energy (including heat and work),
1827:
348:
4037:
This approach to the open system allows describing the growth and development of living objects in thermodynamic terms.
4870:
2569:
1480:
1454:
975:
429:
2348:
5105:
4846:
4748:
4726:
4229:
2920:
381:
5194:
1533:
1004:
403:
2130:
allow transfer of energy as heat and as work, but not of matter, between it and its surroundings. The walls of an
5143:
1702:
2096:. Actual physical materials that provide walls with such idealized properties are not always readily available.
5184:
5179:
3458:
3119:
1633:
165:
82:, which can be specified by the values of a set of thermodynamic state variables. A thermodynamic system is in
4757:
4605:
Pokrovskii V.N. (2005) Extended thermodynamics in a discrete-system approach, Eur. J. Phys. vol. 26, 769–781.
2445:
2148:
1528:
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358:
3690:{\displaystyle dG=\sum _{j}\,\Xi _{j}\,\Delta \xi _{j}+\sum _{\alpha }\,\mu _{\alpha }\,\Delta N_{\alpha },}
1812:. A system in which all processes of change have gone practically to completion is considered in a state of
5090:
3088:
2939:
2223:
1835:
993:
196:
186:
72:
2177:
is the remainder of the universe that lies outside the boundaries of the system. It is also known as the
2229:
One example is fluid being compressed by a piston in a cylinder. Another example of a closed system is a
1820:, one can assume that each intermediate state in the process is at equilibrium. Such a process is called
201:
191:
3894:
3860:
5004:
4894:
2194:
1769:
The classification of thermodynamic systems arose with the development of thermodynamics as a science.
1485:
1449:
161:
4222:
Generalized
Thermodynamics. The Thermodynamics of Irreversible Processes and Generalized Hydrodynamics
2947:
2197:. The environment is ignored in the analysis of the system, except in regards to these interactions.
1523:
5158:
2908:
2217:
2120:
1813:
1278:
1026:
472:
285:
275:
83:
3924:
2342:
the work done by the system. For infinitesimal changes the first law for closed systems may stated:
4919:
4762:
Réflexions sur la puissance motrice du feu et sur les machines propres à développer cette puissance
4086:
2397:
4772:. Physical Chemistry: An Advanced Treatise. Vol. 1. New York: Academic Press. pp. 1–97.
3425:
3112:, if borders are impenetrable for substance, but allow transit of energy in the form of heat, and
2247:
1790:
temperature in the rod will equalize – the rod will come to a state of thermodynamic equilibrium.
5138:
5123:
5113:
5069:
3422:
is a relaxation time of a corresponding variable. It is convenient to consider the initial value
3025:
1690:
1518:
1315:
1196:
1141:
1086:
1018:
957:
493:
482:
148:
4491:
920:
873:
788:
741:
653:
606:
4768:
Haase, R. (1971). "Survey of
Fundamental Laws". In Eyring, H.; Henderson, D.; Jost, W. (eds.).
2966:
2843:
2206:
2156:
2093:
1623:
1340:
424:
178:
153:
68:
4439:
4010:
3983:
1543:
824:
689:
36:
Properties of isolated, closed, and open thermodynamic systems in exchanging energy and matter
4984:
4944:
4081:
3955:
3555:
3517:
2168:
1817:
1737:
1558:
1135:
448:
294:
143:
2773:
1046:
5128:
4670:
4633:
4335:
2726:
2635:
2230:
1638:
1563:
1553:
353:
4553:
8:
5133:
5034:
4886:
4076:
3888:
2916:
1583:
1345:
367:
333:
328:
241:
4674:
4637:
4245:
1578:
557:
4990:
4686:
4660:
4188:
3977:
3973:
3949:
3497:
3474:
3017:
2962:
2924:
2875:
2823:
2803:
2753:
2551:
2531:
2422:
2325:
2305:
2285:
2234:
1672:
1335:
1330:
1283:
899:
852:
767:
720:
632:
585:
515:
499:
386:
338:
323:
313:
122:
116:
2241:
The first law of thermodynamics for energy transfers for closed system may be stated:
5153:
4975:
4842:
4825:
4811:
4773:
4744:
4722:
4445:
4389:
4225:
4091:
4061:
3469:
2982:
1749:
1667:
1628:
1618:
1190:
988:
816:
318:
308:
250:
87:
78:
The physical condition of a thermodynamic system at a given time is described by its
4690:
1799:
system will always tend to a non-equilibrium state with respect to the environment.
63:
Depending on its interaction with the environment, a thermodynamic system may be an
5095:
4678:
4421:
4046:
1588:
1573:
1513:
1508:
1325:
1320:
970:
438:
303:
3857:
The stationary states of the system exist due to exchange of both thermal energy (
1753:
Non-equilibrium thermodynamics is mostly beyond the scope of the present article.
5118:
4066:
4056:
3163:
2986:
2901:
2190:
2116:
2089:
1538:
1386:
1040:
681:
504:
265:
232:
64:
4682:
5085:
5044:
5029:
5014:
4949:
4939:
4934:
4909:
4736:
4589:
4307:
4071:
3462:
2085:
1809:
1745:
1593:
1363:
463:
343:
280:
270:
138:
108:
53:
2485:
For a quasi-reversible heat transfer, the second law of thermodynamics reads:
90:
apparent flows of matter or energy within it or between it and other systems.
5173:
5148:
5064:
5019:
4980:
4954:
4924:
4417:
4051:
2127:
1662:
980:
549:
510:
222:
5054:
5049:
5024:
4970:
4929:
2997:
system's entropy can decrease e.g. when heat is extracted from the system.
2144:
1758:
1613:
1598:
1548:
1031:
4615:
4437:
1568:
376:
3076:
5059:
4855:
4342:, (1st edition 1949) 5th edition 1967, North-Holland, Amsterdam, p. 14.
2970:
2928:
2140:
1657:
1603:
4355:, translated by E.S. Halberstadt, Wiley–Interscience, London, pp. 6–7.
4494:. The Department of Physics and Astronomy of Georgia State University
2943:
2151:
defined in 1824. It could also be just one nuclide (i.e. a system of
255:
52:
separate from its surroundings that can be studied using the laws of
49:
3024:
equilibrium with respect to that substance is possible. By suitable
4665:
4241:
2974:
2186:
1371:
1288:
1080:
488:
260:
93:
3049:. The corresponding extensive variable can be the number of moles
32:
4777:
4340:
Thermodynamics. An
Advanced Treatment for Chemists and Physicists
3492:
2935:
1852:
477:
4546:
Material and Energy
Balances for Engineers and Environmentalists
3415:{\displaystyle \tau _{i}=\tau _{i}(T,x_{1},x_{2},\ldots ,x_{n})}
2173:
The system is the part of the universe being studied, while the
4129:
4104:
2978:
2959:
2572:, used to compute changes in internal energy, is expressed as:
2152:
1856:
1848:
45:
4630:
Thermodynamics of
Complex Systems: Principles and applications
2919:
approximating many real-world situations. It is an acceptable
2233:, a type of constant-volume calorimeter used in measuring the
2115:
A system with walls that prevent all transfers is said to be
2624:{\displaystyle \mathrm {d} U=T\mathrm {d} S-P\mathrm {d} V.}
4839:
Fundamentals of
Equilibrium and Steady-State Thermodynamics
4441:
Thermodynamics of Spontaneous and Non-Spontaneous Processes
1844:
453:
4515:"Open, Closed and Isolated Systems in Physical Chemistry"
4253:
2951:
4788:
Halliday, David; Resnick, Robert; Walker, Jearl (2008).
4594:
Introduction to Thermodynamics of Irreversible Processes
4317:
4277:
4571:
4519:
Foundations of Quantum Mechanics and Physical Chemistry
3032:
called the chemical potential; for component substance
2216:
Adiabatic boundary – not allowing any heat exchange: A
2143:
defined in 1900; it can be a body of steam or air in a
4741:
Thermodynamics and an Introduction to Thermostatistics
4438:
I.M.Kolesnikov; V.A.Vinokurov; S.I.Kolesnikov (2001).
4787:
4653:
Physica A: Statistical Mechanics and Its Applications
4370:
4358:
4289:
4013:
3986:
3958:
3927:
3897:
3863:
3721:
3601:
3558:
3520:
3500:
3477:
3428:
3334:
3177:
3122:
2878:
2846:
2826:
2806:
2776:
2756:
2729:
2647:
2581:
2554:
2534:
2494:
2448:
2425:
2400:
2351:
2328:
2308:
2288:
2250:
1199:
1144:
1089:
1049:
923:
902:
876:
855:
827:
791:
770:
744:
723:
692:
656:
635:
609:
588:
560:
4399:
4189:
Time and irreversibility in axiomatic thermodynamics
4141:
2915:
concept of an isolated system can serve as a useful
2713:{\displaystyle \sum _{j=1}^{m}a_{ij}N_{j}=b_{i}^{0}}
2568:
the entropy of the system. With these relations the
4552:. Imperial College Press. p. 7. Archived from
4202:
4165:
4153:
4124:
Introduction to Chemical Engineering Thermodynamics
4265:
4126:, Fifth Edition (1996), .p.34, italics in original
4026:
3999:
3972:.The middle terms in equations (2) and (3) depict
3964:
3940:
3913:
3879:
3833:
3689:
3582:
3544:
3506:
3483:
3446:
3414:
3304:
3154:
2884:
2864:
2832:
2812:
2792:
2762:
2742:
2712:
2623:
2560:
2540:
2517:
2474:
2431:
2411:
2383:
2334:
2314:
2294:
2271:
2222:Rigid boundary – not allowing exchange of work: A
1839:scenarios of practical thermodynamic equilibrium.
1235:
1180:
1125:
1070:
932:
908:
885:
861:
836:
800:
776:
753:
729:
704:
665:
641:
618:
594:
569:
4721:. New York: American Institute of Physics Press.
2958:could be specified, treating the walls simply as
27:Body of matter in a state of internal equilibrium
5171:
2384:{\displaystyle \mathrm {d} U=\delta Q-\delta W.}
4650:
4428:, Addison-Wesley Publishing, Reading MA, p. 43.
3921:that can be positive or negative; the quantity
3007:
4797:Moran, Michael J.; Shapiro, Howard N. (2008).
4707:
4521:. McGill University (Montreal). Archived from
3980:) due to the relaxation of internal variables
3459:thermodynamics of open non-equilibrium systems
2977:in actual walls is considered, along with the
2950:, which assumed that a system (for example, a
2123:, when its state no longer changes with time.
4871:
1710:
4796:
4596:. 3rd edition, Wiley Interscience, New York.
2394:If the work is due to a volume expansion by
4512:
2954:) was isolated. That is all the mechanical
2934:In the attempt to justify the postulate of
2302:denotes the internal energy of the system,
4878:
4864:
4799:Fundamentals of Engineering Thermodynamics
4627:
4396:, fourth edition, Wiley, Hoboken NJ, p. 4.
4314:, Longmans, Green & Co, London, p. 66.
3060:of the component substance in the system.
2548:denotes the thermodynamic temperature and
1717:
1703:
115:
4710:Thermodynamics with Chemical Applications
4664:
4224:, Kluwer Academic Publishers, Dordrecht,
3814:
3803:
3765:
3754:
3725:
3670:
3659:
3632:
3621:
3289:
3228:
3155:{\displaystyle \xi _{1},\xi _{2},\ldots }
1802:
4885:
4836:
4444:. Nova science Publishers. p. 136.
4376:
4295:
4122:J.M. Smith, H.C. Van Ness, M.M. Abbott.
2475:{\displaystyle \delta W=P\mathrm {d} V.}
1757:other articles, for example the article
92:
31:
5040:Homogeneous charge compression ignition
4805:
4250:, Oxford University Press, London, p.44
4147:
4135:
4110:
2518:{\displaystyle \delta Q=T\mathrm {d} S}
1733:toward change on a macroscopic scale.”
14:
5172:
4810:(3rd ed.). Taylor & Francis.
4735:
4716:
4708:Abbott, M.M.; van Hess, H. G. (1989).
4616:https://dx.doi.org/10.1155/2013/906136
4577:
4405:
4283:
4247:Natural Philosophy of Cause and Chance
4208:
4159:
2872:the total number of atoms of element
2207:Closed system § In thermodynamics
4859:
4824:
4767:
4364:
4323:
4271:
4259:
4171:
4806:Rex, Andrew; Finn, C. B. P. (2017).
3712:
3592:
3168:
3071:
4187:, Brown, H.R., Valente, G. (2015).
24:
4472:. University of California - Davis
4015:
3914:{\displaystyle \Delta N_{\alpha }}
3898:
3880:{\displaystyle \Delta Q_{\alpha }}
3864:
3815:
3766:
3756:
3735:
3671:
3633:
3623:
2981:effect of the ambient, background
2895:
2611:
2597:
2583:
2570:fundamental thermodynamic relation
2508:
2462:
2402:
2353:
2251:
1784:
924:
877:
792:
745:
657:
610:
430:Intensive and extensive properties
25:
5206:
4743:(2nd ed.). New York: Wiley.
3457:The specific contribution to the
1793:
3075:
2200:
2084:Ideally, a wall may be declared
2066:
2056:
2046:
2031:
2021:
2011:
1993:
1983:
1973:
1958:
1948:
1938:
1920:
1910:
1900:
1686:
1685:
1005:Table of thermodynamic equations
227:
4644:
4632:. IOP Publishing, Bristol, UK.
4621:
4608:
4599:
4583:
4537:
4506:
4484:
4466:"A System and Its Surroundings"
4458:
4431:
4411:
4382:
4345:
4329:
4301:
4235:
3276:
2800:the number of atoms of element
2162:
1481:Maxwell's thermodynamic surface
4764:(in French). Paris: Bachelier.
4214:
4177:
4116:
3941:{\displaystyle \mu _{\alpha }}
3409:
3358:
3263:
3257:
3067:
1866:
1215:
1203:
1160:
1148:
1105:
1093:
1065:
1053:
13:
1:
4628:Pokrovskii, Vladimir (2020).
4392:, Bawendi, M.G. (1955/2005).
4097:
2412:{\displaystyle \mathrm {d} V}
2092:, impermeable, permeable, or
1868:Types of transfers permitted
1746:thermodynamic state variables
1382:Mechanical equivalent of heat
4712:(2nd ed.). McGraw Hill.
3447:{\displaystyle \xi _{i}^{0}}
3008:Selective transfer of matter
2985:, Boltzmann's assumption of
2940:second law of thermodynamics
2272:{\displaystyle \Delta U=Q-W}
2224:mechanically isolated system
2065:
2055:
2045:
2030:
2020:
2010:
1992:
1982:
1972:
1957:
1947:
1937:
1919:
1909:
1899:
1836:zeroth law of thermodynamics
994:Onsager reciprocal relations
7:
4945:Stirling (pseudo/adiabatic)
4683:10.1016/j.physa.2018.08.094
4040:
4034:are thermodynamic forces.
3847:
3703:
3318:
1486:Entropy as energy dispersal
1297:"Perpetual motion" machines
1236:{\displaystyle G(T,p)=H-TS}
1181:{\displaystyle A(T,V)=U-TS}
1126:{\displaystyle H(S,p)=U+pV}
100:
10:
5211:
4830:Generalized Thermodynamics
4719:A Survey of Thermodynamics
4701:
4426:Elements of Thermodynamics
2899:
2322:heat added to the system,
2212:property of its boundary.
2204:
2195:other conserved properties
2166:
1764:
933:{\displaystyle \partial T}
886:{\displaystyle \partial V}
801:{\displaystyle \partial p}
754:{\displaystyle \partial V}
666:{\displaystyle \partial T}
619:{\displaystyle \partial S}
5104:
5078:
5003:
4963:
4904:
4893:
4310:, Defay, R. (1950/1954).
2965:. This inevitably led to
2909:thermodynamic equilibrium
2865:{\displaystyle b_{i}^{0}}
2218:thermally isolated system
2121:thermodynamic equilibrium
1878:
1814:thermodynamic equilibrium
1407:An Inquiry Concerning the
84:thermodynamic equilibrium
4837:Tschoegl, N. W. (2000).
4353:Classical Thermodynamics
4087:Two-state quantum system
4027:{\displaystyle \Xi _{j}}
4000:{\displaystyle \xi _{j}}
3026:thermodynamic operations
2080:surroundings is direct.
1932:permeable to energy but
1862:
1420:Heterogeneous Substances
837:{\displaystyle \alpha =}
705:{\displaystyle \beta =-}
18:Boundary (thermodynamic)
5195:Thermodynamic processes
4841:. Amsterdam: Elsevier.
4790:Fundamentals of Physics
4312:Chemical Thermodynamics
3965:{\displaystyle \alpha }
3583:{\displaystyle p=const}
3545:{\displaystyle T=const}
1738:thermodynamic processes
4808:Finn's Thermal Physics
4801:(6th ed.). Wiley.
4792:(8th ed.). Wiley.
4028:
4001:
3966:
3942:
3915:
3881:
3835:
3802:
3691:
3584:
3546:
3508:
3485:
3448:
3416:
3306:
3156:
3038:it is usually denoted
3001:the entire universe).
2886:
2866:
2834:
2814:
2794:
2793:{\displaystyle a_{ij}}
2764:
2750:denotes the number of
2744:
2714:
2668:
2625:
2562:
2542:
2519:
2476:
2433:
2413:
2385:
2336:
2316:
2296:
2273:
2157:quantum thermodynamics
2007:impermeable to matter
1934:impermeable to matter
1859:and its surroundings.
1803:Systems in equilibrium
1237:
1182:
1127:
1072:
1071:{\displaystyle U(S,V)}
934:
910:
887:
863:
838:
802:
778:
755:
731:
706:
667:
643:
620:
596:
571:
550:Specific heat capacity
154:Quantum thermodynamics
97:
37:
5185:Equilibrium chemistry
5180:Thermodynamic systems
4082:Thermodynamic process
4029:
4002:
3967:
3943:
3916:
3882:
3836:
3782:
3692:
3585:
3547:
3509:
3486:
3449:
3417:
3307:
3157:
2923:used in constructing
2887:
2867:
2835:
2815:
2795:
2765:
2745:
2743:{\displaystyle N_{j}}
2715:
2648:
2626:
2563:
2543:
2520:
2477:
2434:
2414:
2386:
2337:
2317:
2297:
2274:
2169:Environment (systems)
2155:) as hypothesized in
1818:thermodynamic process
1418:On the Equilibrium of
1238:
1183:
1136:Helmholtz free energy
1128:
1073:
935:
911:
888:
864:
839:
803:
779:
756:
732:
707:
668:
644:
621:
597:
572:
96:
35:
5190:Thermodynamic cycles
5129:Regenerative cooling
5007:combustion / thermal
4906:Without phase change
4897:combustion / thermal
4887:Thermodynamic cycles
4351:MĂĽnster, A. (1970).
4138:, p. 1–2.
4113:, p. 1–4.
4011:
3984:
3956:
3925:
3895:
3861:
3719:
3599:
3556:
3518:
3498:
3475:
3426:
3332:
3175:
3120:
2876:
2844:
2824:
2804:
2774:
2754:
2727:
2645:
2579:
2552:
2532:
2492:
2446:
2423:
2398:
2349:
2326:
2306:
2286:
2248:
1897:permeable to matter
1826:For a process to be
1431:Motive Power of Fire
1197:
1142:
1087:
1047:
999:Bridgman's equations
976:Fundamental relation
921:
900:
874:
853:
825:
789:
768:
742:
721:
690:
654:
633:
607:
586:
558:
42:thermodynamic system
4717:Bailyn, M. (1994).
4675:2018PhyA..512..359Z
4638:2020tcsp.book.....P
4262:, p. 109, 112.
4148:Rex & Finn 2017
4136:Rex & Finn 2017
4111:Rex & Finn 2017
4077:Thermodynamic cycle
3889:stream of particles
3590:are determined as
3468:The increments of
3443:
3267:
2967:Loschmidt's paradox
2963:boundary conditions
2927:of certain natural
2925:mathematical models
2861:
2709:
1872:
1869:
1409:Source ... Friction
1341:Loschmidt's paradox
533:Material properties
411:Conjugate variables
4592:(1955/1961/1967).
4394:Physical Chemistry
4326:, p. 112–113.
4024:
3997:
3978:entropy production
3974:energy dissipation
3962:
3950:chemical potential
3938:
3911:
3877:
3831:
3753:
3687:
3658:
3620:
3580:
3542:
3504:
3481:
3444:
3429:
3412:
3302:
3247:
3152:
3087:. You can help by
3018:chemical potential
2989:can be justified.
2969:. However, if the
2956:degrees of freedom
2882:
2862:
2847:
2830:
2810:
2790:
2770:-type molecules,
2760:
2740:
2710:
2695:
2621:
2558:
2538:
2515:
2472:
2429:
2409:
2381:
2332:
2312:
2292:
2269:
2235:heat of combustion
1870:
1867:
1673:Order and disorder
1429:Reflections on the
1336:Heat death paradox
1233:
1178:
1123:
1068:
930:
906:
883:
859:
834:
798:
774:
751:
727:
702:
663:
639:
616:
592:
570:{\displaystyle c=}
567:
540:Property databases
516:Reduced properties
500:Chemical potential
464:Functions of state
387:Thermal efficiency
123:Carnot heat engine
98:
86:when there are no
38:
5167:
5166:
5144:Vapor-compression
5070:Staged combustion
4999:
4998:
4964:With phase change
4817:978-1-498-71887-5
4559:on 15 August 2009
4513:Bryan Sanctuary.
4451:978-1-56072-904-4
4286:, p. 15, 17.
4220:Eu, B.C. (2002).
4092:GENERIC formalism
4062:Mechanical system
3855:
3854:
3744:
3711:
3710:
3649:
3611:
3507:{\displaystyle S}
3484:{\displaystyle G}
3470:Gibbs free energy
3326:
3325:
3226:
3203:
3105:
3104:
2983:thermal radiation
2885:{\displaystyle i}
2833:{\displaystyle j}
2813:{\displaystyle i}
2763:{\displaystyle j}
2636:chemical reaction
2561:{\displaystyle S}
2541:{\displaystyle T}
2432:{\displaystyle P}
2335:{\displaystyle W}
2315:{\displaystyle Q}
2295:{\displaystyle U}
2077:
2076:
1879:type of transfer
1871:by types of wall
1750:GENERIC formalism
1727:
1726:
1668:Self-organization
1493:
1492:
1191:Gibbs free energy
989:Maxwell relations
947:
946:
943:
942:
909:{\displaystyle V}
862:{\displaystyle 1}
817:Thermal expansion
811:
810:
777:{\displaystyle V}
730:{\displaystyle 1}
676:
675:
642:{\displaystyle N}
595:{\displaystyle T}
523:
522:
439:Process functions
425:Property diagrams
404:System properties
394:
393:
359:Endoreversibility
251:Equation of state
16:(Redirected from
5202:
5139:Vapor absorption
4902:
4901:
4880:
4873:
4866:
4857:
4856:
4852:
4833:
4821:
4802:
4793:
4781:
4754:
4732:
4713:
4695:
4694:
4668:
4648:
4642:
4641:
4625:
4619:
4612:
4606:
4603:
4597:
4587:
4581:
4580:, p. 19–23.
4575:
4569:
4568:
4566:
4564:
4558:
4551:
4541:
4535:
4534:
4532:
4530:
4510:
4504:
4503:
4501:
4499:
4488:
4482:
4481:
4479:
4477:
4462:
4456:
4455:
4435:
4429:
4415:
4409:
4403:
4397:
4386:
4380:
4374:
4368:
4362:
4356:
4349:
4343:
4336:Guggenheim, E.A.
4333:
4327:
4321:
4315:
4305:
4299:
4293:
4287:
4281:
4275:
4269:
4263:
4257:
4251:
4239:
4233:
4218:
4212:
4206:
4200:
4186:
4181:
4175:
4169:
4163:
4157:
4151:
4145:
4139:
4133:
4127:
4120:
4114:
4108:
4047:Dynamical system
4033:
4031:
4030:
4025:
4023:
4022:
4006:
4004:
4003:
3998:
3996:
3995:
3971:
3969:
3968:
3963:
3947:
3945:
3944:
3939:
3937:
3936:
3920:
3918:
3917:
3912:
3910:
3909:
3886:
3884:
3883:
3878:
3876:
3875:
3849:
3840:
3838:
3837:
3832:
3827:
3826:
3813:
3812:
3801:
3796:
3778:
3777:
3764:
3763:
3752:
3713:
3705:
3696:
3694:
3693:
3688:
3683:
3682:
3669:
3668:
3657:
3645:
3644:
3631:
3630:
3619:
3593:
3589:
3587:
3586:
3581:
3551:
3549:
3548:
3543:
3513:
3511:
3510:
3505:
3490:
3488:
3487:
3482:
3453:
3451:
3450:
3445:
3442:
3437:
3421:
3419:
3418:
3413:
3408:
3407:
3389:
3388:
3376:
3375:
3357:
3356:
3344:
3343:
3320:
3311:
3309:
3308:
3303:
3272:
3268:
3266:
3255:
3243:
3242:
3227:
3225:
3224:
3212:
3204:
3202:
3194:
3193:
3192:
3179:
3169:
3161:
3159:
3158:
3153:
3145:
3144:
3132:
3131:
3100:
3097:
3079:
3072:
3059:
3048:
3037:
2973:behavior of the
2938:increase in the
2891:
2889:
2888:
2883:
2871:
2869:
2868:
2863:
2860:
2855:
2839:
2837:
2836:
2831:
2819:
2817:
2816:
2811:
2799:
2797:
2796:
2791:
2789:
2788:
2769:
2767:
2766:
2761:
2749:
2747:
2746:
2741:
2739:
2738:
2719:
2717:
2716:
2711:
2708:
2703:
2691:
2690:
2681:
2680:
2667:
2662:
2630:
2628:
2627:
2622:
2614:
2600:
2586:
2567:
2565:
2564:
2559:
2547:
2545:
2544:
2539:
2524:
2522:
2521:
2516:
2511:
2481:
2479:
2478:
2473:
2465:
2438:
2436:
2435:
2430:
2418:
2416:
2415:
2410:
2405:
2390:
2388:
2387:
2382:
2356:
2341:
2339:
2338:
2333:
2321:
2319:
2318:
2313:
2301:
2299:
2298:
2293:
2278:
2276:
2275:
2270:
2231:bomb calorimeter
2073:
2070:
2069:
2063:
2060:
2059:
2053:
2050:
2049:
2038:
2035:
2034:
2028:
2025:
2024:
2018:
2015:
2014:
2000:
1997:
1996:
1990:
1987:
1986:
1980:
1977:
1976:
1965:
1962:
1961:
1955:
1952:
1951:
1945:
1942:
1941:
1927:
1924:
1923:
1917:
1914:
1913:
1907:
1904:
1903:
1873:
1719:
1712:
1705:
1689:
1688:
1396:Key publications
1377:
1376:("living force")
1326:Brownian ratchet
1321:Entropy and life
1316:Entropy and time
1267:
1266:
1242:
1240:
1239:
1234:
1187:
1185:
1184:
1179:
1132:
1130:
1129:
1124:
1077:
1075:
1074:
1069:
971:Clausius theorem
966:Carnot's theorem
939:
937:
936:
931:
915:
913:
912:
907:
892:
890:
889:
884:
868:
866:
865:
860:
847:
846:
843:
841:
840:
835:
807:
805:
804:
799:
783:
781:
780:
775:
760:
758:
757:
752:
736:
734:
733:
728:
715:
714:
711:
709:
708:
703:
672:
670:
669:
664:
648:
646:
645:
640:
625:
623:
622:
617:
601:
599:
598:
593:
580:
579:
576:
574:
573:
568:
546:
545:
419:
418:
238:
237:
119:
105:
104:
21:
5210:
5209:
5205:
5204:
5203:
5201:
5200:
5199:
5170:
5169:
5168:
5163:
5100:
5074:
5006:
4995:
4985:Organic Rankine
4959:
4913:
4910:hot air engines
4907:
4896:
4889:
4884:
4849:
4818:
4751:
4729:
4704:
4699:
4698:
4649:
4645:
4626:
4622:
4613:
4609:
4604:
4600:
4588:
4584:
4576:
4572:
4562:
4560:
4556:
4549:
4543:
4542:
4538:
4528:
4526:
4511:
4507:
4497:
4495:
4490:
4489:
4485:
4475:
4473:
4464:
4463:
4459:
4452:
4436:
4432:
4416:
4412:
4404:
4400:
4387:
4383:
4375:
4371:
4367:, p. 1–97.
4363:
4359:
4350:
4346:
4334:
4330:
4322:
4318:
4306:
4302:
4294:
4290:
4282:
4278:
4270:
4266:
4258:
4254:
4240:
4236:
4219:
4215:
4207:
4203:
4184:
4182:
4178:
4170:
4166:
4158:
4154:
4146:
4142:
4134:
4130:
4121:
4117:
4109:
4105:
4100:
4067:Physical system
4057:Isolated system
4043:
4018:
4014:
4012:
4009:
4008:
3991:
3987:
3985:
3982:
3981:
3957:
3954:
3953:
3932:
3928:
3926:
3923:
3922:
3905:
3901:
3896:
3893:
3892:
3871:
3867:
3862:
3859:
3858:
3822:
3818:
3808:
3804:
3797:
3786:
3773:
3769:
3759:
3755:
3748:
3720:
3717:
3716:
3678:
3674:
3664:
3660:
3653:
3640:
3636:
3626:
3622:
3615:
3600:
3597:
3596:
3557:
3554:
3553:
3519:
3516:
3515:
3499:
3496:
3495:
3476:
3473:
3472:
3454:equal to zero.
3438:
3433:
3427:
3424:
3423:
3403:
3399:
3384:
3380:
3371:
3367:
3352:
3348:
3339:
3335:
3333:
3330:
3329:
3256:
3251:
3238:
3234:
3233:
3229:
3220:
3216:
3211:
3195:
3188:
3184:
3180:
3178:
3176:
3173:
3172:
3164:non-equilibrium
3140:
3136:
3127:
3123:
3121:
3118:
3117:
3101:
3095:
3092:
3085:needs expansion
3070:
3058:
3050:
3047:
3039:
3033:
3010:
2987:molecular chaos
2904:
2902:Isolated system
2898:
2896:Isolated system
2877:
2874:
2873:
2856:
2851:
2845:
2842:
2841:
2825:
2822:
2821:
2805:
2802:
2801:
2781:
2777:
2775:
2772:
2771:
2755:
2752:
2751:
2734:
2730:
2728:
2725:
2724:
2704:
2699:
2686:
2682:
2673:
2669:
2663:
2652:
2646:
2643:
2642:
2610:
2596:
2582:
2580:
2577:
2576:
2553:
2550:
2549:
2533:
2530:
2529:
2507:
2493:
2490:
2489:
2461:
2447:
2444:
2443:
2424:
2421:
2420:
2401:
2399:
2396:
2395:
2352:
2350:
2347:
2346:
2327:
2324:
2323:
2307:
2304:
2303:
2287:
2284:
2283:
2249:
2246:
2245:
2209:
2203:
2191:electric charge
2171:
2165:
2126:The walls of a
2071:
2067:
2061:
2057:
2051:
2047:
2036:
2032:
2026:
2022:
2016:
2012:
1998:
1994:
1988:
1984:
1978:
1974:
1963:
1959:
1953:
1949:
1943:
1939:
1925:
1921:
1915:
1911:
1905:
1901:
1865:
1805:
1796:
1787:
1785:Passive systems
1767:
1723:
1678:
1677:
1653:
1645:
1644:
1643:
1503:
1495:
1494:
1473:
1459:
1434:
1430:
1423:
1419:
1412:
1408:
1375:
1368:
1350:
1331:Maxwell's demon
1293:
1264:
1263:
1247:
1246:
1245:
1198:
1195:
1194:
1193:
1143:
1140:
1139:
1138:
1088:
1085:
1084:
1083:
1048:
1045:
1044:
1043:
1041:Internal energy
1036:
1021:
1011:
1010:
985:
960:
950:
949:
948:
922:
919:
918:
901:
898:
897:
875:
872:
871:
854:
851:
850:
826:
823:
822:
790:
787:
786:
769:
766:
765:
743:
740:
739:
722:
719:
718:
691:
688:
687:
682:Compressibility
655:
652:
651:
634:
631:
630:
608:
605:
604:
587:
584:
583:
559:
556:
555:
535:
525:
524:
505:Particle number
458:
417:
406:
396:
395:
354:Irreversibility
266:State of matter
233:Isolated system
218:
208:
207:
206:
181:
171:
170:
166:Non-equilibrium
158:
133:
125:
103:
88:macroscopically
65:isolated system
28:
23:
22:
15:
12:
11:
5:
5208:
5198:
5197:
5192:
5187:
5182:
5165:
5164:
5162:
5161:
5156:
5151:
5146:
5141:
5136:
5131:
5126:
5121:
5116:
5110:
5108:
5102:
5101:
5099:
5098:
5093:
5088:
5082:
5080:
5076:
5075:
5073:
5072:
5067:
5062:
5057:
5052:
5047:
5042:
5037:
5032:
5027:
5022:
5017:
5011:
5009:
5001:
5000:
4997:
4996:
4994:
4993:
4988:
4978:
4973:
4967:
4965:
4961:
4960:
4958:
4957:
4952:
4947:
4942:
4937:
4932:
4927:
4922:
4916:
4914:
4905:
4899:
4891:
4890:
4883:
4882:
4875:
4868:
4860:
4854:
4853:
4847:
4834:
4822:
4816:
4803:
4794:
4785:
4782:
4770:Thermodynamics
4765:
4755:
4749:
4733:
4727:
4714:
4703:
4700:
4697:
4696:
4643:
4620:
4607:
4598:
4582:
4570:
4536:
4525:on 30 May 2012
4505:
4492:"Hyperphysics"
4483:
4457:
4450:
4430:
4410:
4398:
4388:Silbey, R.J.,
4381:
4369:
4357:
4344:
4328:
4316:
4300:
4288:
4276:
4264:
4252:
4234:
4213:
4201:
4176:
4174:, p. 119.
4164:
4152:
4140:
4128:
4115:
4102:
4101:
4099:
4096:
4095:
4094:
4089:
4084:
4079:
4074:
4072:Quantum system
4069:
4064:
4059:
4054:
4049:
4042:
4039:
4021:
4017:
3994:
3990:
3961:
3935:
3931:
3908:
3904:
3900:
3874:
3870:
3866:
3853:
3852:
3843:
3841:
3830:
3825:
3821:
3817:
3811:
3807:
3800:
3795:
3792:
3789:
3785:
3781:
3776:
3772:
3768:
3762:
3758:
3751:
3747:
3743:
3740:
3737:
3734:
3731:
3728:
3724:
3709:
3708:
3699:
3697:
3686:
3681:
3677:
3673:
3667:
3663:
3656:
3652:
3648:
3643:
3639:
3635:
3629:
3625:
3618:
3614:
3610:
3607:
3604:
3579:
3576:
3573:
3570:
3567:
3564:
3561:
3541:
3538:
3535:
3532:
3529:
3526:
3523:
3503:
3480:
3463:Ilya Prigogine
3441:
3436:
3432:
3411:
3406:
3402:
3398:
3395:
3392:
3387:
3383:
3379:
3374:
3370:
3366:
3363:
3360:
3355:
3351:
3347:
3342:
3338:
3324:
3323:
3314:
3312:
3301:
3298:
3295:
3292:
3288:
3285:
3282:
3279:
3275:
3271:
3265:
3262:
3259:
3254:
3250:
3246:
3241:
3237:
3232:
3223:
3219:
3215:
3210:
3207:
3201:
3198:
3191:
3187:
3183:
3151:
3148:
3143:
3139:
3135:
3130:
3126:
3103:
3102:
3096:September 2016
3082:
3080:
3069:
3066:
3054:
3043:
3009:
3006:
2942:, Boltzmann's
2900:Main article:
2897:
2894:
2881:
2859:
2854:
2850:
2829:
2809:
2787:
2784:
2780:
2759:
2737:
2733:
2721:
2720:
2707:
2702:
2698:
2694:
2689:
2685:
2679:
2676:
2672:
2666:
2661:
2658:
2655:
2651:
2632:
2631:
2620:
2617:
2613:
2609:
2606:
2603:
2599:
2595:
2592:
2589:
2585:
2557:
2537:
2526:
2525:
2514:
2510:
2506:
2503:
2500:
2497:
2483:
2482:
2471:
2468:
2464:
2460:
2457:
2454:
2451:
2428:
2419:at a pressure
2408:
2404:
2392:
2391:
2380:
2377:
2374:
2371:
2368:
2365:
2362:
2359:
2355:
2331:
2311:
2291:
2280:
2279:
2268:
2265:
2262:
2259:
2256:
2253:
2227:
2226:
2220:
2205:Main article:
2202:
2199:
2164:
2161:
2094:semi-permeable
2075:
2074:
2064:
2054:
2044:
2040:
2039:
2029:
2019:
2009:
2002:
2001:
1991:
1981:
1971:
1967:
1966:
1956:
1946:
1936:
1929:
1928:
1918:
1908:
1898:
1894:
1893:
1890:
1887:
1884:
1881:
1880:
1877:
1864:
1861:
1804:
1801:
1795:
1794:Active systems
1792:
1786:
1783:
1766:
1763:
1725:
1724:
1722:
1721:
1714:
1707:
1699:
1696:
1695:
1694:
1693:
1680:
1679:
1676:
1675:
1670:
1665:
1660:
1654:
1651:
1650:
1647:
1646:
1642:
1641:
1636:
1631:
1626:
1621:
1616:
1611:
1606:
1601:
1596:
1591:
1586:
1581:
1576:
1571:
1566:
1561:
1556:
1551:
1546:
1541:
1536:
1531:
1526:
1521:
1516:
1511:
1505:
1504:
1501:
1500:
1497:
1496:
1491:
1490:
1489:
1488:
1483:
1475:
1474:
1472:
1471:
1468:
1464:
1461:
1460:
1458:
1457:
1452:
1450:Thermodynamics
1446:
1443:
1442:
1438:
1437:
1436:
1435:
1426:
1424:
1415:
1413:
1404:
1399:
1398:
1392:
1391:
1390:
1389:
1384:
1379:
1367:
1366:
1364:Caloric theory
1360:
1357:
1356:
1352:
1351:
1349:
1348:
1343:
1338:
1333:
1328:
1323:
1318:
1312:
1309:
1308:
1302:
1301:
1300:
1299:
1292:
1291:
1286:
1281:
1275:
1272:
1271:
1265:
1262:
1261:
1258:
1254:
1253:
1252:
1249:
1248:
1244:
1243:
1232:
1229:
1226:
1223:
1220:
1217:
1214:
1211:
1208:
1205:
1202:
1188:
1177:
1174:
1171:
1168:
1165:
1162:
1159:
1156:
1153:
1150:
1147:
1133:
1122:
1119:
1116:
1113:
1110:
1107:
1104:
1101:
1098:
1095:
1092:
1078:
1067:
1064:
1061:
1058:
1055:
1052:
1037:
1035:
1034:
1029:
1023:
1022:
1017:
1016:
1013:
1012:
1009:
1008:
1001:
996:
991:
984:
983:
978:
973:
968:
962:
961:
956:
955:
952:
951:
945:
944:
941:
940:
929:
926:
916:
905:
894:
893:
882:
879:
869:
858:
844:
833:
830:
820:
813:
812:
809:
808:
797:
794:
784:
773:
762:
761:
750:
747:
737:
726:
712:
701:
698:
695:
685:
678:
677:
674:
673:
662:
659:
649:
638:
627:
626:
615:
612:
602:
591:
577:
566:
563:
553:
544:
543:
542:
536:
531:
530:
527:
526:
521:
520:
519:
518:
513:
508:
497:
486:
467:
466:
460:
459:
457:
456:
451:
445:
442:
441:
435:
434:
433:
432:
427:
408:
407:
402:
401:
398:
397:
392:
391:
390:
389:
384:
379:
371:
370:
364:
363:
362:
361:
356:
351:
346:
344:Free expansion
341:
336:
331:
326:
321:
316:
311:
306:
298:
297:
291:
290:
289:
288:
283:
281:Control volume
278:
273:
271:Phase (matter)
268:
263:
258:
253:
245:
244:
236:
235:
230:
225:
219:
214:
213:
210:
209:
205:
204:
199:
194:
189:
183:
182:
177:
176:
173:
172:
169:
168:
157:
156:
151:
146:
141:
135:
134:
131:
130:
127:
126:
121:The classical
120:
112:
111:
109:Thermodynamics
102:
99:
54:thermodynamics
26:
9:
6:
4:
3:
2:
5207:
5196:
5193:
5191:
5188:
5186:
5183:
5181:
5178:
5177:
5175:
5160:
5157:
5155:
5152:
5150:
5147:
5145:
5142:
5140:
5137:
5135:
5134:Transcritical
5132:
5130:
5127:
5125:
5122:
5120:
5117:
5115:
5114:Hampson–Linde
5112:
5111:
5109:
5107:
5106:Refrigeration
5103:
5097:
5094:
5092:
5089:
5087:
5084:
5083:
5081:
5077:
5071:
5068:
5066:
5063:
5061:
5058:
5056:
5053:
5051:
5048:
5046:
5043:
5041:
5038:
5036:
5035:Gas-generator
5033:
5031:
5028:
5026:
5023:
5021:
5020:Brayton/Joule
5018:
5016:
5013:
5012:
5010:
5008:
5002:
4992:
4989:
4986:
4982:
4979:
4977:
4974:
4972:
4969:
4968:
4966:
4962:
4956:
4953:
4951:
4948:
4946:
4943:
4941:
4938:
4936:
4933:
4931:
4928:
4926:
4925:Brayton/Joule
4923:
4921:
4918:
4917:
4915:
4911:
4903:
4900:
4898:
4892:
4888:
4881:
4876:
4874:
4869:
4867:
4862:
4861:
4858:
4850:
4848:0-444-50426-5
4844:
4840:
4835:
4831:
4827:
4826:Tisza, László
4823:
4819:
4813:
4809:
4804:
4800:
4795:
4791:
4786:
4783:
4779:
4775:
4771:
4766:
4763:
4759:
4756:
4752:
4750:0-471-86256-8
4746:
4742:
4738:
4737:Callen, H. B.
4734:
4730:
4728:0-88318-797-3
4724:
4720:
4715:
4711:
4706:
4705:
4692:
4688:
4684:
4680:
4676:
4672:
4667:
4662:
4658:
4654:
4647:
4639:
4635:
4631:
4624:
4617:
4611:
4602:
4595:
4591:
4590:Prigogine, I.
4586:
4579:
4574:
4555:
4548:
4547:
4540:
4524:
4520:
4516:
4509:
4493:
4487:
4471:
4467:
4461:
4453:
4447:
4443:
4442:
4434:
4427:
4423:
4422:Wergeland, H.
4419:
4414:
4408:, p. 17.
4407:
4402:
4395:
4391:
4390:Alberty, R.A.
4385:
4378:
4377:Tschoegl 2000
4373:
4366:
4361:
4354:
4348:
4341:
4338:(1949/1967).
4337:
4332:
4325:
4320:
4313:
4309:
4308:Prigogine, I.
4304:
4297:
4296:Tschoegl 2000
4292:
4285:
4280:
4273:
4268:
4261:
4256:
4249:
4248:
4243:
4238:
4231:
4230:1-4020-0788-4
4227:
4223:
4217:
4211:, p. 22.
4210:
4205:
4199:(7): 628–634.
4198:
4194:
4190:
4183:Marsland, R.
4180:
4173:
4168:
4162:, p. 20.
4161:
4156:
4150:, p. 20.
4149:
4144:
4137:
4132:
4125:
4119:
4112:
4107:
4103:
4093:
4090:
4088:
4085:
4083:
4080:
4078:
4075:
4073:
4070:
4068:
4065:
4063:
4060:
4058:
4055:
4053:
4052:Energy system
4050:
4048:
4045:
4044:
4038:
4035:
4019:
3992:
3988:
3979:
3975:
3959:
3952:of substance
3951:
3933:
3929:
3906:
3902:
3890:
3872:
3868:
3851:
3844:
3842:
3828:
3823:
3819:
3809:
3805:
3798:
3793:
3790:
3787:
3783:
3779:
3774:
3770:
3760:
3749:
3745:
3741:
3738:
3732:
3729:
3726:
3722:
3715:
3714:
3707:
3700:
3698:
3684:
3679:
3675:
3665:
3661:
3654:
3650:
3646:
3641:
3637:
3627:
3616:
3612:
3608:
3605:
3602:
3595:
3594:
3591:
3577:
3574:
3571:
3568:
3565:
3562:
3559:
3539:
3536:
3533:
3530:
3527:
3524:
3521:
3501:
3494:
3478:
3471:
3466:
3464:
3460:
3455:
3439:
3434:
3430:
3404:
3400:
3396:
3393:
3390:
3385:
3381:
3377:
3372:
3368:
3364:
3361:
3353:
3349:
3345:
3340:
3336:
3322:
3315:
3313:
3299:
3296:
3293:
3290:
3286:
3283:
3280:
3277:
3273:
3269:
3260:
3252:
3248:
3244:
3239:
3235:
3230:
3221:
3217:
3213:
3208:
3205:
3199:
3196:
3189:
3185:
3181:
3171:
3170:
3167:
3165:
3149:
3146:
3141:
3137:
3133:
3128:
3124:
3115:
3111:
3099:
3090:
3086:
3083:This section
3081:
3078:
3074:
3073:
3065:
3061:
3057:
3053:
3046:
3042:
3036:
3029:
3027:
3021:
3019:
3013:
3005:
3002:
2998:
2996:
2990:
2988:
2984:
2980:
2976:
2972:
2968:
2964:
2961:
2957:
2953:
2949:
2945:
2941:
2937:
2932:
2930:
2926:
2922:
2918:
2912:
2910:
2903:
2893:
2879:
2857:
2852:
2848:
2827:
2807:
2785:
2782:
2778:
2757:
2735:
2731:
2705:
2700:
2696:
2692:
2687:
2683:
2677:
2674:
2670:
2664:
2659:
2656:
2653:
2649:
2641:
2640:
2639:
2637:
2618:
2615:
2607:
2604:
2601:
2593:
2590:
2587:
2575:
2574:
2573:
2571:
2555:
2535:
2512:
2504:
2501:
2498:
2495:
2488:
2487:
2486:
2469:
2466:
2458:
2455:
2452:
2449:
2442:
2441:
2440:
2426:
2406:
2378:
2375:
2372:
2369:
2366:
2363:
2360:
2357:
2345:
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2343:
2329:
2309:
2289:
2266:
2263:
2260:
2257:
2254:
2244:
2243:
2242:
2239:
2236:
2232:
2225:
2221:
2219:
2215:
2214:
2213:
2208:
2201:Closed system
2198:
2196:
2192:
2188:
2184:
2180:
2176:
2170:
2160:
2158:
2154:
2150:
2146:
2142:
2136:
2133:
2129:
2128:closed system
2124:
2122:
2118:
2113:
2111:
2107:
2103:
2097:
2095:
2091:
2087:
2081:
2042:
2041:
2008:
2005:adynamic and
2004:
2003:
1969:
1968:
1935:
1931:
1930:
1896:
1895:
1891:
1888:
1885:
1883:
1882:
1876:type of wall
1875:
1874:
1860:
1858:
1854:
1850:
1846:
1840:
1837:
1831:
1829:
1824:
1823:
1819:
1815:
1811:
1800:
1791:
1782:
1778:
1774:
1770:
1762:
1760:
1754:
1751:
1747:
1741:
1739:
1734:
1732:
1720:
1715:
1713:
1708:
1706:
1701:
1700:
1698:
1697:
1692:
1684:
1683:
1682:
1681:
1674:
1671:
1669:
1666:
1664:
1663:Self-assembly
1661:
1659:
1656:
1655:
1649:
1648:
1640:
1637:
1635:
1634:van der Waals
1632:
1630:
1627:
1625:
1622:
1620:
1617:
1615:
1612:
1610:
1607:
1605:
1602:
1600:
1597:
1595:
1592:
1590:
1587:
1585:
1582:
1580:
1577:
1575:
1572:
1570:
1567:
1565:
1562:
1560:
1559:von Helmholtz
1557:
1555:
1552:
1550:
1547:
1545:
1542:
1540:
1537:
1535:
1532:
1530:
1527:
1525:
1522:
1520:
1517:
1515:
1512:
1510:
1507:
1506:
1499:
1498:
1487:
1484:
1482:
1479:
1478:
1477:
1476:
1469:
1466:
1465:
1463:
1462:
1456:
1453:
1451:
1448:
1447:
1445:
1444:
1440:
1439:
1433:
1432:
1425:
1422:
1421:
1414:
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1410:
1403:
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1394:
1393:
1388:
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1374:
1370:
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1365:
1362:
1361:
1359:
1358:
1354:
1353:
1347:
1344:
1342:
1339:
1337:
1334:
1332:
1329:
1327:
1324:
1322:
1319:
1317:
1314:
1313:
1311:
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1307:
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1298:
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1290:
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1200:
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1102:
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1079:
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1056:
1050:
1042:
1039:
1038:
1033:
1030:
1028:
1025:
1024:
1020:
1015:
1014:
1007:
1006:
1002:
1000:
997:
995:
992:
990:
987:
986:
982:
981:Ideal gas law
979:
977:
974:
972:
969:
967:
964:
963:
959:
954:
953:
927:
917:
903:
896:
895:
880:
870:
856:
849:
848:
845:
831:
828:
821:
818:
815:
814:
795:
785:
771:
764:
763:
748:
738:
724:
717:
716:
713:
699:
696:
693:
686:
683:
680:
679:
660:
650:
636:
629:
628:
613:
603:
589:
582:
581:
578:
564:
561:
554:
551:
548:
547:
541:
538:
537:
534:
529:
528:
517:
514:
512:
511:Vapor quality
509:
507:
506:
501:
498:
496:
495:
490:
487:
484:
480:
479:
474:
471:
470:
469:
468:
465:
462:
461:
455:
452:
450:
447:
446:
444:
443:
440:
437:
436:
431:
428:
426:
423:
422:
421:
420:
416:
412:
405:
400:
399:
388:
385:
383:
380:
378:
375:
374:
373:
372:
369:
366:
365:
360:
357:
355:
352:
350:
349:Reversibility
347:
345:
342:
340:
337:
335:
332:
330:
327:
325:
322:
320:
317:
315:
312:
310:
307:
305:
302:
301:
300:
299:
296:
293:
292:
287:
284:
282:
279:
277:
274:
272:
269:
267:
264:
262:
259:
257:
254:
252:
249:
248:
247:
246:
243:
240:
239:
234:
231:
229:
226:
224:
223:Closed system
221:
220:
217:
212:
211:
203:
200:
198:
195:
193:
190:
188:
185:
184:
180:
175:
174:
167:
163:
160:
159:
155:
152:
150:
147:
145:
142:
140:
137:
136:
129:
128:
124:
118:
114:
113:
110:
107:
106:
95:
91:
89:
85:
81:
76:
74:
70:
69:closed system
66:
61:
57:
55:
51:
47:
44:is a body of
43:
34:
30:
19:
4991:Regenerative
4920:Bell Coleman
4838:
4832:. MIT Press.
4829:
4807:
4798:
4789:
4769:
4761:
4758:Carnot, Sadi
4740:
4718:
4709:
4656:
4652:
4646:
4629:
4623:
4610:
4601:
4593:
4585:
4573:
4561:. Retrieved
4554:the original
4545:
4539:
4527:. Retrieved
4523:the original
4518:
4508:
4496:. Retrieved
4486:
4474:. Retrieved
4469:
4460:
4440:
4433:
4425:
4418:ter Haar, D.
4413:
4401:
4393:
4384:
4379:, p. 3.
4372:
4360:
4352:
4347:
4339:
4331:
4319:
4311:
4303:
4298:, p. 5.
4291:
4279:
4274:, p. 7.
4267:
4255:
4246:
4237:
4221:
4216:
4204:
4196:
4193:Am. J. Phys.
4192:
4179:
4167:
4155:
4143:
4131:
4118:
4106:
4036:
3856:
3845:
3701:
3467:
3461:was made by
3456:
3327:
3316:
3113:
3109:
3106:
3093:
3089:adding to it
3084:
3062:
3055:
3051:
3044:
3040:
3034:
3030:
3022:
3014:
3011:
3003:
2999:
2994:
2991:
2933:
2921:idealization
2913:
2905:
2820:in molecule
2722:
2633:
2527:
2484:
2393:
2281:
2240:
2228:
2210:
2182:
2178:
2175:surroundings
2174:
2172:
2163:Surroundings
2145:steam engine
2137:
2131:
2125:
2114:
2109:
2105:
2102:surroundings
2101:
2098:
2082:
2078:
2006:
1933:
1841:
1832:
1825:
1822:quasistatic.
1821:
1806:
1797:
1788:
1779:
1775:
1771:
1768:
1759:Flow process
1755:
1742:
1735:
1730:
1728:
1524:Carathéodory
1455:Heat engines
1427:
1416:
1405:
1387:Motive power
1372:
1032:Free entropy
1003:
503:
502: /
492:
491: /
483:introduction
476:
475: /
414:
377:Heat engines
215:
164: /
79:
77:
62:
58:
41:
39:
29:
5159:Ionocaloric
5154:Vuilleumier
4976:Hygroscopic
4659:: 359–366.
4578:Bailyn 1994
4406:Callen 1985
4284:Callen 1985
4209:Bailyn 1994
4160:Bailyn 1994
3068:Open system
2979:randomizing
2179:environment
2149:Sadi Carnot
2132:open system
2110:environment
1346:Synergetics
1027:Free energy
473:Temperature
334:Quasistatic
329:Isenthalpic
286:Instruments
276:Equilibrium
228:Open system
162:Equilibrium
144:Statistical
73:open system
5174:Categories
5124:Pulse tube
5096:Mixed/dual
4666:1808.00108
4365:Haase 1971
4324:Tisza 1966
4272:Haase 1971
4260:Tisza 1966
4172:Tisza 1966
4098:References
2971:stochastic
2167:See also:
2147:, such as
2141:Max Planck
2090:diathermal
2043:isolating
1970:adiabatic
1855:between a
1828:reversible
1658:Nucleation
1502:Scientists
1306:Philosophy
1019:Potentials
382:Heat pumps
339:Polytropic
324:Isentropic
314:Isothermal
5119:Kleemenko
5005:Internal
4778:73-117081
4739:(1985) .
4016:Ξ
3989:ξ
3960:α
3934:α
3930:μ
3907:α
3899:Δ
3873:α
3865:Δ
3824:α
3816:Δ
3810:α
3806:η
3788:α
3784:∑
3771:ξ
3767:Δ
3757:Ξ
3746:∑
3742:−
3736:Δ
3680:α
3672:Δ
3666:α
3662:μ
3655:α
3651:∑
3638:ξ
3634:Δ
3624:Ξ
3613:∑
3431:ξ
3394:…
3350:τ
3337:τ
3297:…
3249:ξ
3245:−
3236:ξ
3218:τ
3209:−
3186:ξ
3150:…
3138:ξ
3125:ξ
2975:molecules
2948:equations
2944:H-theorem
2929:phenomena
2650:∑
2605:−
2496:δ
2450:δ
2373:δ
2370:−
2364:δ
2264:−
2252:Δ
2183:reservoir
2108:, or the
2106:reservoir
2086:adiabatic
1639:Waterston
1589:von Mayer
1544:de Donder
1534:Clapeyron
1514:Boltzmann
1509:Bernoulli
1470:Education
1441:Timelines
1225:−
1170:−
958:Equations
925:∂
878:∂
829:α
793:∂
746:∂
700:−
694:β
658:∂
611:∂
319:Adiabatic
309:Isochoric
295:Processes
256:Ideal gas
139:Classical
50:radiation
5086:Combined
5045:Humphrey
5030:Expander
5015:Atkinson
4950:Stoddard
4940:Stirling
4935:Ericsson
4895:External
4828:(1966).
4760:(1824).
4691:53605597
4470:ChemWiki
4424:(1966).
4244:(1949).
4242:Born, M.
4041:See also
4007:, while
3887:) and a
3114:isolated
2187:momentum
2117:isolated
1731:tendency
1691:Category
1629:Thompson
1539:Clausius
1519:Bridgman
1373:Vis viva
1355:Theories
1289:Gas laws
1081:Enthalpy
489:Pressure
304:Isobaric
261:Real gas
149:Chemical
132:Branches
101:Overview
71:, or an
5149:Siemens
5065:Scuderi
4981:Rankine
4702:Sources
4671:Bibcode
4634:Bibcode
3493:entropy
2936:entropy
2840:, and
2181:or the
1886:Matter
1853:entropy
1765:History
1614:Smeaton
1609:Rankine
1599:Onsager
1584:Maxwell
1579:Massieu
1284:Entropy
1279:General
1270:History
1260:Culture
1257:History
481: (
478:Entropy
415:italics
216:Systems
48:and/or
5055:Miller
5050:Lenoir
5025:Diesel
4971:Kalina
4955:Manson
4930:Carnot
4845:
4814:
4776:
4747:
4725:
4689:
4448:
4228:
3328:where
3110:closed
2995:closed
2960:mirror
2723:where
2528:where
2439:then:
2282:where
2153:quarks
1857:system
1849:energy
1810:phases
1604:Planck
1594:Nernst
1569:Kelvin
1529:Carnot
819:
684:
552:
494:Volume
409:Note:
368:Cycles
197:Second
187:Zeroth
46:matter
5079:Mixed
4687:S2CID
4661:arXiv
4563:9 May
4557:(PDF)
4550:(PDF)
4529:9 May
4498:9 May
4476:9 May
2946:used
2917:model
2193:, or
1892:Heat
1889:Work
1863:Walls
1652:Other
1619:Stahl
1574:Lewis
1564:Joule
1554:Gibbs
1549:Duhem
242:State
202:Third
192:First
80:state
5091:HEHC
5060:Otto
4843:ISBN
4812:ISBN
4774:LCCN
4745:ISBN
4723:ISBN
4565:2012
4531:2012
4500:2012
4478:2012
4446:ISBN
4226:ISBN
3552:and
3491:and
2104:, a
1845:mass
1624:Tait
454:Heat
449:Work
179:Laws
67:, a
4679:doi
4657:512
4185:III
3948:is
3514:at
3091:.
2952:gas
1851:or
1847:or
1744:to
1467:Art
413:in
5176::
4685:.
4677:.
4669:.
4655:.
4517:.
4468:.
4420:,
4197:83
4195:,
4191:,
3020:.
2931:.
2911:.
2189:,
2159:.
2088:,
1761:.
56:.
40:A
4987:)
4983:(
4912:)
4908:(
4879:e
4872:t
4865:v
4851:.
4820:.
4780:.
4753:.
4731:.
4693:.
4681::
4673::
4663::
4640:.
4636::
4618:.
4567:.
4533:.
4502:.
4480:.
4454:.
4232:.
4020:j
3993:j
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3702:(
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3609:=
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3391:,
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2467:V
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2358:U
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2330:W
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2258:=
2255:U
2072:N
2062:N
2052:N
2037:Y
2027:N
2017:N
1999:N
1989:Y
1979:N
1964:Y
1954:Y
1944:N
1926:N
1916:N
1906:Y
1718:e
1711:t
1704:v
1231:S
1228:T
1222:H
1219:=
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1213:p
1210:,
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1167:U
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1158:V
1155:,
1152:T
1149:(
1146:A
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1118:p
1115:+
1112:U
1109:=
1106:)
1103:p
1100:,
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1063:V
1060:,
1057:S
1054:(
1051:U
928:T
904:V
881:V
857:1
832:=
796:p
772:V
749:V
725:1
697:=
661:T
637:N
614:S
590:T
565:=
562:c
485:)
20:)
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