1963:). Because the person changed the stationary position of the box, that person exerted energy on that box. The work exerted can also be called "useful energy", because energy was converted from one form into the intended purpose, i.e. mechanical use. For the case of the person pushing the box, the energy in the form of internal (or potential) energy obtained through metabolism was converted into work to push the box. This energy conversion, however, was not straightforward: while some internal energy went into pushing the box, some was diverted away (lost) in the form of heat (transferred thermal energy).
33:
1603:
4639:, in which he introduced the preliminary outline of the principles of his new equation able to predict or estimate the tendencies of various natural processes to ensue when bodies or systems are brought into contact. By studying the interactions of homogeneous substances in contact, i.e., bodies, being in composition part solid, part liquid, and part vapor, and by using a three-dimensional
2029:, and the energy lost in the form of heat is what is called the "useful energy" of the body, or the work of the body performed on an object. In thermodynamics, this is what is known as "free energy". In other words, free energy is a measure of work (useful energy) a system can perform at constant temperature.
4496:
in a coal furnace to boil water, and use this heat to vaporize steam, and then use the enhanced high-pressure energy of the vaporized steam to push a piston. Thus, we might naively reason that one can entirely convert the initial combustion heat of the chemical reaction into the work of pushing the
4383:
we find: "As motion was explained by the
Newtonian concept of force, chemists wanted a similar concept of ādriving forceā for chemical change. Why do chemical reactions occur, and why do they stop at certain points? Chemists called the āforceā that caused chemical reactions affinity, but it lacked
2562:
This definition of free energy is useful for gas-phase reactions or in physics when modeling the behavior of isolated systems kept at a constant volume. For example, if a researcher wanted to perform a combustion reaction in a bomb calorimeter, the volume is kept constant throughout the course of a
4788:
Up until this point, the general view had been such that: āall chemical reactions drive the system to a state of equilibrium in which the affinities of the reactions vanishā. Over the next 60 years, the term affinity came to be replaced with the term free energy. According to chemistry historian
4742:
stated, in opposition to
Berthelot and Thomas' hypothesis that chemical affinity is a measure of the heat of reaction of chemical reaction as based on the principle of maximal work, that affinity is not the heat given out in the formation of a compound but rather it is the largest quantity of work
2431:
Thus, in traditional use, the term "free" was attached to Gibbs free energy for systems at constant pressure and temperature, or to
Helmholtz free energy for systems at constant temperature, to mean āavailable in the form of useful work.ā With reference to the Gibbs free energy, we need to add the
1958:
The basic definition of "energy" is a measure of a body's (in thermodynamics, the system's) ability to cause change. For example, when a person pushes a heavy box a few metres forward, that person exerts mechanical energy, also known as work, on the box over a distance of a few meters forward. The
2355:, was regarded as a mixture of two components; the free or perceptible caloric could affect a thermometer, whereas the other component, the latent caloric, could not. The use of the words "latent heat" implied a similarity to latent heat in the more usual sense; it was regarded as chemically
4458:
Based on these and other ideas, Berthelot and
Thomsen, as well as others, considered the heat given out in the formation of a compound as a measure of the affinity, or the work done by the chemical forces. This view, however, was not entirely correct. In 1847, the English physicist
2451:
meeting to set unified terminologies for the international scientific community, in which the adjective āfreeā was supposedly banished. This standard, however, has not yet been universally adopted, and many published articles and books still include the descriptive āfreeā.
4706:
of the parts of the body, and (when different parts of the body are in different states) in the proportion in which the body is divided between the different states. The condition of stable equilibrium is that the value of the expression in the parenthesis shall be a
4242:
while the engine produces nonzero work. It is important to note that for heat engines and other thermal systems, the free energies do not offer convenient characterizations; internal energy and enthalpy are the preferred potentials for characterizing thermal systems.
4147:
This tells us that the change in free energy equals the reversible or maximum work for a process performed at constant temperature. Under other conditions, free-energy change is not equal to work; for instance, for a reversible adiabatic expansion of an ideal gas,
3730:
3828:
2981:
1833:
work needed to "make space for additional molecules" produced by various processes. Gibbs free energy change therefore equals work not associated with system expansion or compression, at constant temperature and pressure, hence its utility to
2324:, in which heat was the lightest of the four elements. In a similar manner, during these years, heat was beginning to be distinguished into different classification categories, such as "free heat", "combined heat", "radiant heat",
4651:
graph, Gibbs was able to determine three states of equilibrium, i.e., "necessarily stable", "neutral", and "unstable", and whether or not changes will ensue. In 1876, Gibbs built on this framework by introducing the concept of
4336:. Thus, a negative value of the change in free energy is a necessary condition for a process to be spontaneous; this is the most useful form of the second law of thermodynamics in chemistry. In chemical equilibrium at constant
4141:
4743:
which can be gained when the reaction is carried out in a reversible manner, e.g., electrical work in a reversible cell. The maximum work is thus regarded as the diminution of the free, or available, energy of the system (
4497:
piston. Clausius showed, however, that we must take into account the work that the molecules of the working body, i.e., the water molecules in the cylinder, do on each other as they pass or transform from one step of or
3983:
2251:(for Helmholtz free energy) does indeed indicate that a spontaneous change in a non-reactive system's free energy (NOT the internal energy) comprises the available energy to do work (compression in this case)
2460:
Just like the general concept of energy, free energy has a few definitions suitable for different conditions. In physics, chemistry, and biology, these conditions are thermodynamic parameters (temperature
1322:
4463:
showed that he could raise the temperature of water by turning a paddle wheel in it, thus showing that heat and mechanical work were equivalent or proportional to each other, i.e., approximately,
1950:
most often refers to the Gibbs free energy. The values of the two free energies are usually quite similar and the intended free energy function is often implicit in manuscripts and presentations.
4195:
4238:
4656:
so to take into account chemical reactions and states of bodies that are chemically different from each other. In his own words, to summarize his results in 1873, Gibbs states:
4589:. Thus, the heat used to transform the working body of molecules from one state to the next cannot be used to do external work, e.g., to push the piston. Clausius defined this
4443:
formulated the principle that the evolution of heat in a reaction is the same whether the process is accomplished in one-step process or in a number of stages. This is known as
2369:
During the early 19th century, the concept of perceptible or free caloric began to be referred to as "free heat" or "heat set free". In 1824, for example, the French physicist
3547:
3405:
3637:
4334:
4305:
3738:
3501:
3348:
3235:
3131:
3027:
2891:
2176:
1904:
4583:
4543:
3465:
2249:
1157:
1102:
1047:
2590:
2141:
854:
807:
722:
675:
587:
540:
2633:
2027:
758:
626:
3378:
3302:
4626:
4395:, which states that light and heat are forms of matter attracted or repelled by other forms of matter, with forces analogous to gravitation or to chemical affinity.
2691:
2557:
2414:
2114:
represents energy not available to perform work. However, this is incorrect. For instance, in an isothermal expansion of an ideal gas, the internal energy change is
2067:
992:
4416:, in which all chemical changes occurring without intervention of outside energy tend toward the production of bodies or of a system of bodies which liberate heat.
3578:
3438:
3189:
3085:
2307:
2278:
1689:, it is not absolute but depends on the choice of a zero point. Therefore, only relative free energy values, or changes in free energy, are physically meaningful.
3629:
2199:
2112:
491:
4018:
3892:
3872:
3602:
3263:
3159:
3055:
2885:
2754:
2734:
2714:
2653:
2610:
2519:
2499:
2479:
2089:
2004:
1984:
830:
783:
698:
651:
563:
516:
4067:
2366:
of a gas, the absolute heat remained constant but the observed rise in temperature implied that some latent caloric had become "free" or perceptible.
5217:
5156:
2448:
5355:
4985:
2347:
stated: āIn general, one can change the first hypothesis into the second by changing the words āfree heat, combined heat, and heat releasedā into ā
1632:
3904:
4989:
5309:
1333:
5216:
1221:
1959:
mathematical definition of this form of energy is the product of the force exerted on the object and the distance by which the box moved (
5291:
5192:
455:
2820:
1311:
4431:
by showing that the heat given out in a reaction is equal to the heat absorbed in the reverse reaction. They also investigated the
2377:", speaks of quantities of heat āabsorbed or set freeā in different transformations. In 1882, the German physicist and physiologist
2521:, etc.). Scientists have come up with several ways to define free energy. The mathematical expression of Helmholtz free energy is:
2592:. In solution chemistry, on the other hand, most chemical reactions are kept at constant pressure. Under this condition, the heat
2374:
1344:
1712:
loss in the course of such work. Since first-law energy is always conserved, it is evident that free energy is an expendable,
5371:
1685:, and its sign indicates whether the process is thermodynamically favorable or forbidden. Since free energy usually contains
914:
1625:
1212:
881:
448:
326:
4849:
Stoner, Clinton D. (2000). Inquiries into the Nature of Free Energy and
Entropy in Respect to Biochemical Thermodynamics.
2831:, which create entropy. Even for homogeneous "bulk" materials, the free energy functions depend on the (often suppressed)
2006:
of a body (entropy is a measure of disorder in a system). The difference between the change in internal energy, which is
1864:
264:
5394:
4152:
1396:
1370:
891:
345:
5005:"A Thermodynamic Model for Lithium-Ion Battery Degradation: Application of the Degradation-Entropy Generation Theorem"
1899:
a system isothermally. The
Helmholtz free energy has a special theoretical importance since it is proportional to the
5235:
5155:
5140:
5115:
5086:
5053:
4961:
4923:
297:
4439:
of a number of substances, and amounts of heat given out in combustion. In a similar manner, in 1840 Swiss chemist
2635:
of the system. Under constant pressure and temperature, the free energy in a reaction is known as Gibbs free energy
4034:
method is a numerical approach for determining the values of free energies, based on quantum dynamical principles.
1449:
920:
319:
4773:= constant), whilst the heat given out is usually a measure of the diminution of the total energy of the system (
4585:). Clausius originally called this the "transformation content" of the body, and then later changed the name to
2201:
term supposedly not available to perform work. But it is noteworthy that the derivative form of the free energy:
1618:
5310:"A historical/epistemological account of the foundation of the key ideas supporting chemical equilibrium theory"
4801:
led to the replacement of the term "affinity" by the term "free energy" in much of the
English-speaking world.
1549:
81:
2370:
2316:, i.e., that heat is a form of energy having relation to vibratory motion, was beginning to supplant both the
1891:), the Helmholtz function is completely general: its decrease is the maximum amount of work which can be done
1444:
4474:
4207:
2351:, loss of vis viva, and increase of vis viva.ā" In this manner, the total mass of caloric in a body, called
1524:
1297:
274:
4410:. In 1875, after quantifying the heats of reaction for a large number of compounds, Berthelot proposed the
2037:
4825:
4252:
3605:
1713:
909:
112:
102:
3604:
in the system. If these quantities do not appear, it is impossible to describe compositional changes. The
4637:
A Method of
Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces
4478:
1693:
117:
107:
5267:
5168:
5078:
3851:
3725:{\displaystyle \mathrm {d} A=-p\,\mathrm {d} V-S\,\mathrm {d} T+\sum _{i}\mu _{i}\,\mathrm {d} N_{i}\,}
2789:
1401:
1365:
143:
77:
4738:
Hence, in 1882, after the introduction of these arguments by
Clausius and Gibbs, the German scientist
4387:
During the entire 18th century, the dominant view with regard to heat and light was that put forth by
3823:{\displaystyle \mathrm {d} G=V\,\mathrm {d} p-S\,\mathrm {d} T+\sum _{i}\mu _{i}\,\mathrm {d} N_{i}\,}
3507:
3383:
2976:{\displaystyle \int \left(T\,\mathrm {d} S-p\,\mathrm {d} V+\sum _{i}\mu _{i}\mathrm {d} N_{i}\right)}
2439:
An increasing number of books and journal articles do not include the attachment "free", referring to
2071:
This expression has commonly been interpreted to mean that work is extracted from the internal energy
1716:
kind of energy. Several free energy functions may be formulated based on system criteria. Free energy
1439:
5399:
4661:
4448:
4412:
4031:
1762:
1194:
388:
201:
191:
4356:
The quantity called "free energy" is a more advanced and accurate replacement for the outdated term
5404:
5260:"Glossary of Terms in Quantities and Units in Clinical Chemistry (IUPAC-IFCC Recommendations 1996)"
4310:
4281:
3469:
3308:
3195:
3091:
2987:
2836:
2146:
5107:
4732:
4640:
4548:
4508:
3442:
2204:
1721:
1606:
1434:
1231:
1112:
1057:
1002:
934:
873:
409:
398:
64:
2566:
2117:
836:
789:
704:
657:
569:
522:
5259:
5227:
5221:
5160:
4452:
4027:, the amount of increase of free energy when the area of surface increases by every unit area.
1717:
1539:
1256:
340:
94:
69:
5046:
Reflections on the Motive Power of Fire ā and other Papers on the Second Law of
Thermodynamics
2615:
2009:
1459:
740:
605:
4759:
4739:
4489:
3363:
3269:
3033:
2563:
reaction. Therefore, the heat of the reaction is a direct measure of the free energy change,
2444:
2425:
2378:
1912:
1846:
1808:
1678:
1674:
1474:
1051:
364:
210:
59:
4596:
3894:, conditions which are easy to achieve experimentally, and which approximately characterize
2661:
2527:
2384:
962:
4424:
3556:
3411:
1835:
1658:
1554:
1479:
1469:
269:
131:
3165:
3061:
2283:
2254:
8:
4703:
4498:
4493:
4399:
4024:
2321:
1895:
a system at constant temperature, and it can increase at most by the amount of work done
1499:
1261:
283:
249:
244:
157:
3611:
2181:
2094:
1494:
473:
5360:
5329:
5283:
5184:
4979:
4891:
4653:
4451:
in the early 19th century, Hess's law came to be viewed as a consequence of the law of
4368:. The term affinity, as used in chemical relation, dates back to at least the time of
4003:
3989:
3877:
3857:
3843:
3587:
3248:
3144:
3040:
2870:
2840:
2739:
2719:
2699:
2638:
2595:
2504:
2484:
2464:
2074:
1989:
1969:
1908:
1883: 'work'). Since it makes no reference to any quantities involved in work (such as
1825:, because, in addition to subsuming any entropy change due merely to heat, a change in
1682:
1588:
1251:
1246:
1199:
815:
768:
683:
636:
548:
501:
431:
415:
302:
254:
239:
229:
38:
32:
2696:
These functions have a minimum in chemical equilibrium, as long as certain variables (
5367:
5333:
5231:
5136:
5111:
5082:
5049:
5026:
4967:
4957:
4929:
4919:
4895:
4883:
4830:
4744:
4660:
If we wish to express in a single equation the necessary and sufficient condition of
4420:
4365:
3241:
2832:
2824:
2797:
2757:
2360:
1732:
1583:
1544:
1534:
1106:
904:
732:
234:
224:
166:
5287:
5188:
4863:
4020:
times a corresponding increase in the entropy of the system and/or its surrounding.
2756:) are held constant. In addition, they also have theoretical importance in deriving
5321:
5275:
5176:
5071:
5016:
4879:
4875:
4794:
4407:
4256:
3993:
2828:
2785:
2767:
1686:
1504:
1489:
1429:
1424:
1241:
1236:
886:
354:
219:
4136:{\displaystyle \Delta A=\Delta U-T\Delta S=\Delta U-q_{\text{rev}}=w_{\text{rev}}}
1812:
4774:
4716:
4648:
4485:
4428:
4369:
3354:
2863:
2363:
1876:
1725:
1709:
1662:
1454:
1302:
956:
597:
420:
181:
148:
4403:
4380:
2317:
2313:
1839:
1705:
1654:
1646:
1509:
1279:
379:
259:
196:
186:
54:
24:
5325:
5021:
5004:
4971:
5388:
5030:
4933:
4887:
4820:
4798:
4632:
4432:
2805:
2801:
2329:
2325:
1578:
896:
465:
426:
138:
5279:
5180:
3978:{\displaystyle (\mathrm {d} G)_{T,p}=\sum _{i}\mu _{i}\,\mathrm {d} N_{i}\,}
4502:
4444:
4440:
4388:
4200:
1926:
Historically, the term 'free energy' has been used for either quantity. In
1529:
1514:
1464:
947:
4274:, applies. For a process at constant temperature and pressure without non-
3988:
Any decrease in the Gibbs function of a system is the upper limit for any
1966:
For a reversible process, heat is the product of the absolute temperature
4460:
4436:
3997:
3581:
1484:
292:
4953:
Modern thermodynamics : from heat engines to dissipative structures
2784:
contraction. Other forms of work which must sometimes be considered are
1573:
1519:
16:
State function whose change relates to the system's maximal work output
4951:
2332:, "absolute heat", "latent caloric", "free" or "perceptible" caloric (
2309:. Similar expression can be written for the Gibbs free energy change.
4913:
3608:
for processes at uniform pressure and temperature are (assuming only
2793:
2777:
2344:
1943:
1919:; and to gas-phase chemists and engineers, who do not want to ignore
1916:
1900:
171:
5226:(2nd ed.). Oxford: Blackwell Scientific Publications. pp.
5220:
Commission on Physicochemical Symbols Terminology and Units (1993).
4785:
is the amount of energy "free" for work under the given conditions.
3854:
in the system. The second relation is especially useful at constant
4665:
3996:
work that can be captured in the surroundings, or it may simply be
3137:
2348:
1815:
1796:
1754:
1666:
1287:
1204:
996:
404:
176:
4724:
4644:
4586:
2340:
1927:
1770:
1670:
393:
5161:"Glossary of Atmospheric Chemistry Terms (Recommendations 1990)"
4492:
needed amendment. That is, one can use the heat derived from a
1673:, etc.). The change in the free energy is the maximum amount of
4815:
4810:
4360:, which was used by chemists in previous years to describe the
4307:. Similarly, for a process at constant temperature and volume,
4246:
2813:
2809:
2781:
2428:
under the given conditions, specifically constant temperature.
5257:
5258:
Lehmann, H. P.; Fuentes-Arderiu, X.; Bertello, L. F. (1996).
3895:
1934:
most often refers to the Helmholtz free energy, denoted by
1871:. Thus its appellation "work content", and the designation
369:
4702:
refers to the variation produced by any variations in the
4791:
Thermodynamics and the Free Energy of Chemical Reactions
4664:
for a substance when surrounded by a medium of constant
4949:
1867:
work done on, or obtainable from, a system at constant
1700:
to perform thermodynamic work at constant temperature,
5044:
Mendoza, E. (1988). Clapeyron, E.; Carnot, R. (eds.).
4255:, for any process that occurs in a closed system, the
4862:
Osara, Jude A.; Bryant, Michael D. (September 2019).
4599:
4551:
4511:
4313:
4284:
4210:
4203:, the free-energy change after a full cycle is zero,
4155:
4070:
4006:
3907:
3880:
3860:
3741:
3640:
3614:
3590:
3559:
3510:
3472:
3445:
3414:
3386:
3366:
3311:
3272:
3251:
3198:
3168:
3147:
3094:
3064:
3043:
2990:
2894:
2873:
2742:
2722:
2702:
2664:
2641:
2618:
2598:
2569:
2530:
2507:
2487:
2467:
2387:
2286:
2257:
2207:
2184:
2149:
2120:
2097:
2077:
2040:
2012:
1992:
1972:
1115:
1060:
1005:
965:
839:
818:
792:
771:
743:
707:
686:
660:
639:
608:
572:
551:
525:
504:
476:
3898:
creatures. Under these conditions, it simplifies to
5223:
Quantities, Units and Symbols in Physical Chemistry
5159:Commission on Atmospheric Chemistry, J. G. (1990).
2381:coined the phrase āfree energyā for the expression
5359:
5353:
5070:
4620:
4577:
4537:
4328:
4299:
4232:
4189:
4135:
4012:
3977:
3886:
3866:
3822:
3724:
3623:
3596:
3572:
3541:
3495:
3459:
3432:
3399:
3372:
3342:
3296:
3257:
3229:
3183:
3153:
3125:
3079:
3049:
3021:
2975:
2879:
2748:
2728:
2708:
2685:
2647:
2627:
2604:
2584:
2551:
2513:
2493:
2473:
2408:
2301:
2272:
2243:
2193:
2170:
2135:
2106:
2083:
2061:
2021:
1998:
1978:
1151:
1096:
1041:
986:
848:
824:
801:
777:
752:
716:
692:
669:
645:
620:
581:
557:
534:
510:
485:
5218:International Union of Pure and Applied Chemistry
5157:International Union of Pure and Applied Chemistry
4190:{\displaystyle \Delta A=w_{\text{rev}}-S\Delta T}
5386:
2612:of the reaction is equal to the enthalpy change
4789:Henry Leicester, the influential 1923 textbook
2436:for non-volume work and compositional changes.
4199:Importantly, for a heat engine, including the
4037:
1953:
5003:Osara, Jude; Bryant, Michael (3 April 2019).
2819:In most cases of interest there are internal
2443:as simply Gibbs energy (and likewise for the
2424:) determines the amount of energy āfreeā for
1626:
5378:Chapter 4, Section 1, Paragraph 2 (page 103)
4984:: CS1 maint: multiple names: authors list (
4247:Free energy change and spontaneous processes
3536:
3523:
3337:
3324:
3224:
3211:
3120:
3107:
3016:
3003:
2032:Mathematically, free energy is expressed as
5002:
4861:
3580:is the number of molecules (alternatively,
4988:) CS1 maint: numeric names: authors list (
4379:by Nobel Laureate and chemistry professor
1633:
1619:
31:
5347:
5068:
5020:
4473:. This statement came to be known as the
4406:had attempted to quantify affinity using
3974:
3958:
3819:
3803:
3771:
3756:
3721:
3705:
3673:
3658:
3456:
2921:
2906:
4398:In the 19th century, the French chemist
1863:. Its change is equal to the amount of
5043:
4711:In this description, as used by Gibbs,
4233:{\displaystyle \Delta _{\text{cyc}}A=0}
2375:Reflections on the Motive Power of Fire
5387:
5307:
5101:
4911:
4864:"Thermodynamics of grease degradation"
4278:work, this inequality transforms into
4042:For a reversible isothermal process, Ī
2359:to the molecules of the body. In the
2320:, i.e., that heat is a fluid, and the
1692:The free energy is the portion of any
5130:
5095:
5297:from the original on 9 October 2022.
4945:
4943:
4907:
4905:
2432:qualification that it is the energy
2312:In the 18th and 19th centuries, the
5198:from the original on 9 October 2022
4912:Callen, Herbert B. (October 1966).
13:
4314:
4285:
4212:
4181:
4156:
4101:
4092:
4080:
4071:
3960:
3912:
3805:
3773:
3758:
3743:
3707:
3675:
3660:
3642:
3388:
3367:
2954:
2923:
2908:
2843:), including the internal energy.
2619:
2576:
2162:
2121:
2013:
840:
793:
708:
661:
573:
526:
346:Intensive and extensive properties
14:
5416:
4940:
4902:
4477:and was a precursory form of the
1842:chemists, including biochemists.
1677:that the system can perform in a
4950:Kondepudi, Dilip, 1952- (1998).
4675:, this equation may be written:
4057:and therefore the definition of
3542:{\displaystyle T,V,\{\mu _{i}\}}
3400:{\displaystyle \Phi _{\text{G}}}
2447:). This is the result of a 1988
2178:is derived exclusively from the
1602:
1601:
921:Table of thermodynamic equations
5301:
5251:
5210:
5149:
1397:Maxwell's thermodynamic surface
5124:
5062:
5037:
4996:
4880:10.1016/j.triboint.2019.05.020
4855:
4843:
4484:By 1865, the German physicist
3920:
3908:
2455:
1131:
1119:
1076:
1064:
1021:
1009:
981:
969:
1:
5366:. John Wiley & Sons Ltd.
4836:
4475:mechanical equivalent of heat
4419:In addition to this, in 1780
4329:{\displaystyle \Delta A<0}
4300:{\displaystyle \Delta G<0}
3496:{\displaystyle \mu _{i}N_{i}}
3343:{\displaystyle T,p,\{N_{i}\}}
3230:{\displaystyle S,p,\{N_{i}\}}
3126:{\displaystyle T,V,\{N_{i}\}}
3022:{\displaystyle S,V,\{N_{i}\}}
1708:. Free energy is subject to
1298:Mechanical equivalent of heat
4826:Second law of thermodynamics
4253:second law of thermodynamics
2171:{\displaystyle w=-T\Delta S}
910:Onsager reciprocal relations
7:
5048:. Dover Publications, Inc.
4804:
4578:{\displaystyle P_{2},V_{2}}
4538:{\displaystyle P_{1},V_{1}}
4479:first law of thermodynamics
4038:Work and free energy change
3460:{\displaystyle \sum _{i}\,}
2808:, and work due to electric
2280:and the unavailable energy
2244:{\displaystyle dA=-SdT-PdV}
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:
5421:
5308:Quilez, Juan (July 2019).
5079:Cambridge University Press
4447:. With the advent of the
4351:
4344:without electrical work, d
2585:{\displaystyle q=\Delta U}
2136:{\displaystyle \Delta U=0}
1986:and the change in entropy
1849:is defined in contrast as
849:{\displaystyle \partial T}
802:{\displaystyle \partial V}
717:{\displaystyle \partial p}
670:{\displaystyle \partial V}
582:{\displaystyle \partial T}
535:{\displaystyle \partial S}
5395:Thermodynamic free energy
5326:10.1007/s10698-018-9320-0
5133:Methods of Thermodynamics
5069:Baierlein, Ralph (2003).
5022:10.3390/inventions4020023
4662:thermodynamic equilibrium
4505:to the next, e.g., from (
4449:mechanical theory of heat
4413:principle of maximum work
4143:(at constant temperature)
4032:path integral Monte Carlo
2812:. These are described by
2416:, in which the change in
1845:The historically earlier
1651:thermodynamic free energy
1323:An Inquiry Concerning the
5314:Foundations of Chemistry
5104:A to Z of Thermodynamics
4427:laid the foundations of
2837:thermodynamic potentials
2804:used in the approach to
2766:may be added, e.g., for
2628:{\displaystyle \Delta H}
2022:{\displaystyle \Delta U}
1915:. (Hence its utility to
1791:is the internal energy,
1336:Heterogeneous Substances
753:{\displaystyle \alpha =}
621:{\displaystyle \beta =-}
5280:10.1351/pac199668040957
5181:10.1351/pac199062112167
5108:Oxford University Press
5102:Perrot, Pierre (1998).
4868:Tribology International
4402:and the Danish chemist
4375:From the 1998 textbook
3373:{\displaystyle \Omega }
3297:{\displaystyle U+pV-TS}
2823:and processes, such as
2143:and the expansion work
1961:Work = Force Ć Distance
1807:is the most useful for
5135:. Dover Publications.
5131:Reiss, Howard (1965).
4709:
4622:
4621:{\displaystyle dQ=TdS}
4579:
4539:
4453:conservation of energy
4330:
4301:
4257:inequality of Clausius
4234:
4191:
4137:
4014:
3979:
3888:
3868:
3824:
3726:
3625:
3598:
3574:
3543:
3497:
3461:
3434:
3401:
3374:
3344:
3298:
3259:
3231:
3185:
3155:
3127:
3081:
3051:
3023:
2977:
2881:
2750:
2730:
2710:
2687:
2686:{\displaystyle G=H-TS}
2649:
2629:
2606:
2586:
2553:
2552:{\displaystyle A=U-TS}
2515:
2495:
2475:
2410:
2409:{\displaystyle A=U-TS}
2339:In 1780, for example,
2303:
2274:
2245:
2195:
2172:
2137:
2108:
2085:
2063:
2062:{\displaystyle A=U-TS}
2023:
2000:
1980:
1811:involving a system at
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
5362:Modern Thermodynamics
4760:Helmholtz free energy
4740:Hermann von Helmholtz
4658:
4623:
4580:
4540:
4490:equivalence principle
4384:a clear definition."
4377:Modern Thermodynamics
4331:
4302:
4235:
4192:
4138:
4015:
3980:
3889:
3869:
3825:
3727:
3626:
3599:
3575:
3573:{\displaystyle N_{i}}
3544:
3498:
3462:
3435:
3433:{\displaystyle U-TS-}
3402:
3375:
3355:Landau potential, or
3345:
3299:
3260:
3232:
3186:
3156:
3128:
3082:
3052:
3034:Helmholtz free energy
3024:
2978:
2882:
2751:
2731:
2711:
2688:
2650:
2630:
2607:
2587:
2554:
2516:
2496:
2476:
2411:
2379:Hermann von Helmholtz
2304:
2275:
2246:
2196:
2173:
2138:
2109:
2086:
2064:
2024:
2001:
1981:
1913:statistical mechanics
1847:Helmholtz free energy
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:
4597:
4549:
4509:
4488:had shown that this
4425:Pierre-Simon Laplace
4393:Newtonian hypothesis
4311:
4282:
4208:
4153:
4068:
4004:
3905:
3878:
3858:
3739:
3638:
3612:
3588:
3557:
3508:
3470:
3443:
3412:
3384:
3364:
3309:
3270:
3249:
3196:
3184:{\displaystyle U+pV}
3166:
3145:
3092:
3080:{\displaystyle U-TS}
3062:
3041:
2988:
2892:
2871:
2740:
2720:
2700:
2662:
2639:
2616:
2596:
2567:
2528:
2505:
2485:
2465:
2385:
2302:{\displaystyle -SdT}
2284:
2273:{\displaystyle -PdV}
2255:
2205:
2182:
2147:
2118:
2095:
2075:
2038:
2010:
1990:
1970:
1763:absolute temperature
1683:constant temperature
1659: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:
4591:transformation heat
4494:combustion reaction
4400:Marcellin Berthelot
4025:surface free energy
2841:extensive functions
2835:, as do all proper
2322:four element theory
1722:Legendre transforms
1704:, work mediated by
1325:Source ... Friction
1257:Loschmidt's paradox
449:Material properties
327:Conjugate variables
5354:Kondepudi, Dilip;
4654:chemical potential
4618:
4575:
4535:
4366:chemical reactions
4326:
4297:
4230:
4187:
4133:
4010:
3975:
3947:
3884:
3864:
3844:chemical potential
3820:
3792:
3722:
3694:
3624:{\displaystyle pV}
3621:
3594:
3570:
3539:
3493:
3457:
3455:
3430:
3397:
3370:
3340:
3294:
3255:
3227:
3181:
3151:
3123:
3077:
3047:
3019:
2973:
2942:
2877:
2858:Natural variables
2825:chemical reactions
2821:degrees of freedom
2760:. Work other than
2746:
2726:
2706:
2683:
2645:
2625:
2602:
2582:
2549:
2511:
2491:
2471:
2406:
2334:calorique sensible
2299:
2270:
2241:
2194:{\displaystyle TS}
2191:
2168:
2133:
2107:{\displaystyle TS}
2104:
2081:
2059:
2019:
1996:
1976:
1909:canonical ensemble
1905:partition function
1829:also excludes the
1661:(the others being
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
5373:978-0-471-97394-2
5175:(11): 2167ā2219.
4831:Superconductivity
4745:Gibbs free energy
4727:of the body, and
4421:Antoine Lavoisier
4408:heats of reaction
4251:According to the
4218:
4172:
4130:
4117:
4013:{\displaystyle T}
3938:
3887:{\displaystyle p}
3867:{\displaystyle T}
3783:
3685:
3597:{\displaystyle i}
3552:
3551:
3446:
3394:
3258:{\displaystyle G}
3242:Gibbs free energy
3154:{\displaystyle H}
3050:{\displaystyle F}
2933:
2880:{\displaystyle U}
2829:phase transitions
2780:materials and in
2758:Maxwell relations
2749:{\displaystyle p}
2729:{\displaystyle V}
2709:{\displaystyle T}
2648:{\displaystyle G}
2605:{\displaystyle q}
2514:{\displaystyle p}
2494:{\displaystyle V}
2474:{\displaystyle T}
2373:, in his famous "
2336:), among others.
2084:{\displaystyle U}
1999:{\displaystyle S}
1979:{\displaystyle T}
1954:Meaning of "free"
1733:Gibbs free energy
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
5412:
5400:Energy (physics)
5379:
5377:
5365:
5351:
5345:
5344:
5342:
5340:
5305:
5299:
5298:
5296:
5274:(4): 957ā100 0.
5268:Pure Appl. Chem.
5264:
5255:
5249:
5248:
5246:
5244:
5214:
5208:
5207:
5205:
5203:
5197:
5169:Pure Appl. Chem.
5165:
5153:
5147:
5146:
5128:
5122:
5121:
5099:
5093:
5092:
5076:
5066:
5060:
5059:
5041:
5035:
5034:
5024:
5000:
4994:
4993:
4983:
4975:
4947:
4938:
4937:
4909:
4900:
4899:
4859:
4853:
4847:
4795:Gilbert N. Lewis
4695:
4671:and temperature
4627:
4625:
4624:
4619:
4584:
4582:
4581:
4576:
4574:
4573:
4561:
4560:
4544:
4542:
4541:
4536:
4534:
4533:
4521:
4520:
4472:
4335:
4333:
4332:
4327:
4306:
4304:
4303:
4298:
4241:
4239:
4237:
4236:
4231:
4220:
4219:
4216:
4198:
4196:
4194:
4193:
4188:
4174:
4173:
4170:
4142:
4140:
4139:
4134:
4132:
4131:
4128:
4119:
4118:
4115:
4019:
4017:
4016:
4011:
3984:
3982:
3981:
3976:
3973:
3972:
3963:
3957:
3956:
3946:
3934:
3933:
3915:
3893:
3891:
3890:
3885:
3873:
3871:
3870:
3865:
3829:
3827:
3826:
3821:
3818:
3817:
3808:
3802:
3801:
3791:
3776:
3761:
3746:
3731:
3729:
3728:
3723:
3720:
3719:
3710:
3704:
3703:
3693:
3678:
3663:
3645:
3630:
3628:
3627:
3622:
3603:
3601:
3600:
3595:
3579:
3577:
3576:
3571:
3569:
3568:
3548:
3546:
3545:
3540:
3535:
3534:
3502:
3500:
3499:
3494:
3492:
3491:
3482:
3481:
3466:
3464:
3463:
3458:
3454:
3439:
3437:
3436:
3431:
3406:
3404:
3403:
3398:
3396:
3395:
3392:
3379:
3377:
3376:
3371:
3349:
3347:
3346:
3341:
3336:
3335:
3303:
3301:
3300:
3295:
3264:
3262:
3261:
3256:
3236:
3234:
3233:
3228:
3223:
3222:
3190:
3188:
3187:
3182:
3160:
3158:
3157:
3152:
3132:
3130:
3129:
3124:
3119:
3118:
3086:
3084:
3083:
3078:
3056:
3054:
3053:
3048:
3028:
3026:
3025:
3020:
3015:
3014:
2982:
2980:
2979:
2974:
2972:
2968:
2967:
2966:
2957:
2952:
2951:
2941:
2926:
2911:
2886:
2884:
2883:
2878:
2846:
2845:
2775:
2765:
2755:
2753:
2752:
2747:
2735:
2733:
2732:
2727:
2715:
2713:
2712:
2707:
2692:
2690:
2689:
2684:
2654:
2652:
2651:
2646:
2634:
2632:
2631:
2626:
2611:
2609:
2608:
2603:
2591:
2589:
2588:
2583:
2558:
2556:
2555:
2550:
2520:
2518:
2517:
2512:
2500:
2498:
2497:
2492:
2480:
2478:
2477:
2472:
2445:Helmholtz energy
2415:
2413:
2412:
2407:
2308:
2306:
2305:
2300:
2279:
2277:
2276:
2271:
2250:
2248:
2247:
2242:
2200:
2198:
2197:
2192:
2177:
2175:
2174:
2169:
2142:
2140:
2139:
2134:
2113:
2111:
2110:
2105:
2090:
2088:
2087:
2082:
2068:
2066:
2065:
2060:
2028:
2026:
2025:
2020:
2005:
2003:
2002:
1997:
1985:
1983:
1982:
1977:
1962:
1941:
1937:
1922:
1890:
1886:
1874:
1870:
1862:
1832:
1828:
1824:
1821:and temperature
1820:
1806:
1802:
1794:
1790:
1786:
1768:
1760:
1752:
1748:
1687:potential energy
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:
5420:
5419:
5415:
5414:
5413:
5411:
5410:
5409:
5405:State functions
5385:
5384:
5383:
5382:
5374:
5356:Prigogine, Ilya
5352:
5348:
5338:
5336:
5306:
5302:
5294:
5262:
5256:
5252:
5242:
5240:
5238:
5215:
5211:
5201:
5199:
5195:
5163:
5154:
5150:
5143:
5129:
5125:
5118:
5100:
5096:
5089:
5073:Thermal Physics
5067:
5063:
5056:
5042:
5038:
5001:
4997:
4977:
4976:
4964:
4948:
4941:
4926:
4910:
4903:
4860:
4856:
4851:Entropy Vol. 2.
4848:
4844:
4839:
4807:
4775:Internal energy
4717:internal energy
4696:
4678:
4649:internal energy
4598:
4595:
4594:
4569:
4565:
4556:
4552:
4550:
4547:
4546:
4529:
4525:
4516:
4512:
4510:
4507:
4506:
4486:Rudolf Clausius
4464:
4429:thermochemistry
4370:Albertus Magnus
4354:
4312:
4309:
4308:
4283:
4280:
4279:
4273:
4249:
4215:
4211:
4209:
4206:
4205:
4204:
4169:
4165:
4154:
4151:
4150:
4149:
4127:
4123:
4114:
4110:
4069:
4066:
4065:
4052:
4040:
4005:
4002:
4001:
4000:, appearing as
3968:
3964:
3959:
3952:
3948:
3942:
3923:
3919:
3911:
3906:
3903:
3902:
3879:
3876:
3875:
3859:
3856:
3855:
3841:
3813:
3809:
3804:
3797:
3793:
3787:
3772:
3757:
3742:
3740:
3737:
3736:
3715:
3711:
3706:
3699:
3695:
3689:
3674:
3659:
3641:
3639:
3636:
3635:
3613:
3610:
3609:
3589:
3586:
3585:
3564:
3560:
3558:
3555:
3554:
3530:
3526:
3509:
3506:
3505:
3487:
3483:
3477:
3473:
3471:
3468:
3467:
3450:
3444:
3441:
3440:
3413:
3410:
3409:
3391:
3387:
3385:
3382:
3381:
3365:
3362:
3361:
3357:grand potential
3356:
3331:
3327:
3310:
3307:
3306:
3271:
3268:
3267:
3250:
3247:
3246:
3218:
3214:
3197:
3194:
3193:
3167:
3164:
3163:
3146:
3143:
3142:
3114:
3110:
3093:
3090:
3089:
3063:
3060:
3059:
3042:
3039:
3038:
3010:
3006:
2989:
2986:
2985:
2962:
2958:
2953:
2947:
2943:
2937:
2922:
2907:
2902:
2898:
2893:
2890:
2889:
2872:
2869:
2868:
2864:Internal energy
2771:
2768:electrochemical
2761:
2741:
2738:
2737:
2721:
2718:
2717:
2701:
2698:
2697:
2663:
2660:
2659:
2640:
2637:
2636:
2617:
2614:
2613:
2597:
2594:
2593:
2568:
2565:
2564:
2529:
2526:
2525:
2506:
2503:
2502:
2486:
2483:
2482:
2466:
2463:
2462:
2458:
2386:
2383:
2382:
2285:
2282:
2281:
2256:
2253:
2252:
2206:
2203:
2202:
2183:
2180:
2179:
2148:
2145:
2144:
2119:
2116:
2115:
2096:
2093:
2092:
2076:
2073:
2072:
2039:
2036:
2035:
2011:
2008:
2007:
1991:
1988:
1987:
1971:
1968:
1967:
1960:
1956:
1939:
1935:
1920:
1888:
1884:
1872:
1868:
1850:
1830:
1826:
1822:
1818:
1804:
1803:is the volume.
1800:
1792:
1788:
1774:
1766:
1758:
1750:
1736:
1726:internal energy
1696:energy that is
1663:internal energy
1655:state functions
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:
5418:
5408:
5407:
5402:
5397:
5381:
5380:
5372:
5346:
5300:
5250:
5236:
5209:
5148:
5141:
5123:
5116:
5094:
5087:
5061:
5054:
5036:
4995:
4962:
4956:. John Wiley.
4939:
4924:
4915:Thermodynamics
4901:
4854:
4841:
4840:
4838:
4835:
4834:
4833:
4828:
4823:
4818:
4813:
4806:
4803:
4758:= constant or
4723:refers to the
4715:refers to the
4677:
4617:
4614:
4611:
4608:
4605:
4602:
4572:
4568:
4564:
4559:
4555:
4532:
4528:
4524:
4519:
4515:
4404:Julius Thomsen
4381:Ilya Prigogine
4353:
4350:
4325:
4322:
4319:
4316:
4296:
4293:
4290:
4287:
4271:
4248:
4245:
4229:
4226:
4223:
4214:
4186:
4183:
4180:
4177:
4168:
4164:
4161:
4158:
4145:
4144:
4126:
4122:
4113:
4109:
4106:
4103:
4100:
4097:
4094:
4091:
4088:
4085:
4082:
4079:
4076:
4073:
4050:
4039:
4036:
4023:An example is
4009:
3986:
3985:
3971:
3967:
3962:
3955:
3951:
3945:
3941:
3937:
3932:
3929:
3926:
3922:
3918:
3914:
3910:
3883:
3863:
3837:
3831:
3830:
3816:
3812:
3807:
3800:
3796:
3790:
3786:
3782:
3779:
3775:
3770:
3767:
3764:
3760:
3755:
3752:
3749:
3745:
3733:
3732:
3718:
3714:
3709:
3702:
3698:
3692:
3688:
3684:
3681:
3677:
3672:
3669:
3666:
3662:
3657:
3654:
3651:
3648:
3644:
3620:
3617:
3593:
3567:
3563:
3550:
3549:
3538:
3533:
3529:
3525:
3522:
3519:
3516:
3513:
3503:
3490:
3486:
3480:
3476:
3453:
3449:
3429:
3426:
3423:
3420:
3417:
3407:
3390:
3369:
3359:
3351:
3350:
3339:
3334:
3330:
3326:
3323:
3320:
3317:
3314:
3304:
3293:
3290:
3287:
3284:
3281:
3278:
3275:
3265:
3254:
3244:
3238:
3237:
3226:
3221:
3217:
3213:
3210:
3207:
3204:
3201:
3191:
3180:
3177:
3174:
3171:
3161:
3150:
3140:
3134:
3133:
3122:
3117:
3113:
3109:
3106:
3103:
3100:
3097:
3087:
3076:
3073:
3070:
3067:
3057:
3046:
3036:
3030:
3029:
3018:
3013:
3009:
3005:
3002:
2999:
2996:
2993:
2983:
2971:
2965:
2961:
2956:
2950:
2946:
2940:
2936:
2932:
2929:
2925:
2920:
2917:
2914:
2910:
2905:
2901:
2897:
2887:
2876:
2866:
2860:
2859:
2856:
2853:
2850:
2745:
2725:
2705:
2694:
2693:
2682:
2679:
2676:
2673:
2670:
2667:
2644:
2624:
2621:
2601:
2581:
2578:
2575:
2572:
2560:
2559:
2548:
2545:
2542:
2539:
2536:
2533:
2510:
2490:
2470:
2457:
2454:
2405:
2402:
2399:
2396:
2393:
2390:
2318:caloric theory
2314:theory of heat
2298:
2295:
2292:
2289:
2269:
2266:
2263:
2260:
2240:
2237:
2234:
2231:
2228:
2225:
2222:
2219:
2216:
2213:
2210:
2190:
2187:
2167:
2164:
2161:
2158:
2155:
2152:
2132:
2129:
2126:
2123:
2103:
2100:
2080:
2058:
2055:
2052:
2049:
2046:
2043:
2018:
2015:
1995:
1975:
1955:
1952:
1706:thermal energy
1653:is one of the
1647:thermodynamics
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:
5417:
5406:
5403:
5401:
5398:
5396:
5393:
5392:
5390:
5375:
5369:
5364:
5363:
5357:
5350:
5335:
5331:
5327:
5323:
5319:
5315:
5311:
5304:
5293:
5289:
5285:
5281:
5277:
5273:
5270:
5269:
5261:
5254:
5239:
5237:0-632-03583-8
5233:
5229:
5225:
5224:
5219:
5213:
5194:
5190:
5186:
5182:
5178:
5174:
5171:
5170:
5162:
5158:
5152:
5144:
5142:0-486-69445-3
5138:
5134:
5127:
5119:
5117:0-19-856552-6
5113:
5109:
5105:
5098:
5090:
5088:0-521-65838-1
5084:
5080:
5075:
5074:
5065:
5057:
5055:0-486-44641-7
5051:
5047:
5040:
5032:
5028:
5023:
5018:
5014:
5010:
5006:
4999:
4991:
4987:
4981:
4973:
4969:
4965:
4963:0-471-97393-9
4959:
4955:
4954:
4946:
4944:
4935:
4931:
4927:
4925:0-471-13035-4
4921:
4917:
4916:
4908:
4906:
4897:
4893:
4889:
4885:
4881:
4877:
4873:
4869:
4865:
4858:
4852:
4846:
4842:
4832:
4829:
4827:
4824:
4822:
4821:Merle Randall
4819:
4817:
4814:
4812:
4809:
4808:
4802:
4800:
4799:Merle Randall
4796:
4792:
4786:
4784:
4780:
4776:
4772:
4768:
4764:
4761:
4757:
4753:
4749:
4746:
4741:
4736:
4735:of the body.
4734:
4730:
4726:
4722:
4719:of the body,
4718:
4714:
4708:
4705:
4701:
4693:
4689:
4685:
4681:
4676:
4674:
4670:
4667:
4663:
4657:
4655:
4650:
4646:
4642:
4638:
4634:
4633:Willard Gibbs
4629:
4615:
4612:
4609:
4606:
4603:
4600:
4592:
4588:
4570:
4566:
4562:
4557:
4553:
4530:
4526:
4522:
4517:
4513:
4504:
4500:
4495:
4491:
4487:
4482:
4480:
4476:
4471:
4467:
4462:
4456:
4454:
4450:
4446:
4442:
4438:
4434:
4433:specific heat
4430:
4426:
4422:
4417:
4415:
4414:
4409:
4405:
4401:
4396:
4394:
4391:, called the
4390:
4385:
4382:
4378:
4373:
4371:
4367:
4363:
4359:
4349:
4347:
4343:
4339:
4323:
4320:
4317:
4294:
4291:
4288:
4277:
4270:
4266:
4262:
4258:
4254:
4244:
4227:
4224:
4221:
4202:
4184:
4178:
4175:
4166:
4162:
4159:
4124:
4120:
4111:
4107:
4104:
4098:
4095:
4089:
4086:
4083:
4077:
4074:
4064:
4063:
4062:
4060:
4056:
4049:
4045:
4035:
4033:
4028:
4026:
4021:
4007:
3999:
3995:
3991:
3969:
3965:
3953:
3949:
3943:
3939:
3935:
3930:
3927:
3924:
3916:
3901:
3900:
3899:
3897:
3881:
3861:
3853:
3849:
3845:
3840:
3836:
3814:
3810:
3798:
3794:
3788:
3784:
3780:
3777:
3768:
3765:
3762:
3753:
3750:
3747:
3735:
3734:
3716:
3712:
3700:
3696:
3690:
3686:
3682:
3679:
3670:
3667:
3664:
3655:
3652:
3649:
3646:
3634:
3633:
3632:
3618:
3615:
3607:
3606:differentials
3591:
3583:
3565:
3561:
3531:
3527:
3520:
3517:
3514:
3511:
3504:
3488:
3484:
3478:
3474:
3451:
3447:
3427:
3424:
3421:
3418:
3415:
3408:
3360:
3358:
3353:
3352:
3332:
3328:
3321:
3318:
3315:
3312:
3305:
3291:
3288:
3285:
3282:
3279:
3276:
3273:
3266:
3252:
3245:
3243:
3240:
3239:
3219:
3215:
3208:
3205:
3202:
3199:
3192:
3178:
3175:
3172:
3169:
3162:
3148:
3141:
3139:
3136:
3135:
3115:
3111:
3104:
3101:
3098:
3095:
3088:
3074:
3071:
3068:
3065:
3058:
3044:
3037:
3035:
3032:
3031:
3011:
3007:
3000:
2997:
2994:
2991:
2984:
2969:
2963:
2959:
2948:
2944:
2938:
2934:
2930:
2927:
2918:
2915:
2912:
2903:
2899:
2895:
2888:
2874:
2867:
2865:
2862:
2861:
2857:
2854:
2851:
2848:
2847:
2844:
2842:
2838:
2834:
2830:
2826:
2822:
2817:
2815:
2811:
2807:
2806:absolute zero
2803:
2802:magnetization
2799:
2795:
2791:
2787:
2783:
2779:
2774:
2769:
2764:
2759:
2743:
2723:
2703:
2680:
2677:
2674:
2671:
2668:
2665:
2658:
2657:
2656:
2642:
2622:
2599:
2579:
2573:
2570:
2546:
2543:
2540:
2537:
2534:
2531:
2524:
2523:
2522:
2508:
2488:
2468:
2453:
2450:
2446:
2442:
2437:
2435:
2429:
2427:
2423:
2419:
2403:
2400:
2397:
2394:
2391:
2388:
2380:
2376:
2372:
2367:
2365:
2362:
2358:
2354:
2353:absolute heat
2350:
2346:
2342:
2337:
2335:
2331:
2330:heat capacity
2327:
2326:specific heat
2323:
2319:
2315:
2310:
2296:
2293:
2290:
2287:
2267:
2264:
2261:
2258:
2238:
2235:
2232:
2229:
2226:
2223:
2220:
2217:
2214:
2211:
2208:
2188:
2185:
2165:
2159:
2156:
2153:
2150:
2130:
2127:
2124:
2101:
2098:
2078:
2069:
2056:
2053:
2050:
2047:
2044:
2041:
2033:
2030:
2016:
1993:
1973:
1964:
1951:
1949:
1945:
1933:
1929:
1924:
1918:
1914:
1910:
1906:
1902:
1898:
1894:
1882:
1878:
1866:
1861:
1857:
1853:
1848:
1843:
1841:
1837:
1817:
1814:
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1798:
1785:
1781:
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1772:
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1739:
1734:
1729:
1727:
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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:
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1501:
1498:
1496:
1493:
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1481:
1478:
1476:
1475:von Helmholtz
1473:
1471:
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1466:
1463:
1461:
1458:
1456:
1453:
1451:
1448:
1446:
1443:
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1381:
1379:
1378:
1372:
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1367:
1364:
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1125:
1122:
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1024:
1018:
1015:
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931:
930:
923:
922:
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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:
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765:
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761:
747:
744:
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701:
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680:
679:
664:
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633:
632:
629:
615:
612:
609:
602:
599:
596:
595:
576:
566:
552:
545:
544:
529:
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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:
5361:
5349:
5337:. Retrieved
5317:
5313:
5303:
5271:
5266:
5253:
5241:. Retrieved
5222:
5212:
5200:. Retrieved
5172:
5167:
5151:
5132:
5126:
5103:
5097:
5072:
5064:
5045:
5039:
5012:
5008:
4998:
4952:
4914:
4871:
4867:
4857:
4850:
4845:
4790:
4787:
4782:
4778:
4770:
4769:= constant,
4766:
4762:
4755:
4754:= constant,
4751:
4747:
4737:
4728:
4720:
4712:
4710:
4699:
4697:
4691:
4687:
4683:
4679:
4672:
4668:
4659:
4636:
4630:
4590:
4503:engine cycle
4483:
4469:
4465:
4457:
4441:Germain Hess
4418:
4411:
4397:
4392:
4389:Isaac Newton
4386:
4376:
4374:
4364:that caused
4361:
4357:
4355:
4345:
4341:
4337:
4275:
4268:
4264:
4260:
4250:
4201:Carnot cycle
4146:
4058:
4054:
4047:
4043:
4041:
4029:
4022:
3987:
3847:
3838:
3834:
3832:
3553:
2818:
2810:polarization
2772:
2762:
2695:
2561:
2459:
2440:
2438:
2433:
2430:
2421:
2417:
2368:
2356:
2352:
2338:
2333:
2311:
2070:
2034:
2031:
1965:
1957:
1947:
1942:), while in
1931:
1925:
1896:
1892:
1880:
1859:
1855:
1851:
1844:
1783:
1779:
1775:
1745:
1741:
1737:
1735:is given by
1730:
1710:irreversible
1701:
1697:
1691:
1650:
1644:
1440:CarathƩodory
1371:Heat engines
1343:
1332:
1321:
1303:Motive power
1288:
948:Free entropy
942:
919:
419:
418: /
408:
407: /
399:introduction
392:
391: /
330:
293:Heat engines
80: /
18:
5243:28 December
5202:28 December
4874:: 433ā445.
4461:James Joule
4437:latent heat
4061:results in
2833:composition
2501:, pressure
2456:Application
2371:Sadi Carnot
2364:compression
1948:free energy
1932:free energy
1262:Synergetics
943:Free energy
389:Temperature
250:Quasistatic
245:Isenthalpic
202:Instruments
192:Equilibrium
144:Open system
78:Equilibrium
60:Statistical
5389:Categories
5339:2 November
5320:(2): 223.
5009:Inventions
4972:1167078377
4837:References
4777:). Thus,
4635:published
3998:dissipated
3990:isothermal
3584:) of type
2773:f dx
2770:cells, or
2763:p dV
1921:p dV
1917:physicists
1875:(from
1865:reversible
1831:p dV
1714:second-law
1574:Nucleation
1418:Scientists
1222:Philosophy
935:Potentials
298:Heat pumps
255:Polytropic
240:Isentropic
230:Isothermal
5334:102566121
5031:2411-5134
5015:(2): 23.
4980:cite book
4934:651933140
4918:. Wiley.
4896:182266032
4888:0301-679X
4631:In 1873,
4445:Hess' law
4315:Δ
4286:Δ
4213:Δ
4182:Δ
4176:−
4157:Δ
4108:−
4102:Δ
4093:Δ
4087:−
4081:Δ
4072:Δ
3950:μ
3940:∑
3852:component
3795:μ
3785:∑
3766:−
3697:μ
3687:∑
3668:−
3653:−
3528:μ
3475:μ
3448:∑
3428:−
3419:−
3389:Φ
3368:Ω
3286:−
3069:−
2945:μ
2935:∑
2916:−
2896:∫
2798:adiabatic
2675:−
2620:Δ
2577:Δ
2541:−
2481:, volume
2398:−
2361:adiabatic
2345:Lavoisier
2288:−
2259:−
2230:−
2218:−
2163:Δ
2157:−
2122:Δ
2051:−
2014:Δ
1944:chemistry
1901:logarithm
1809:processes
1718:functions
1698:available
1694:first-law
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
5358:(1998).
5292:Archived
5288:95196393
5193:Archived
5189:53117465
4805:See also
4707:minimum.
4666:pressure
4358:affinity
3994:isobaric
3846:for the
3138:Enthalpy
2855:Formula
2796:, as in
2794:magnetic
2776:work in
2349:vis viva
1907:for the
1836:solution
1816:pressure
1813:constant
1797:pressure
1787:, where
1755:enthalpy
1749:, where
1667:enthalpy
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
4731:is the
4725:entropy
4645:entropy
4587:entropy
4501:of the
4352:History
3842:is the
3631:work):
2852:Symbol
2814:tensors
2778:elastic
2341:Laplace
1928:physics
1923:work.)
1903:of the
1795:is the
1771:entropy
1769:is the
1761:is the
1753:is the
1724:of the
1679:process
1671:entropy
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
5370:
5332:
5286:
5234:
5187:
5139:
5114:
5085:
5052:
5029:
4970:
4960:
4932:
4922:
4894:
4886:
4816:Exergy
4811:Energy
4733:volume
4641:volume
4545:) to (
3896:living
3833:where
2790:strain
2786:stress
2782:muscle
2716:, and
2091:while
1881:Arbeit
1877:German
1799:, and
1765:, and
1649:, the
1520:Planck
1510:Nernst
1485:Kelvin
1445:Carnot
735:
600:
468:
410:Volume
325:Note:
284:Cycles
113:Second
103:Zeroth
5330:S2CID
5295:(PDF)
5284:S2CID
5263:(PDF)
5196:(PDF)
5185:S2CID
5164:(PDF)
4892:S2CID
4704:state
4698:when
4694:) = 0
4499:state
4362:force
4348:= 0.
4263:>
3582:moles
2849:Name
2449:IUPAC
2357:bound
1879:
1840:phase
1657:of a
1568:Other
1535:Stahl
1490:Lewis
1480:Joule
1470:Gibbs
1465:Duhem
158:State
118:Third
108:First
5368:ISBN
5341:2021
5245:2006
5232:ISBN
5204:2006
5137:ISBN
5112:ISBN
5083:ISBN
5050:ISBN
5027:ISSN
4990:link
4986:link
4968:OCLC
4958:ISBN
4930:OCLC
4920:ISBN
4884:ISSN
4797:and
4435:and
4423:and
4340:and
4321:<
4292:<
4272:surr
4030:The
3874:and
2827:and
2434:free
2426:work
2420:(or
2343:and
1938:(or
1887:and
1731:The
1720:are
1702:i.e.
1675:work
1540:Tait
370:Heat
365:Work
95:Laws
5322:doi
5276:doi
5177:doi
5017:doi
4876:doi
4872:137
4793:by
4781:or
4765:at
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4593:as
4259:, Ī
4217:cyc
4171:rev
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2736:or
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1383:Art
329:in
5391::
5328:.
5318:21
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4982:}}
4978:{{
4966:.
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4276:PV
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3992:,
3380:,
2816:.
2800:de
2792:,
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2328:,
1946:,
1930:,
1897:on
1893:by
1860:TS
1858:ā
1854:=
1784:pV
1782:+
1778:=
1773:.
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5376:.
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3121:}
3116:i
3112:N
3108:{
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3008:N
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2900:(
2875:U
2839:(
2788:-
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2672:H
2669:=
2666:G
2643:G
2623:H
2600:q
2580:U
2574:=
2571:q
2547:S
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2535:=
2532:A
2509:p
2489:V
2469:T
2441:G
2422:G
2418:A
2404:S
2401:T
2395:U
2392:=
2389:A
2297:T
2294:d
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2268:V
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2215:=
2212:A
2209:d
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2166:S
2160:T
2154:=
2151:w
2131:0
2128:=
2125:U
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2045:=
2042:A
2017:U
1994:S
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1940:F
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1135:=
1132:)
1129:p
1126:,
1123:T
1120:(
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1092:S
1089:T
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1080:=
1077:)
1074:V
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1068:T
1065:(
1062:A
1037:V
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1031:+
1028:U
1025:=
1022:)
1019:p
1016:,
1013:S
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1007:H
982:)
979:V
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973:S
970:(
967:U
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797:V
773:1
748:=
712:p
688:V
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641:1
613:=
577:T
553:N
530:S
506:T
481:=
478:c
401:)
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