Thermodynamics

Annotated color version of the original 1824 Carnot heat engineshowing the hot body (boiler), working body (system, steam), andcold body (water), the letters labeled according to the stoppingpoints in Carnot cycle

Thermodynamics is a branch of physics concerned withheat and temperature and their relation to energy andwork. It defines macroscopic variables, such as internalenergy, entropy, and pressure, that partly describe a bodyof matter or radiation. It states that the behavior of thosevariables is subject to general constraints, that are com-mon to all materials, not the peculiar properties of partic-ular materials. These general constraints are expressed inthe four laws of thermodynamics. Thermodynamics de-scribes the bulk behavior of the body, not themicroscopicbehaviors of the very large numbers of its microscopicconstituents, such as molecules. Its laws are explained bystatistical mechanics, in terms of the microscopic con-stituents.Thermodynamics applies to a wide variety of topics inscience and engineering, especially Physical chemistry,Chemical engineering, thermal power generation andsteam and combustion turbines.Historically, thermodynamics developed out of a desireto increase the efficiency and power output of early steamengines, particularly through the work of the Frenchphysicist Nicolas Léonard Sadi Carnot (1824) who be-lieved that the efficiency of heat engines was the key thatcould help France win the Napoleonic Wars.[1] The Irish-born British physicist Lord Kelvin was the first to formu-

late a concise definition of thermodynamics in 1854:[2]

“Thermo-dynamics is the subject of the re-lation of heat to forces acting between contigu-ous parts of bodies, and the relation of heat toelectrical agency.”

Initially, thermodynamics, as applied to heat engines, wasconcerned with the thermal properties of their 'workingmaterials’, such as steam, in an effort to increase the ef-ficiency and power output of engines. Thermodynam-ics was later expanded to the study of energy transfersin chemical processes, such as the investigation, pub-lished in 1840, of the heats of chemical reactions[3] byGermain Hess, which was not originally explicitly con-cerned with the relation between energy exchanges byheat and work. From this evolved the study of Chemicalthermodynamics and the role of entropy in chemical re-actions.[4][5][6][7][8][9][10][11][12]

1 Introduction

Thermodynamics arose from the study of two distinctkinds of transfer of energy, as heat and as work, and therelation of those to the system’s macroscopic variablesof volume, pressure and temperature.[13][14] Transfers ofmatter are also studied in thermodynamics.The plain term 'thermodynamics’ refers to a macro-scopic description of bodies and processes.[15] “Anyreference to atomic constitution is foreign to classicalthermodynamics.”[16] The qualified term 'statistical ther-modynamics’ refers to descriptions of bodies and pro-cesses in terms of the atomic constitution of matter,mainly described by sets of items all alike, so as to haveequal probabilities.Thermodynamic equilibrium is one of the most impor-tant concepts for thermodynamics.[17] The temperatureof a thermodynamic system is well defined, and is per-haps the most characteristic quantity of thermodynamics.As the systems and processes of interest are taken fur-ther from thermodynamic equilibrium, their exact ther-modynamical study becomes more difficult. Relativelysimple approximate calculations, however, using the vari-ables of equilibrium thermodynamics, are of much prac-tical value. In many important practical cases, as in heatengines or refrigerators, the systems consist of many sub-systems at different temperatures and pressures. In engi-neering practice, thermodynamic calculations deal effec-

1

2 2 HISTORY

tively with such systems provided the equilibrium ther-modynamic variables are nearly enough well-defined.Central to thermodynamic analysis are the defini-tions of the system, which is of interest, and of itssurroundings.[8][18] The surroundings of a thermody-namic system consist of physical devices and of otherthermodynamic systems that can interact with it. An ex-ample of a thermodynamic surrounding is a heat bath,which is held at a prescribed temperature, regardless ofhow much heat might be drawn from it.There are four fundamental kinds of physical enti-ties in thermodynamics, states of a system, walls of asystem,[19][20][21] thermodynamic processes of a system,and thermodynamic operations. This allows two funda-mental approaches to thermodynamic reasoning, that interms of states of a system, and that in terms of cyclicprocesses of a system.A thermodynamic system can be defined in terms ofits states. In this way, a thermodynamic system is amacroscopic physical object, explicitly specified in termsof macroscopic physical and chemical variables that de-scribe its macroscopic properties. The macroscopic statevariables of thermodynamics have been recognized in thecourse of empirical work in physics and chemistry.[9] Al-ways associated with the material that constitutes a sys-tem, its working substance, are the walls that delimit thesystem, and connect it with its surroundings. The statevariables chosen for the system should be appropriate forthe natures of the walls and surroundings.[22]

A thermodynamic operation is an artificial physical ma-nipulation that changes the definition of a system or itssurroundings. Usually it is a change of the permeability orsome other feature of a wall of the system,[23] that allowsenergy (as heat or work) or matter (mass) to be exchangedwith the environment. For example, the partition be-tween two thermodynamic systems can be removed soas to produce a single system. A thermodynamic opera-tion usually leads to a thermodynamic process of transferof mass or energy that changes the state of the system,and the transfer occurs in natural accord with the lawsof thermodynamics. Besides thermodynamic operations,changes in the surroundings can also initiate thermody-namic processes.A thermodynamic system can also be defined in termsof the cyclic processes that it can undergo.[24] A cyclicprocess is a cyclic sequence of thermodynamic opera-tions and processes that can be repeated indefinitely oftenwithout changing the final state of the system.For thermodynamics and statistical thermodynamics toapply to a physical system, it is necessary that its inter-nal atomic mechanisms fall into one of two classes:

• those so rapid that, in the time frame of the processof interest, the atomic states rapidly bring system toits own state of internal thermodynamic equilibrium;and

• those so slow that, in the time frame of the processof interest, they leave the system unchanged.[25][26]

The rapid atomic mechanisms account for the internalenergy of the system. They mediate the macroscopicchanges that are of interest for thermodynamics andstatistical thermodynamics, because they quickly bringthe system near enough to thermodynamic equilibrium.“When intermediate rates are present, thermodynamicsand statistical mechanics cannot be applied.”[25] Such in-termediate rate atomic processes do not bring the systemnear enough to thermodynamic equilibrium in the timeframe of the macroscopic process of interest. This sepa-ration of time scales of atomic processes is a theme thatrecurs throughout the subject.For example, classical thermodynamics is characterizedby its study of materials that have equations of state orcharacteristic equations. They express equilibrium re-lations between macroscopic mechanical variables andtemperature and internal energy. They express the con-stitutive peculiarities of the material of the system. Aclassical material can usually be described by a func-tion that makes pressure dependent on volume and tem-perature, the resulting pressure being established muchmore rapidly than any imposed change of volume ortemperature.[27][28][29][30]

The present article takes a gradual approach to the sub-ject, starting with a focus on cyclic processes and ther-modynamic equilibrium, and then gradually beginning tofurther consider non-equilibrium systems.Thermodynamic facts can often be explained by view-ing macroscopic objects as assemblies of very manymicroscopic or atomic objects that obey Hamiltoniandynamics.[8][31][32] The microscopic or atomic objectsexist in species, the objects of each species being allalike. Because of this likeness, statistical methods canbe used to account for the macroscopic properties ofthe thermodynamic system in terms of the propertiesof the microscopic species. Such explanation is calledstatistical thermodynamics; also often it is referred to bythe term 'statistical mechanics', though this term can havea wider meaning, referring to 'microscopic objects’, suchas economic quantities, that do not obey Hamiltoniandynamics.[31]

2 History

The history of thermodynamics as a scientific disci-pline generally begins with Otto von Guericke who, in1650, built and designed the world’s first vacuum pumpand demonstrated a vacuum using his Magdeburg hemi-spheres. Guericke was driven to make a vacuum inorder to disprove Aristotle's long-held supposition that'nature abhors a vacuum'. Shortly after Guericke, thephysicist and chemist Robert Boyle had learned of Gu-ericke’s designs and, in 1656, in coordination with the

2.1 Etymology 3

The thermodynamicists representative of the original eight found-ing schools of thermodynamics. The schools with themost-lastingeffect in founding the modern versions of thermodynamics arethe Berlin school, particularly as established in Rudolf Clau-sius’s 1865 textbook TheMechanical Theory of Heat, the Viennaschool, while the statistical mechanics of Ludwig Boltzmann, andthe Gibbsian school at Yale University, led by the American engi-neer Willard Gibbs' 1876 On the Equilibrium of HeterogeneousSubstances launched chemical thermodynamics.

scientist Robert Hooke, built an air pump.[33] Using thispump, Boyle and Hooke noticed a correlation betweenpressure, temperature, and volume. In time, they for-mulated Boyle’s Law, which states that for a gas at con-stant temperature, its pressure and volume are inverselyproportional. In 1679, based on these concepts, an asso-ciate of Boyle’s named Denis Papin built a steam digester,which was a closed vessel with a tightly fitting lid that con-fined steam until a high pressure was generated. Laterdesigns implemented a steam release valve that kept themachine from exploding. By watching the valve rhyth-mically move up and down, Papin conceived of the ideaof a piston and a cylinder engine. He did not, however,follow through with his design. Nevertheless, in 1697,based on Papin’s designs, the engineer Thomas Saverybuilt the first engine, followed by Thomas Newcomen in1712. Although these early engines were crude and ineffi-cient, they attracted the attention of the leading scientistsof the time.The concepts of heat capacity and latent heat, which werenecessary for development of thermodynamics, were de-veloped by Professor Joseph Black at the University ofGlasgow, where James Watt worked as an instrumentmaker. Watt consulted with Black on tests of his steamengine, but it was Watt who conceived the idea of theexternal condenser, greatly raising the steam engine'sefficiency.[34] All the previous work led Sadi Carnot, the“father of thermodynamics”, to publish Reflections on theMotive Power of Fire (1824), a discourse on heat, power,energy and engine efficiency. The paper outlined the ba-sic energetic relations between the Carnot engine, the

Carnot cycle, and motive power. It marked the start ofthermodynamics as a modern science.[11]

The first thermodynamic textbook was written in 1859by William Rankine, originally trained as a physicist anda professor of civil and mechanical engineering at theUniversity of Glasgow.[35] The first and second laws ofthermodynamics emerged simultaneously in the 1850s,primarily out of the works of William Rankine, RudolfClausius, and William Thomson (Lord Kelvin).The foundations of statistical thermodynamics were setout by physicists such as James Clerk Maxwell, LudwigBoltzmann, Max Planck, Rudolf Clausius and J. WillardGibbs.From 1873 to '76, the American mathematical physicistJosiah Willard Gibbs published a series of three papers,the most famous being "On the equilibrium of heteroge-neous substances".[4] Gibbs showed how thermodynamicprocesses, including chemical reactions, could be graphi-cally analyzed. By studying the energy, entropy, volume,chemical potential, temperature and pressure of thethermodynamic system, one can determine whether aprocess would occur spontaneously.[36] Chemical ther-modynamics was further developed by Pierre Duhem,[5]Gilbert N. Lewis, Merle Randall,[6] and E. A. Guggen-heim,[7][8] who applied the mathematical methods ofGibbs.

The lifetimes of some of the most important contributors to ther-modynamics.

2.1 Etymology

The etymology of thermodynamics has an intricate his-tory. It was first spelled in a hyphenated form as an ad-jective (thermo-dynamic) in 1849 and from 1854 to 1859as the hyphenated noun thermo-dynamics to represent thescience of heat and motive power and thereafter as ther-modynamics.The components of the word thermo-dynamic are derivedfrom theGreekwords θέρμη therme, meaning “heat,” andδύναμις dynamis, meaning “power” (Haynie claims thatthe word was coined around 1840).[37][38]

4 3 BRANCHES OF DESCRIPTION

The term thermo-dynamicwas first used in January 1849by William Thomson, later Lord Kelvin, in the phrase aperfect thermo-dynamic engine to describe Sadi Carnot’sheat engine.[39]:545 In April 1849, Thomson added an ap-pendix to his paper and used the term thermodynamic inthe phrase the object of a thermodynamic engine.[39]:569

Pierre Perrot claims that the term thermodynamics wascoined by James Joule in 1858 to designate the sci-ence of relations between heat and power.[11] Joule, how-ever, never used that term, but did use the term perfectthermo-dynamic engine in reference to Thomson’s 1849phraseology,[39]:545 and Thomson’s note on Joules’ 1851paper On the Air-Engine.In 1854, thermo-dynamics, as a functional term to denotethe general study of the action of heat, was first used byWilliam Thomson in his paper On the Dynamical Theoryof Heat.[2]

In 1859, the closed compound form thermodynam-ics was first used by William Rankine in A Manualof the Steam Engine in a chapter on the Principles ofThermodynamics.[40]

3 Branches of description

Thermodynamic systems are theoretical constructionsused to model physical systems that exchange matter andenergy in terms of the laws of thermodynamics. Thestudy of thermodynamical systems has developed intoseveral related branches, each using a different funda-mental model as a theoretical or experimental basis, orapplying the principles to varying types of systems.

3.1 Classical thermodynamics

Classical thermodynamics accounts for the adventures ofa thermodynamic system in terms, either of its time-invariant equilibrium states, or else of its continually re-peated cyclic processes, but, formally, not both in thesame account. It uses only time-invariant, or equilib-rium, macroscopic quantities measureable in the labora-tory, counting as time-invariant a long-term time-averageof a quantity, such as a flow, generated by a continu-ally repetitive process.[41][42] In classical thermodynam-ics, rates of change are not admitted as variables of inter-est. An equilibrium state stands endlessly without changeover time, while a continually repeated cyclic processruns endlessly without a net change in the system overtime.In the account in terms of equilibrium states of a system,a state of thermodynamic equilibrium in a simple systemis spatially homogeneous.In the classical account solely in terms of a cyclic process,the spatial interior of the 'working body' of that processis not considered; the 'working body' thus does not have a

defined internal thermodynamic state of its own becauseno assumption is made that it should be in thermody-namic equilibrium; only its inputs and outputs of energyas heat and work are considered.[43] It is common to de-scribe a cycle theoretically as composed of a sequenceof very many thermodynamic operations and processes.This creates a link to the description in terms of equilib-rium states. The cycle is then theoretically described as acontinuous progression of equilibrium states.Classical thermodynamics was originally concerned withthe transformation of energy in a cyclic process, andthe exchange of energy between closed systems definedonly by their equilibrium states. The distinction betweentransfers of energy as heat and as work was central.As classical thermodynamics developed, the distinctionbetween heat and work became less central. This was be-cause there was more interest in open systems, for whichthe distinction between heat and work is not simple, andis beyond the scope of the present article. Alongside theamount of heat transferred as a fundamental quantity, en-tropy was gradually found to be a more generally appli-cable concept, especially when considering chemical re-actions. Massieu in 1869 considered entropy as the ba-sic dependent thermodynamic variable, with energy po-tentials and the reciprocal of the thermodynamic tem-perature as fundamental independent variables. Massieufunctions can be useful in present-day non-equilibriumthermodynamics. In 1875, in the work of Josiah WillardGibbs, entropy was considered a fundamental indepen-dent variable, while internal energy was a dependentvariable.[44]

All actual physical processes are to some degree irre-versible. Classical thermodynamics can consider irre-versible processes, but its account in exact terms is re-stricted to variables that refer only to initial and final statesof thermodynamic equilibrium, or to rates of input andoutput that do not change with time. For example, clas-sical thermodynamics can consider time-average rates offlows generated by continually repeated irreversible cyclicprocesses. Also it can consider irreversible changes be-tween equilibrium states of systems consisting of severalphases (as defined below in this article), or with remov-able or replaceable partitions. But for systems that aredescribed in terms of equilibrium states, it considers nei-ther flows, nor spatial inhomogeneities in simple systemswith no externally imposed force fields such as gravity. Inthe account in terms of equilibrium states of a system, de-scriptions of irreversible processes refer only to initial andfinal static equilibrium states; the time it takes to changethermodynamic state is not considered.[45][46]

3.2 Local equilibrium thermodynamics

Local equilibrium thermodynamics is concerned withthe time courses and rates of progress of irreversibleprocesses in systems that are smoothly spatially inho-

3.4 Statistical thermodynamics 5

mogeneous. It admits time as a fundamental quantity,but only in a restricted way. Rather than consideringtime-invariant flows as long-term-average rates of cyclicprocesses, local equilibrium thermodynamics considerstime-varying flows in systems that are described by statesof local thermodynamic equilibrium, as follows.For processes that involve only suitably small and smoothspatial inhomogeneities and suitably small changes withtime, a good approximation can be found through the as-sumption of local thermodynamic equilibrium. Withinthe large or global region of a process, for a suitably smalllocal region, this approximation assumes that a quantityknown as the entropy of the small local region can be de-fined in a particular way. That particular way of defini-tion of entropy is largely beyond the scope of the presentarticle, but here it may be said that it is entirely derivedfrom the concepts of classical thermodynamics; in par-ticular, neither flow rates nor changes over time are ad-mitted into the definition of the entropy of the small lo-cal region. It is assumed without proof that the instanta-neous global entropy of a non-equilibrium system can befound by adding up the simultaneous instantaneous en-tropies of its constituent small local regions. Local equi-librium thermodynamics considers processes that involvethe time-dependent production of entropy by dissipativeprocesses, in which kinetic energy of bulk flow and chem-ical potential energy are converted into internal energyat time-rates that are explicitly accounted for. Time-varying bulk flows and specific diffusional flows are con-sidered, but they are required to be dependent variables,derived only from material properties described only bystatic macroscopic equilibrium states of small local re-gions. The independent state variables of a small localregion are only those of classical thermodynamics.

3.3 Generalized or extended thermody-namics

Like local equilibrium thermodynamics, generalized orextended thermodynamics also is concerned with the timecourses and rates of progress of irreversible processes insystems that are smoothly spatially inhomogeneous. Itdescribes time-varying flows in terms of states of suit-ably small local regions within a global region that issmoothly spatially inhomogeneous, rather than consid-ering flows as time-invariant long-term-average rates ofcyclic processes. In its accounts of processes, general-ized or extended thermodynamics admits time as a fun-damental quantity in a more far-reaching way than doeslocal equilibrium thermodynamics. The states of smalllocal regions are defined by macroscopic quantities thatare explicitly allowed to vary with time, including time-varying flows. Generalized thermodynamics might tacklesuch problems as ultrasound or shock waves, in whichthere are strong spatial inhomogeneities and changes intime fast enough to outpace a tendency towards local ther-modynamic equilibrium. Generalized or extended ther-

modynamics is a diverse and developing project, ratherthan a more or less completed subject such as is classicalthermodynamics.[47][48]

For generalized or extended thermodynamics, the defi-nition of the quantity known as the entropy of a smalllocal region is in terms beyond those of classical thermo-dynamics; in particular, flow rates are admitted into thedefinition of the entropy of a small local region. The in-dependent state variables of a small local region includeflow rates, which are not admitted as independent vari-ables for the small local regions of local equilibrium ther-modynamics.Outside the range of classical thermodynamics, the def-inition of the entropy of a small local region is no sim-ple matter. For a thermodynamic account of a process interms of the entropies of small local regions, the defini-tion of entropy should be such as to ensure that the secondlaw of thermodynamics applies in each small local region.It is often assumed without proof that the instantaneousglobal entropy of a non-equilibrium system can be foundby adding up the simultaneous instantaneous entropies ofits constituent small local regions. For a given physicalprocess, the selection of suitable independent local non-equilibrium macroscopic state variables for the construc-tion of a thermodynamic description calls for qualitativephysical understanding, rather than being a simply math-ematical problem concerned with a uniquely determinedthermodynamic description. A suitable definition of theentropy of a small local region depends on the physicallyinsightful and judicious selection of the independent localnon-equilibrium macroscopic state variables, and differ-ent selections provide different generalized or extendedthermodynamical accounts of one and the same givenphysical process. This is one of the several good reasonsfor considering entropy as an epistemic physical variable,rather than as a simply material quantity. According to arespected author: “There is no compelling reason to be-lieve that the classical thermodynamic entropy is a mea-surable property of nonequilibrium phenomena, ...”[49]

3.4 Statistical thermodynamics

Statistical thermodynamics, also called statistical me-chanics, emerged with the development of atomic andmolecular theories in the second half of the 19th cen-tury and early 20th century. It provides an explanation ofclassical thermodynamics. It considers the microscopicinteractions between individual particles and their collec-tive motions, in terms of classical or of quantummechan-ics. Its explanation is in terms of statistics that rest on thefact the system is composed of several species of parti-cles or collective motions, the members of each speciesrespectively being in some sense all alike.

6 5 NON-EQUILIBRIUM THERMODYNAMICS

4 Thermodynamic equilibrium

Equilibrium thermodynamics studies transformations ofmatter and energy in systems at or near thermodynamicequilibrium. In thermodynamic equilibrium, a system’sproperties are, by definition, unchanging in time. In ther-modynamic equilibrium no macroscopic change is occur-ring or can be triggered; within the system, every micro-scopic process is balanced by its opposite; this is calledthe principle of detailed balance. A central aim in equi-librium thermodynamics is: given a system in a well-defined initial state, subject to specified constraints, tocalculate what the equilibrium state of the system is.[50]

In theoretical studies, it is often convenient to considerthe simplest kind of thermodynamic system. This isdefined variously by different authors.[45][51][52][53][54][55]For the present article, the following definition is conve-nient, as abstracted from the definitions of various au-thors. A region of material with all intensive propertiescontinuous in space and time is called a phase. A simplesystem is for the present article defined as one that con-sists of a single phase of a pure chemical substance, withno interior partitions.Within a simple isolated thermodynamic system in ther-modynamic equilibrium, in the absence of externally im-posed force fields, all properties of thematerial of the sys-tem are spatially homogeneous.[56]Much of the basic the-ory of thermodynamics is concerned with homogeneoussystems in thermodynamic equilibrium.[4][57]

Most systems found in nature or considered in engi-neering are not in thermodynamic equilibrium, exactlyconsidered. They are changing or can be triggered tochange over time, and are continuously and discontinu-ously subject to flux of matter and energy to and fromother systems.[21] For example, according to Callen, “inabsolute thermodynamic equilibrium all radioactive ma-terials would have decayed completely and nuclear reac-tions would have transmuted all nuclei to the most sta-ble isotopes. Such processes, which would take cosmictimes to complete, generally can be ignored.”.[21] Suchprocesses being ignored, many systems in nature are closeenough to thermodynamic equilibrium that for many pur-poses their behaviour can be well approximated by equi-librium calculations.

4.1 Quasi-static transfers between simplesystems are nearly in thermodynamicequilibrium and are reversible

It very much eases and simplifies theoretical thermody-namical studies to imagine transfers of energy and matterbetween two simple systems that proceed so slowly that atall times each simple system considered separately is nearenough to thermodynamic equilibrium. Such processesare sometimes called quasi-static and are near enough to

being reversible.[58][59]

4.2 Natural processes are partly describedby tendency towards thermodynamicequilibrium and are irreversible

If not initially in thermodynamic equilibrium, simple iso-lated thermodynamic systems, as time passes, tend toevolve naturally towards thermodynamic equilibrium. Inthe absence of externally imposed force fields, they be-come homogeneous in all their local properties. Such ho-mogeneity is an important characteristic of a system inthermodynamic equilibrium in the absence of externallyimposed force fields.Many thermodynamic processes can be modeled by com-pound or composite systems, consisting of several ormany contiguous component simple systems, initially notin thermodynamic equilibrium, but allowed to transfermass and energy between them. Natural thermodynamicprocesses are described in terms of a tendency towardsthermodynamic equilibrium within simple systems and intransfers between contiguous simple systems. Such natu-ral processes are irreversible.[60]

5 Non-equilibrium thermodynam-ics

Non-equilibrium thermodynamics[61] is a branch of ther-modynamics that deals with systems that are not inthermodynamic equilibrium; it is also called thermody-namics of irreversible processes. Non-equilibrium ther-modynamics is concerned with transport processes andwith the rates of chemical reactions.[62] Non-equilibriumsystems can be in stationary states that are not homoge-neous even when there is no externally imposed field offorce; in this case, the description of the internal state ofthe system requires a field theory.[63][64][65] One of themethods of dealing with non-equilibrium systems is tointroduce so-called 'internal variables’. These are quan-tities that express the local state of the system, besidesthe usual local thermodynamic variables; in a sense suchvariables might be seen as expressing the 'memory' ofthe materials. Hysteresis may sometimes be describedin this way. In contrast to the usual thermodynamic vari-ables, 'internal variables’ cannot be controlled by exter-nal manipulations.[66] This approach is usually unneces-sary for gases and liquids, but may be useful for solids.[67]Many natural systems still today remain beyond the scopeof currently known macroscopic thermodynamic meth-ods.

7

6 Laws of thermodynamics

Main article: Laws of thermodynamics

Thermodynamics states a set of four laws that are valid forall systems that fall within the constraints implied by each.In the various theoretical descriptions of thermodynamicsthese lawsmay be expressed in seemingly differing forms,but the most prominent formulations are the following:

• Zeroth law of thermodynamics: If two systems areeach in thermal equilibriumwith a third, they are alsoin thermal equilibrium with each other.

This statement implies that thermal equilibrium is anequivalence relation on the set of thermodynamic sys-tems under consideration. Systems are said to be in ther-mal equilibrium with each other if spontaneous molecu-lar thermal energy exchanges between them do not leadto a net exchange of energy. This law is tacitly assumedin every measurement of temperature. For two bodiesknown to be at the same temperature, deciding if theyare in thermal equilibrium when put into thermal con-tact does not require actually bringing them into contactand measuring any changes of their observable proper-ties in time.[68] In traditional statements, the law providesan empirical definition of temperature and justificationfor the construction of practical thermometers. In con-trast to absolute thermodynamic temperatures, empiricaltemperatures are measured just by the mechanical prop-erties of bodies, such as their volumes, without relianceon the concepts of energy, entropy or the first, second,or third laws of thermodynamics.[53][69] Empirical tem-peratures lead to calorimetry for heat transfer in terms ofthe mechanical properties of bodies, without reliance onmechanical concepts of energy.The physical content of the zeroth law has long been rec-ognized. For example, Rankine in 1853 defined temper-ature as follows: “Two portions of matter are said to haveequal temperatures when neither tends to communicateheat to the other.”[70] Maxwell in 1872 stated a “Law ofEqual Temperatures”.[71] He also stated: “All Heat is ofthe same kind.”[72] Planck explicitly assumed and statedit in its customary present-day wording in his formula-tion of the first two laws.[73] By the time the desire aroseto number it as a law, the other three had already been as-signed numbers, and so it was designated the zeroth law.

• First law of thermodynamics: The increase ininternal energy of a closed system is equal tothe difference of the heat supplied to the sys-tem and the work done by it: ΔU = Q – W[74][75][76][77][78][79][80][81][82][83][84] (Note that due tothe ambiguity of what constitutes positive work,some sources state that ΔU = Q + W, in which casework done on the system is positive.)

The first law of thermodynamics asserts the existence ofa state variable for a system, the internal energy, and tellshow it changes in thermodynamic processes. The law al-lows a given internal energy of a system to be reached byany combination of heat and work. It is important thatinternal energy is a variable of state of the system (seeThermodynamic state) whereas heat and work are vari-ables that describe processes or changes of the state ofsystems.The first law observes that the internal energy of anisolated system obeys the principle of conservation ofenergy, which states that energy can be transformed(changed from one form to another), but cannot be cre-ated or destroyed.[85][86][87][88][89]

• Second law of thermodynamics: Heat cannot spon-taneously flow from a colder location to a hotter lo-cation.

The second law of thermodynamics is an expression ofthe universal principle of dissipation of kinetic and po-tential energy observable in nature. The second law is anobservation of the fact that over time, differences in tem-perature, pressure, and chemical potential tend to evenout in a physical system that is isolated from the outsideworld. Entropy is a measure of howmuch this process hasprogressed. The entropy of an isolated system that is notin equilibrium tends to increase over time, approaching amaximum value at equilibrium.In classical thermodynamics, the second law is a basicpostulate applicable to any system involving heat energytransfer; in statistical thermodynamics, the second law isa consequence of the assumed randomness of molecularchaos. There are many versions of the second law, butthey all have the same effect, which is to explain the phe-nomenon of irreversibility in nature.

• Third law of thermodynamics: As a system ap-proaches absolute zero the entropy of the system ap-proaches a minimum value.

The third law of thermodynamics is a statistical law of na-ture regarding entropy and the impossibility of reachingabsolute zero of temperature. This law provides an ab-solute reference point for the determination of entropy.The entropy determined relative to this point is the abso-lute entropy. Alternate definitions of the third law are,“the entropy of all systems and of all states of a system issmallest at absolute zero,” or equivalently “it is impossi-ble to reach the absolute zero of temperature by any finitenumber of processes”.Absolute zero is −273.15 °C (degrees Celsius), or−459.67 °F (degrees Fahrenheit) or 0 K (kelvin).

8 8 STATES AND PROCESSES

SYSTEM

SURROUNDINGS

BOUNDARY

A diagram of a generic thermodynamic system

7 System models

An important concept in thermodynamics is thethermodynamic system, a precisely defined region ofthe universe under study. Everything in the universeexcept the system is known as the surroundings. Asystem is separated from the remainder of the universeby a boundary, which may be actual, or merely notionaland fictive, but by convention delimits a finite volume.Transfers of work, heat, or matter between the systemand the surroundings take place across this boundary.The boundary may or may not have properties thatrestrict what can be transferred across it. A systemmay have several distinct boundary sectors or partitionsseparating it from the surroundings, each characterizedby how it restricts transfers, and being permeable to itscharacteristic transferred quantities.The volume can be the region surrounding a single atomresonating energy, as Max Planck defined in 1900; itcan be a body of steam or air in a steam engine, suchas Sadi Carnot defined in 1824; it can be the body of atropical cyclone, as Kerry Emanuel theorized in 1986 inthe field of atmospheric thermodynamics; it could also bejust one nuclide (i.e. a system of quarks) as hypothesizedin quantum thermodynamics.Anything that passes across the boundary needs to be ac-counted for in a proper transfer balance equation. Ther-modynamics is largely about such transfers.Boundary sectors are of various characters: rigid, flexi-ble, fixed, moveable, actually restrictive, and fictive or notactually restrictive. For example, in an engine, a fixedboundary sector means the piston is locked at its posi-tion; then no pressure-volume work is done across it. Inthat same engine, a moveable boundary allows the pis-ton to move in and out, permitting pressure-volume work.There is no restrictive boundary sector for the whole earthincluding its atmosphere, and so roughly speaking, nopressure-volume work is done on or by the whole earth

system. Such a system is sometimes said to be diabati-cally heated or cooled by radiation.[90][91]

Thermodynamics distinguishes classes of systems by theirboundary sectors.

• An open system has a boundary sector that is per-meable to matter; such a sector is usually permeablealso to energy, but the energy that passes cannot ingeneral be uniquely sorted into heat and work com-ponents. Open system boundaries may be either ac-tually restrictive, or else non-restrictive.

• A closed system has no boundary sector that is per-meable to matter, but in general its boundary is per-meable to energy. For closed systems, boundariesare totally prohibitive of matter transfer.

• An adiabatically isolated system has only adiabaticboundary sectors. Energy can be transferred aswork, but transfers of matter and of energy as heatare prohibited.

• A purely diathermically isolated system has onlyboundary sectors permeable only to heat; it is some-times said to be adynamically isolated and closed tomatter transfer. A process in which no work is trans-ferred is sometimes called adynamic.[92]

• An isolated system has only isolating boundary sec-tors. Nothing can be transferred into or out of it.

Engineering and natural processes are often described ascomposites of many different component simple systems,sometimes with unchanging or changing partitions be-tween them. A change of partition is an example of athermodynamic operation.

8 States and processes

There are three fundamental kinds of entity inthermodynamics—states of a system, processes ofa system, and thermodynamic operations. This al-lows three fundamental approaches to thermodynamicreasoning—that in terms of states of thermodynamicequilibrium of a system, and that in terms of time-invariant processes of a system, and that in terms ofcyclic processes of a system.The approach through states of thermodynamic equilib-rium of a system requires a full account of the state ofthe system as well as a notion of process from one stateto another of a system, but may require only an idealizedor partial account of the state of the surroundings of thesystem or of other systems.The method of description in terms of states of ther-modynamic equilibrium has limitations. For example,processes in a region of turbulent flow, or in a burn-ing gas mixture, or in a Knudsen gas may be beyond

8.1 Account in terms of states of thermodynamic equilibrium 9

“the province of thermodynamics”.[93][94][95] This prob-lem can sometimes be circumvented through the methodof description in terms of cyclic or of time-invariant flowprocesses. This is part of the reason why the foundersof thermodynamics often preferred the cyclic process de-scription.Approaches through processes of time-invariant flow ofa system are used for some studies. Some processes, forexample Joule-Thomson expansion, are studied throughsteady-flow experiments, but can be accounted for bydistinguishing the steady bulk flow kinetic energy fromthe internal energy, and thus can be regarded as withinthe scope of classical thermodynamics defined in termsof equilibrium states or of cyclic processes.[41][96] Otherflow processes, for example thermoelectric effects, areessentially defined by the presence of differential flowsor diffusion so that they cannot be adequately accountedfor in terms of equilibrium states or classical cyclicprocesses.[97][98]

The notion of a cyclic process does not require a full ac-count of the state of the system, but does require a fullaccount of how the process occasions transfers of matterand energy between the principal system (which is oftencalled theworking body) and its surroundings, whichmustinclude at least two heat reservoirs at different known andfixed temperatures, one hotter than the principal systemand the other colder than it, as well as a reservoir that canreceive energy from the system as work and can do workon the system. The reservoirs can alternatively be re-garded as auxiliary idealized component systems, along-side the principal system. Thus an account in terms ofcyclic processes requires at least four contributory com-ponent systems. The independent variables of this ac-count are the amounts of energy that enter and leave theidealized auxiliary systems. In this kind of account, theworking body is often regarded as a “black box”,[99] andits own state is not specified. In this approach, the notionof a properly numerical scale of empirical temperatureis a presupposition of thermodynamics, not a notion con-structed by or derived from it.

8.1 Account in terms of states of thermo-dynamic equilibrium

When a system is at thermodynamic equilibrium undera given set of conditions of its surroundings, it is said tobe in a definite thermodynamic state, which is fully de-scribed by its state variables.If a system is simple as defined above, and is in thermo-dynamic equilibrium, and is not subject to an externallyimposed force field, such as gravity, electricity, or mag-netism, then it is homogeneous, that is say, spatially uni-form in all respects.[100]

In a sense, a homogeneous system can be regarded as spa-tially zero-dimensional, because it has no spatial varia-tion.

If a system in thermodynamic equilibrium is homoge-neous, then its state can be described by a few physicalvariables, which are mostly classifiable as intensive vari-ables and extensive variables.[8][31][65][101][102]

An intensive variable is one that is unchanged with thethermodynamic operation of scaling of a system.An extensive variable is one that simply scales with thescaling of a system, without the further requirement usedjust below here, of additivity even when there is inhomo-geneity of the added systems.Examples of extensive thermodynamic variables are totalmass and total volume. Under the above definition, en-tropy is also regarded as an extensive variable. Examplesof intensive thermodynamic variables are temperature,pressure, and chemical concentration; intensive thermo-dynamic variables are defined at each spatial point andeach instant of time in a system. Physical macroscopicvariables can be mechanical, material, or thermal.[31]Temperature is a thermal variable; according to Guggen-heim, “themost important conception in thermodynamicsis temperature.”[8]

Intensive variables have the property that if any numberof systems, each in its own separate homogeneous ther-modynamic equilibrium state, all with the same respec-tive values of all of their intensive variables, regardlessof the values of their extensive variables, are laid con-tiguously with no partition between them, so as to form anew system, then the values of the intensive variables ofthe new system are the same as those of the separate con-stituent systems. Such a composite system is in a homo-geneous thermodynamic equilibrium. Examples of inten-sive variables are temperature, chemical concentration,pressure, density of mass, density of internal energy, and,when it can be properly defined, density of entropy.[103]In other words, intensive variables are not altered by thethermodynamic operation of scaling.For the immediately present account just below, an al-ternative definition of extensive variables is considered,that requires that if any number of systems, regardlessof their possible separate thermodynamic equilibrium ornon-equilibrium states or intensive variables, are laid sideby side with no partition between them so as to form a newsystem, then the values of the extensive variables of thenew system are the sums of the values of the respectiveextensive variables of the individual separate constituentsystems. Obviously, there is no reason to expect sucha composite system to be in a homogeneous thermody-namic equilibrium. Examples of extensive variables inthis alternative definition are mass, volume, and internalenergy. They depend on the total quantity of mass in thesystem.[104] In other words, although extensive variablesscale with the system under the thermodynamic operationof scaling, nevertheless the present alternative definitionof an extensive variable requires more than this: it re-quires also its additivity regardless of the inhomogeneity(or equality or inequality of the values of the intensive

10 8 STATES AND PROCESSES

variables) of the component systems.Though, when it can be properly defined, density of en-tropy is an intensive variable, for inhomogeneous sys-tems, entropy itself does not fit into this alternative clas-sification of state variables.[105][106] The reason is that en-tropy is a property of a system as a whole, and not nec-essarily related simply to its constituents separately. It istrue that for any number of systems each in its own sep-arate homogeneous thermodynamic equilibrium, all withthe same values of intensive variables, removal of the par-titions between the separate systems results in a compos-ite homogeneous system in thermodynamic equilibrium,with all the values of its intensive variables the same asthose of the constituent systems, and it is reservedly orconditionally true that the entropy of such a restrictivelydefined composite system is the sum of the entropies ofthe constituent systems. But if the constituent systems donot satisfy these restrictive conditions, the entropy of acomposite system cannot be expected to be the sum of theentropies of the constituent systems, because the entropyis a property of the composite system as a whole. There-fore, though under these restrictive reservations, entropysatisfies some requirements for extensivity defined justabove, entropy in general does not fit the immediatelypresent definition of an extensive variable.Being neither an intensive variable nor an extensive vari-able according to the immediately present definition, en-tropy is thus a stand-out variable, because it is a state vari-able of a system as a whole.[105] A non-equilibrium sys-tem can have a very inhomogeneous dynamical structure.This is one reason for distinguishing the study of equilib-rium thermodynamics from the study of non-equilibriumthermodynamics.The physical reason for the existence of extensive vari-ables is the time-invariance of volume in a given iner-tial reference frame, and the strictly local conservation ofmass, momentum, angular momentum, and energy. Asnoted by Gibbs, entropy is unlike energy and mass, be-cause it is not locally conserved.[105] The stand-out quan-tity entropy is never conserved in real physical processes;all real physical processes are irreversible.[107] The mo-tion of planets seems reversible on a short time scale (mil-lions of years), but their motion, according to Newton’slaws, is mathematically an example of deterministicchaos. Eventually a planet suffers an unpredictable col-lision with an object from its surroundings, outer spacein this case, and consequently its future course is radi-cally unpredictable. Theoretically this can be expressedby saying that every natural process dissipates some infor-mation from the predictable part of its activity into the un-predictable part. The predictable part is expressed in thegeneralized mechanical variables, and the unpredictablepart in heat.Other state variables can be regarded as conditionally 'ex-tensive' subject to reservation as above, but not exten-sive as defined above. Examples are the Gibbs free en-

ergy, the Helmholtz free energy, and the enthalpy. Con-sequently, just because for some systems under particularconditions of their surroundings such state variables areconditionally conjugate to intensive variables, such con-jugacy does not make such state variables extensive asdefined above. This is another reason for distinguishingthe study of equilibrium thermodynamics from the studyof non-equilibrium thermodynamics. In another way ofthinking, this explains why heat is to be regarded as aquantity that refers to a process and not to a state of asystem.A system with no internal partitions, and in thermody-namic equilibrium, can be inhomogeneous in the follow-ing respect: it can consist of several so-called 'phases’,each homogeneous in itself, in immediate contiguity withother phases of the system, but distinguishable by theirhaving various respectively different physical characters,with discontinuity of intensive variables at the bound-aries between the phases; a mixture of different chem-ical species is considered homogeneous for this purposeif it is physically homogeneous.[108] For example, a vesselcan contain a system consisting of water vapour overly-ing liquid water; then there is a vapour phase and a liquidphase, each homogeneous in itself, but still in thermody-namic equilibrium with the other phase. For the imme-diately present account, systems with multiple phases arenot considered, though for many thermodynamic ques-tions, multiphase systems are important.

8.1.1 Equation of state

The macroscopic variables of a thermodynamic system inthermodynamic equilibrium, in which temperature is welldefined, can be related to one another through equationsof state or characteristic equations.[27][28][29][30] They ex-press the constitutive peculiarities of the material of thesystem. The equation of state must comply with somethermodynamic constraints, but cannot be derived fromthe general principles of thermodynamics alone.

8.2 Thermodynamic processes betweenstates of thermodynamic equilibrium

A thermodynamic process is defined by changes of stateinternal to the system of interest, combined with trans-fers of matter and energy to and from the surroundingsof the system or to and from other systems. A system isdemarcated from its surroundings or from other systemsby partitions that more or less separate them, and maymove as a piston to change the volume of the system andthus transfer work.

8.2 Thermodynamic processes between states of thermodynamic equilibrium 11

8.2.1 Dependent and independent variables for aprocess

A process is described by changes in values of state vari-ables of systems or by quantities of exchange of mat-ter and energy between systems and surroundings. Thechange must be specified in terms of prescribed variables.The choice of which variables are to be used is made inadvance of consideration of the course of the process,and cannot be changed. Certain of the variables cho-sen in advance are called the independent variables.[109]From changes in independent variables may be derivedchanges in other variables called dependent variables.For example a process may occur at constant pressurewith pressure prescribed as an independent variable, andtemperature changed as another independent variable,and then changes in volume are considered as depen-dent. Careful attention to this principle is necessary inthermodynamics.[110][111]

8.2.2 Changes of state of a system

In the approach through equilibrium states of the system,a process can be described in two main ways.In one way, the system is considered to be connected tothe surroundings by some kind of more or less separat-ing partition, and allowed to reach equilibrium with thesurroundings with that partition in place. Then, while theseparative character of the partition is kept unchanged,the conditions of the surroundings are changed, and exerttheir influence on the system again through the separatingpartition, or the partition is moved so as to change the vol-ume of the system; and a new equilibrium is reached. Forexample, a system is allowed to reach equilibrium with aheat bath at one temperature; then the temperature of theheat bath is changed and the system is allowed to reacha new equilibrium; if the partition allows conduction ofheat, the new equilibrium is different from the old equi-librium.In the other way, several systems are connected to oneanother by various kinds of more or less separating par-titions, and to reach equilibrium with each other, withthose partitions in place. In this way, one may speak ofa 'compound system'. Then one or more partitions is re-moved or changed in its separative properties or moved,and a new equilibrium is reached. The Joule-Thomsonexperiment is an example of this; a tube of gas is sepa-rated from another tube by a porous partition; the volumeavailable in each of the tubes is determined by respectivepistons; equilibrium is established with an initial set ofvolumes; the volumes are changed and a new equilibriumis established.[112][113][114][115][116] Another example is inseparation and mixing of gases, with use of chemicallysemi-permeable membranes.[117]

8.2.3 Commonly considered thermodynamic pro-cesses

It is often convenient to study a thermodynamic processin which a single variable, such as temperature, pressure,or volume, etc., is held fixed. Furthermore, it is useful togroup these processes into pairs, in which each variableheld constant is one member of a conjugate pair.Several commonly studied thermodynamic processes are:

• Isobaric process: occurs at constant pressure

• Isochoric process: occurs at constant volume (alsocalled isometric/isovolumetric)

• Isothermal process: occurs at a constanttemperature

• Adiabatic process: occurs without loss or gain of en-ergy as heat

• Isentropic process: a reversible adiabatic processoccurs at a constant entropy, but is a fictional ideal-ization. Conceptually it is possible to actually physi-cally conduct a process that keeps the entropy of thesystem constant, allowing systematically controlledremoval of heat, by conduction to a cooler body, tocompensate for entropy produced within the systemby irreversible work done on the system. Such isen-tropic conduct of a process seems called for whenthe entropy of the system is considered as an inde-pendent variable, as for example when the internalenergy is considered as a function of the entropy andvolume of the system, the natural variables of the in-ternal energy as studied by Gibbs.

• Isenthalpic process: occurs at a constant enthalpy

• Isolated process: no matter or energy (neither aswork nor as heat) is transferred into or out of thesystem

It is sometimes of interest to study a process in whichseveral variables are controlled, subject to some specifiedconstraint. In a system in which a chemical reaction canoccur, for example, in which the pressure and temper-ature can affect the equilibrium composition, a processmight occur in which temperature is held constant butpressure is slowly altered, just so that chemical equilib-rium is maintained all the way. There is a correspondingprocess at constant temperature in which the final pres-sure is the same but is reached by a rapid jump. Thenit can be shown that the volume change resulting fromthe rapid jump process is smaller than that from the slowequilibrium process.[118] The work transferred differs be-tween the two processes.

12 11 POTENTIALS

8.3 Account in terms of cyclic processes

A cyclic process[24] is a process that can be repeated in-definitely often without changing the final state of the sys-tem in which the process occurs. The only traces of theeffects of a cyclic process are to be found in the surround-ings of the system or in other systems. This is the kind ofprocess that concerned early thermodynamicists such asSadi Carnot, and in terms of which Kelvin defined abso-lute temperature,[119][120] before the use of the quantityof entropy by Rankine[121] and its clear identification byClausius.[122] For some systems, for example with someplastic working substances, cyclic processes are practi-cally nearly unfeasible because the working substance un-dergoes practically irreversible changes.[64] This is whymechanical devices are lubricated with oil and one of thereasons why electrical devices are often useful.A cyclic process of a system requires in its surroundingsat least two heat reservoirs at different temperatures, oneat a higher temperature that supplies heat to the system,the other at a lower temperature that accepts heat fromthe system. The early work on thermodynamics tendedto use the cyclic process approach, because it was inter-ested in machines that converted some of the heat fromthe surroundings into mechanical power delivered to thesurroundings, without too much concern about the inter-nal workings of the machine. Such a machine, whilereceiving an amount of heat from a higher temperaturereservoir, always needs a lower temperature reservoir thataccepts some lesser amount of heat. The difference inamounts of heat is equal to the amount of heat convertedto work.[87][123] Later, the internal workings of a systembecame of interest, and they are described by the statesof the system. Nowadays, instead of arguing in terms ofcyclic processes, some writers are inclined to derive theconcept of absolute temperature from the concept of en-tropy, a variable of state.

9 Instrumentation

There are two types of thermodynamic instruments, themeter and the reservoir. A thermodynamic meter is anydevice that measures any parameter of a thermodynamicsystem. In some cases, the thermodynamic parameter isactually defined in terms of an idealized measuring in-strument. For example, the zeroth law states that if twobodies are in thermal equilibrium with a third body, theyare also in thermal equilibrium with each other. Thisprinciple, as noted by James Maxwell in 1872, assertsthat it is possible to measure temperature. An idealizedthermometer is a sample of an ideal gas at constant pres-sure. From the ideal gas law PV=nRT, the volume ofsuch a sample can be used as an indicator of temper-ature; in this manner it defines temperature. Althoughpressure is defined mechanically, a pressure-measuringdevice, called a barometer may also be constructed from

a sample of an ideal gas held at a constant temperature.A calorimeter is a device that measures and define theinternal energy of a system.A thermodynamic reservoir is a system so large thatit does not appreciably alter its state parameters whenbrought into contact with the test system. It is used toimpose a particular value of a state parameter upon thesystem. For example, a pressure reservoir is a system ata particular pressure, which imposes that pressure uponany test system that it is mechanically connected to. TheEarth’s atmosphere is often used as a pressure reservoir.

10 Conjugate variables

Main article: Conjugate variables

A central concept of thermodynamics is that of energy.By the First Law, the total energy of a system and its sur-roundings is conserved. Energy may be transferred intoa system by heating, compression, or addition of matter,and extracted from a system by cooling, expansion, orextraction of matter. In mechanics, for example, energytransfer equals the product of the force applied to a bodyand the resulting displacement.Conjugate variables are pairs of thermodynamic con-cepts, with the first being akin to a “force” applied tosome thermodynamic system, the second being akin tothe resulting “displacement,” and the product of the twoequalling the amount of energy transferred. The commonconjugate variables are:

• Pressure-volume (the mechanical parameters);

• Temperature-entropy (thermal parameters);

• Chemical potential-particle number (material pa-rameters).

11 Potentials

Thermodynamic potentials are different quantitativemeasures of the stored energy in a system. Potentials areused to measure energy changes in systems as they evolvefrom an initial state to a final state. The potential used de-pends on the constraints of the system, such as constanttemperature or pressure. For example, the Helmholtz andGibbs energies are the energies available in a system todo useful work when the temperature and volume or thepressure and temperature are fixed, respectively.The five most well known potentials are:where T is the temperature, S the entropy, p the pressure,V the volume, µ the chemical potential,N the number ofparticles in the system, and i is the count of particles typesin the system.

13

Thermodynamic potentials can be derived from the en-ergy balance equation applied to a thermodynamic sys-tem. Other thermodynamic potentials can also be ob-tained through Legendre transformation.

12 Axiomatics

Most accounts of thermodynamics presuppose the lawof conservation of mass, sometimes with,[124] and some-times without,[125][126][127] explicit mention. Particularattention is paid to the law in accounts of non-equilibriumthermodynamics.[128][129] One statement of this law is“The total mass of a closed system remains constant.”[9]Another statement of it is “In a chemical reaction, matteris neither created nor destroyed.”[130] Implied in this isthat matter and energy are not considered to be intercon-verted in such accounts. The full generality of the law ofconservation of energy is thus not used in such accounts.In 1909, Constantin Carathéodory presented[53] a purelymathematical axiomatic formulation, a description oftenreferred to as geometrical thermodynamics, and some-times said to take the “mechanical approach”[82] to ther-modynamics. The Carathéodory formulation is restrictedto equilibrium thermodynamics and does not attemptto deal with non-equilibrium thermodynamics, forcesthat act at a distance on the system, or surface tensioneffects.[131] Moreover, Carathéodory’s formulation doesnot deal with materials like water near 4 °C, which havea density extremum as a function of temperature at con-stant pressure.[132][133] Carathéodory used the law of con-servation of energy as an axiom from which, along withthe contents of the zeroth law, and some other assump-tions including his own version of the second law, he de-rived the first law of thermodynamics.[134] Consequentlyone might also describe Carathėodory’s work as lying inthe field of energetics,[135] which is broader than thermo-dynamics. Carathéodory presupposed the law of conser-vation of mass without explicit mention of it.Since the time of Carathėodory, other influential ax-iomatic formulations of thermodynamics have appeared,which like Carathéodory’s, use their own respective ax-ioms, different from the usual statements of the four laws,to derive the four usually stated laws.[136][137][138]

Many axiomatic developments assume the existence ofstates of thermodynamic equilibrium and of states ofthermal equilibrium. States of thermodynamic equilib-rium of compound systems allow their component sim-ple systems to exchange heat and matter and to do workon each other on their way to overall joint equilibrium.Thermal equilibrium allows them only to exchange heat.The physical properties of glass depend on its history ofbeing heated and cooled and, strictly speaking, glass isnot in thermodynamic equilibrium.[67]

According to Herbert Callen's widely cited 1985 text onthermodynamics: “An essential prerequisite for the mea-

surability of energy is the existence of walls that do notpermit transfer of energy in the form of heat.”.[139] Ac-cording to Werner Heisenberg's mature and careful ex-amination of the basic concepts of physics, the theory ofheat has a self-standing place.[140]

From the viewpoint of the axiomatist, there are severaldifferent ways of thinking about heat, temperature, andthe second law of thermodynamics. The Clausius wayrests on the empirical fact that heat is conducted alwaysdown, never up, a temperature gradient. The Kelvin wayis to assert the empirical fact that conversion of heat intowork by cyclic processes is never perfectly efficient. Amore mathematical way is to assert the existence of afunction of state called the entropy that tells whether ahypothesized process occurs spontaneously in nature. Amore abstract way is that of Carathéodory that in ef-fect asserts the irreversibility of some adiabatic processes.For these different ways, there are respective correspond-ing different ways of viewing heat and temperature.The Clausius–Kelvin–Planck way This way prefersideas close to the empirical origins of thermodynamics.It presupposes transfer of energy as heat, and empiri-cal temperature as a scalar function of state. Accord-ing to Gislason and Craig (2005): “Most thermodynamicdata come from calorimetry...”[141] According to Kon-depudi (2008): “Calorimetry is widely used in presentday laboratories.”[142] In this approach, what is often cur-rently called the zeroth law of thermodynamics is de-duced as a simple consequence of the presupposition ofthe nature of heat and empirical temperature, but it is notnamed as a numbered law of thermodynamics. Planckattributed this point of view to Clausius, Kelvin, andMaxwell. Planck wrote (on page 90 of the seventh edi-tion, dated 1922, of his treatise) that he thought that noproof of the second law of thermodynamics could everwork that was not based on the impossibility of a perpet-ual motion machine of the second kind. In that treatise,Planck makes no mention of the 1909 Carathéodory way,which was well known by 1922. Planck for himself chosea version of what is just above called the Kelvin way.[143]The development by Truesdell and Bharatha (1977) is soconstructed that it can deal naturally with cases like thatof water near 4 °C.[137]

The way that assumes the existence of entropy as afunction of state This way also presupposes transfer ofenergy as heat, and it presupposes the usually stated formof the zeroth law of thermodynamics, and from these twoit deduces the existence of empirical temperature. Thenfrom the existence of entropy it deduces the existence ofabsolute thermodynamic temperature.[8][136]

The Carathéodory way This way presupposes that thestate of a simple one-phase system is fully specifiable byjust one more state variable than the known exhaustivelist of mechanical variables of state. It does not explic-itly name empirical temperature, but speaks of the one-dimensional “non-deformation coordinate”. This satisfies

14 15 SEE ALSO

the definition of an empirical temperature, that lies on aone-dimensional manifold. The Carathéodory way needsto assume moreover that the one-dimensional manifoldhas a definite sense, which determines the direction ofirreversible adiabatic process, which is effectively assum-ing that heat is conducted from hot to cold. This way pre-supposes the often currently stated version of the zerothlaw, but does not actually name it as one of its axioms.[131]According to one author, Carathéodory’s principle, whichis his version of the second law of thermodynamics, doesnot imply the increase of entropy when work is done un-der adiabatic conditions (as was noted by Planck[144]).Thus Carathéodory’s way leaves unstated a further empir-ical fact that is needed for a full expression of the secondlaw of thermodynamics.[145]

13 Scope of thermodynamics

Originally thermodynamics concerned material and ra-diative phenomena that are experimentally reproducible.For example, a state of thermodynamic equilibrium is asteady state reached after a system has aged so that itno longer changes with the passage of time. But morethan that, for thermodynamics, a system, defined by itsbeing prepared in a certain way must, consequent on ev-ery particular occasion of preparation, upon aging, reachone and the same eventual state of thermodynamic equi-librium, entirely determined by the way of preparation.Such reproducibility is because the systems consist of somany molecules that the molecular variations betweenparticular occasions of preparation have negligible orscarcely discernable effects on the macroscopic variablesthat are used in thermodynamic descriptions. This ledto Boltzmann’s discovery that entropy had a statistical orprobabilistic nature. Probabilistic and statistical explana-tions arise from the experimental reproducibility of thephenomena.[146]

Gradually, the laws of thermodynamics came to be usedto explain phenomena that occur outside the experimen-tal laboratory. For example, phenomena on the scale ofthe earth’s atmosphere cannot be reproduced in a lab-oratory experiment. But processes in the atmospherecan be modeled by use of thermodynamic ideas, ex-tended well beyond the scope of laboratory equilibriumthermodynamics.[147][148][149] A parcel of air can, nearenough for many studies, be considered as a closed ther-modynamic system, one that is allowed to move over sig-nificant distances. The pressure exerted by the surround-ing air on the lower face of a parcel of air may differ fromthat on its upper face. If this results in rising of the par-cel of air, it can be considered to have gained potentialenergy as a result of work being done on it by the com-bined surrounding air below and above it. As it rises, sucha parcel usually expands because the pressure is lower atthe higher altitudes that it reaches. In that way, the ris-ing parcel also does work on the surrounding atmosphere.

For many studies, such a parcel can be considered nearlyto neither gain nor lose energy by heat conduction to itssurrounding atmosphere, and its rise is rapid enough toleave negligible time for it to gain or lose heat by radia-tion; consequently the rising of the parcel is near enoughadiabatic. Thus the adiabatic gas law accounts for its in-ternal state variables, provided that there is no precipita-tion into water droplets, no evaporation of water droplets,and no sublimation in the process. More precisely, therising of the parcel is likely to occasion friction and tur-bulence, so that some potential and some kinetic energyof bulk converts into internal energy of air considered aseffectively stationary. Friction and turbulence thus op-pose the rising of the parcel.[150][151]

14 Applied fields• Atmospheric thermodynamics

• Biological thermodynamics

• Black hole thermodynamics

• Chemical thermodynamics

• Equilibrium thermodynamics

• Geology

• Industrial ecology (re: Exergy)

• Maximum entropy thermodynamics

• Non-equilibrium thermodynamics

• Philosophy of thermal and statistical physics

• Psychrometrics

• Quantum thermodynamics

• Statistical thermodynamics

• Thermoeconomics

15 See also

Entropy production

15.1 Lists and timelines

• List of important publications in thermodynamics

• List of textbooks in statistical mechanics

• List of thermal conductivities

• List of thermodynamic properties

• Table of thermodynamic equations

• Timeline of thermodynamics

15

15.2 Wikibooks

• Engineering Thermodynamics

• Entropy for Beginners

16 References[1] Clausius, Rudolf (1850). On the Motive Power of Heat,

and on the Laws which can be deduced from it for the The-ory of Heat. Poggendorff’s Annalen der Physik, LXXIX(Dover Reprint). ISBN 0-486-59065-8.

[2] Thomson, W. (1854). “On the Dynamical Theory ofHeat. Part V. Thermo-electric Currents”. Transac-tions of the Royal Society of Edinburgh 21 (part I):123. doi:10.1017/s0080456800032014. reprinted inSir William Thomson, LL.D. D.C.L., F.R.S. (1882).Mathematical and Physical Papers 1. London, Cam-bridge: C.J. Clay, M.A. & Son, Cambridge UniversityPress. p. 232. Hence Thermo-dynamics falls naturallyinto two Divisions, of which the subjects are respectively,the relation of heat to the forces acting between contiguousparts of bodies, and the relation of heat to electrical agency.

[3] Hess, H. (1840). Thermochemische Untersuchungen,Annalen der Physik und Chemie (Poggendorff, Leipzig)126(6): 385–404.

[4] Gibbs, Willard, J. (1876). Transactions of the ConnecticutAcademy, III, pp. 108–248, Oct. 1875 – May 1876, andpp. 343–524, May 1877 – July 1878.

[5] Duhem, P.M.M. (1886). Le Potential Thermodynamiqueet ses Applications, Hermann, Paris.

[6] Lewis, Gilbert N.; Randall, Merle (1923). Thermo-dynamics and the Free Energy of Chemical Substances.McGraw-Hill Book Co. Inc.

[7] Guggenheim, E.A. (1933). Modern Thermodynamics bythe Methods of J.W. Gibbs, Methuen, London.

[8] Guggenheim, E.A. (1949/1967)

[9] Ilya Prigogine, I. & Defay, R., translated by D.H. Everett(1954). Chemical Thermodynamics. Longmans, Green &Co., London. Includes classical non-equilibrium thermo-dynamics.

[10] Enrico Fermi (1956). Thermodynamics. Courier DoverPublications. p. ix. ISBN 0-486-60361-X. OCLC230763036 54033021.

[11] Perrot, Pierre (1998). A to Z of Thermodynamics. Ox-ford University Press. ISBN 0-19-856552-6. OCLC123283342 38073404.

[12] Clark, John, O.E. (2004). The Essential Dictionary ofScience. Barnes & Noble Books. ISBN 0-7607-4616-8.OCLC 58732844 63473130.

[13] Bridgman, P.W. (1943). The Nature of Thermodynamics,Harvard University Press, Cambridge MA, p. 48.

[14] Partington, J.R. (1949), page 118.

[15] Reif, F. (1965). Fundamentals of Statistical and ThermalPhysics, McGraw-Hill Book Company, New York, page122.

[16] Fowler, R., Guggenheim, E.A. (1939), p. 3.

[17] Tisza, L. (1966), p. 18.

[18] Adkins, C.J. (1968/1983), p. 4.

[19] Born, M. (1949), p. 44.

[20] Tisza, L. (1966), pp. 109, 112.

[21] Callen, H.B. (1960/1985), pp. 15, 17.

[22] Callen, H.B. (1960/1985), p. 427.

[23] Tisza, L. (1966), pp. 41, 109, 121, originally publishedas 'The thermodynamics of phase equilibrium', Annals ofPhysics, 13: 1–92.

[24] Serrin, J. (1986). Chapter 1, 'An Outline of Thermody-namical Structure', pp. 3–32, especially p. 8, in Serrin, J.(1986).

[25] Fowler, R., Guggenheim, E.A. (1939), p. 13.

[26] Tisza, L. (1966), pp. 79–80.

[27] Planck, M. 1923/1926, page 5.

[28] Partington, p. 121.

[29] Adkins, pp. 19–20.

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17 Cited bibliography

• Adkins, C.J. (1968/1975). Equilibrium Thermo-dynamics, second edition, McGraw-Hill, London,ISBN 0-07-084057-1.

• Bailyn, M. (1994). A Survey of Thermodynam-ics, American Institute of Physics Press, New York,ISBN 0-88318-797-3.

• Born, M. (1949). Natural Philosophy of Cause andChance, Oxford University Press, London.

• Bryan, G.H. (1907). Thermodynamics. An Intro-ductory Treatise dealing mainly with First Princi-ples and their Direct Applications, B.G. Teubner,Leipzig.

• Callen, H.B. (1960/1985). Thermodynamics and anIntroduction to Thermostatistics, (1st edition 1960)2nd edition 1985, Wiley, New York, ISBN 0-471-86256-8.

• Eu, B.C. (2002). Generalized Thermodynam-ics. The Thermodynamics of Irreversible Processesand Generalized Hydrodynamics, Kluwer AcademicPublishers, Dordrecht, ISBN 1-4020-0788-4.

• Fowler, R., Guggenheim, E.A. (1939). Statisti-cal Thermodynamics, Cambridge University Press,Cambridge UK.

• Gibbs, J.W. (1875). On the equilibrium of hetero-geneous substances, Transactions of the ConnecticutAcademy of Arts and Sciences, 3: 108–248.

• Grandy, W.T., Jr (2008). Entropy and the TimeEvolution of Macroscopic Systems, Oxford Univer-sity Press, Oxford, ISBN 978-0-19-954617-6.

• Guggenheim, E.A. (1949/1967). Thermodynamics.An Advanced Treatment for Chemists and Physicists,(1st edition 1949) 5th edition 1967, North-Holland,Amsterdam.

• Haase, R. (1971). Survey of Fundamental Laws,chapter 1 of Thermodynamics, pages 1–97 of vol-ume 1, ed. W. Jost, of Physical Chemistry. An Ad-vanced Treatise, ed. H. Eyring, D. Henderson, W.Jost, Academic Press, New York, lcn 73–117081.

• Kondepudi, D., Prigogine, I. (1998). Modern Ther-modynamics. From Heat Engines to DissipativeStructures, John Wiley & Sons, ISBN 0-471-97393-9.

• Lebon, G., Jou, D., Casas-Vázquez, J. (2008).Understanding Non-equilibrium Thermodynamics,Springer, Berlin, ISBN 978-3-540-74251-7.

• Partington, J.R. (1949). An Advanced Treatise onPhysical Chemistry, volume 1, Fundamental Princi-ples. The Properties of Gases, Longmans, Green andCo., London.

• Pippard, A.B. (1957). The Elements of ClassicalThermodynamics, Cambridge University Press.

19

• Planck, M.(1897/1903). Treatise on Thermody-namics, translated by A. Ogg, Longmans, Green &Co., London.

• Planck, M. (1923/1926). Treatise on Thermody-namics, third English edition translated by A. Oggfrom the seventh German edition, Longmans, Green& Co., London.

• Serrin, J. (1986). New Perspectives in Thermody-namics, edited by J. Serrin, Springer, Berlin, ISBN3-540-15931-2.

• Sommerfeld, A. (1952/1956). Thermodynamicsand Statistical Mechanics, Academic Press, NewYork.

• Tschoegl, N.W. (2000). Fundamentals of Equilib-rium and Steady-State Thermodynamics, Elsevier,Amsterdam, ISBN 0-444-50426-5.

• Tisza, L. (1966). Generalized Thermodynamics,M.I.T Press, Cambridge MA.

• Truesdell, C.A. (1980). The Tragicomical Historyof Thermodynamics, 1822–1854, Springer, NewYork, ISBN 0-387-90403-4.

18 Further reading

• Goldstein, Martin, and Inge F. (1993). The Refrig-erator and the Universe. Harvard University Press.ISBN 0-674-75325-9. OCLC 32826343. A non-technical introduction, good on historical and inter-pretive matters.

• Kazakov, Andrei (July–August 2008). “WebThermo Tables – an On-Line Version of the TRCThermodynamic Tables”. Journal of Research of theNational Institutes of Standards and Technology 113(4): 209–220. doi:10.6028/jres.113.016.

The following titles are more technical:

• Cengel, Yunus A., & Boles, Michael A. (2002).Thermodynamics – an Engineering Approach. Mc-Graw Hill. ISBN 0-07-238332-1. OCLC45791449 52263994 57548906.

• Fermi, E. (1956). Thermodynamics, Dover, NewYork.

• Kittel, Charles & Kroemer, Herbert (1980). Ther-mal Physics. W. H. Freeman Company. ISBN0-7167-1088-9. OCLC 32932988 482366395171399.

19 External links• Thermodynamics Data & Property CalculationWebsites

• Thermodynamics OpenCourseWare from theUniversity of Notre Dame

• Thermodynamics at ScienceWorld

• Biochemistry Thermodynamics

• Engineering Thermodynamics – A Graphical Ap-proach

20 20 TEXT AND IMAGE SOURCES, CONTRIBUTORS, AND LICENSES

20 Text and image sources, contributors, and licenses

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