Thermodynamics

Thermodynamicsis the branch ofphysicsthat studiesheat,work,andtemperatureand their relation toenergy,entropy,and the physical properties ofmatterandradiation.The behavior of these quantities is governed by the fourlaws of thermodynamics,which convey a quantitative description using measurable macroscopicphysical quantities,but may be explained in terms ofmicroscopicconstituents bystatistical mechanics.Thermodynamics plays a role in a wide variety of topics inscienceandengineering.

Historically, thermodynamics developed out of a desire to increase theefficiencyof earlysteam engines,particularly through the work of French physicistSadi Carnot(1824) who believed that engine efficiency was the key that could help France win theNapoleonic Wars.Scots-Irish physicistLord Kelvinwas the first to formulate a concise definition of thermodynamics in 1854which stated, "Thermo-dynamics is the subject of the relation of heat to forces acting between contiguous parts of bodies, and the relation of heat to electrical agency." German physicist and mathematicianRudolf Clausiusrestated Carnot's principle known as theCarnot cycleand gave to thetheory of heata truer and sounder basis. His most important paper, "On the Moving Force of Heat",published in 1850, first stated thesecond law of thermodynamics.In 1865 he introduced the concept of entropy. In 1870 he introduced thevirial theorem,which applied to heat.

The initial application of thermodynamics tomechanical heat engineswas quickly extended to the study of chemical compounds and chemical reactions.Chemical thermodynamicsstudies the nature of the role of entropy in the process ofchemical reactionsand has provided the bulk of expansion and knowledge of the field. Other formulations of thermodynamics emerged.Statistical thermodynamics,or statistical mechanics, concerns itself withstatisticalpredictions of the collective motion of particles from their microscopic behavior. In 1909,Constantin Carathéodorypresented a purely mathematical approach in anaxiomaticformulation, a description often referred to asgeometrical thermodynamics.

Introduction

A description of any thermodynamic system employs the fourlaws of thermodynamicsthat form an axiomatic basis.The first lawspecifies that energy can be transferred between physical systems asheat,aswork,and with transfer of matter.The second lawdefines the existence of a quantity calledentropy,that describes the direction, thermodynamically, that a system can evolve and quantifies the state of order of a system and that can be used to quantify the useful work that can be extracted from the system.

In thermodynamics, interactions between large ensembles of objects are studied and categorized. Central to this are the concepts of the thermodynamicsystemand itssurroundings.A system is composed of particles, whose average motions define its properties, and those properties are in turn related to one another throughequations of state.Properties can be combined to expressinternal energyandthermodynamic potentials,which are useful for determining conditions forequilibriumandspontaneous processes.

With these tools, thermodynamics can be used to describe how systems respond to changes in their environment. This can be applied to a wide variety of topics inscienceandengineering,such asengines,phase transitions,chemical reactions,transport phenomena,and evenblack holes.The results of thermodynamics are essential for other fields ofphysicsand forchemistry,chemical engineering,corrosion engineering,aerospace engineering,mechanical engineering,electrical engineering,cell biology,biomedical engineering,materials science,andeconomics,to name a few.

This article is focused mainly on classical thermodynamics which primarily studies systems inthermodynamic equilibrium.Non-equilibrium thermodynamicsis often treated as an extension of the classical treatment, but statistical mechanics has brought many advances to that field.

History

Thethermodynamicistsof the original eight founding schools of thermodynamics. The schools with the most-lasting influence on the modern versions of thermodynamics are the Berlin school, particularlyRudolf Clausius's 1865 textbookThe Mechanical Theory of Heat,the Vienna school, with thestatistical mechanicsofLudwig Boltzmann,and the Gibbsian school at Yale University ofWillard Gibbs' 1876 and his bookOn the Equilibrium of Heterogeneous Substanceswhich launchedchemical thermodynamics.

Thehistory of thermodynamicsas a scientific discipline generally begins withOtto von Guerickewho, in 1650, built and designed the world's firstvacuum pumpand demonstrated avacuumusing hisMagdeburg hemispheres.Guericke was driven to make a vacuum to disproveAristotle's long-held supposition that 'nature abhors a vacuum'. Shortly after Guericke, the Anglo-Irish physicist and chemistRobert Boylehad learned of Guericke's designs and, in 1656, in coordination with English scientistRobert Hooke,built an air pump.Using this pump, Boyle and Hooke noticed a correlation betweenpressure,temperature,andvolume.In time,Boyle's Lawwas formulated, which states that pressure and volume areinversely proportional.Then, in 1679, based on these concepts, an associate of Boyle's namedDenis Papinbuilt asteam digester,which was a closed vessel with a tightly fitting lid that confined steam until a high pressure was generated.

Later designs implemented a steam release valve that kept the machine from exploding. By watching the valve rhythmically move up and down, Papin conceived of the idea of apistonand a cylinder engine. He did not, however, follow through with his design. Nevertheless, in 1697, based on Papin's designs, engineerThomas Saverybuilt the first engine, followed byThomas Newcomenin 1712. Although these early engines were crude and inefficient, they attracted the attention of the leading scientists of the time.

The fundamental concepts ofheat capacityandlatent heat,which were necessary for the development of thermodynamics, were developed by ProfessorJoseph Blackat the University of Glasgow, whereJames Wattwas employed as an instrument maker. Black and Watt performed experiments together, but it was Watt who conceived the idea of theexternal condenserwhich resulted in a large increase insteam engineefficiency.Drawing on all the previous work ledSadi Carnot,the "father of thermodynamics", to publishReflections on the Motive Power of Fire(1824), a discourse on heat, power, energy and engine efficiency. The book outlined the basic energetic relations between theCarnot engine,theCarnot cycle,and motive power. It marked the start of thermodynamics as a modern science.

The first thermodynamic textbook was written in 1859 byWilliam Rankine,originally trained as a physicist and a civil and mechanical engineering professor at theUniversity of Glasgow.The first and second laws of thermodynamics emerged simultaneously in the 1850s, primarily out of the works of William Rankine,Rudolf Clausius,andWilliam Thomson(Lord Kelvin). The foundations of statistical thermodynamics were set out by physicists such asJames Clerk Maxwell,Ludwig Boltzmann,Max Planck,Rudolf ClausiusandJ. Willard Gibbs.

Clausius, who first stated the basic ideas of the second law in his paper "On the Moving Force of Heat",published in 1850, and is called "one of the founding fathers of thermodynamics",introduced the concept ofentropyin 1865.

During the years 1873–76 the American mathematical physicistJosiah Willard Gibbspublished a series of three papers, the most famous beingOn the Equilibrium of Heterogeneous Substances,in which he showed howthermodynamic processes,includingchemical reactions,could be graphically analyzed, by studying theenergy,entropy,volume,temperatureandpressureof thethermodynamic systemin such a manner, one can determine if a process would occur spontaneously.AlsoPierre Duhemin the 19th century wrote about chemical thermodynamics.During the early 20th century, chemists such asGilbert N. Lewis,Merle Randall,andE. A. Guggenheimapplied the mathematical methods of Gibbs to the analysis of chemical processes.

Etymology

Thermodynamicshas an intricate etymology.

By a surface-level analysis, the word consists of two parts that can be traced back to Ancient Greek. Firstly,thermo-( "of heat"; used in words such asthermometer) can be traced back to the rootθέρμηtherme,meaning "heat". Secondly, the worddynamics( "science of force [or power]" )can be traced back to the rootδύναμιςdynamis,meaning "power".

In 1849, the adjectivethermo-dynamicis used by William Thomson.

In 1854, the nounthermo-dynamicsis used by Thomson and William Rankine to represent the science of generalized heat engines.

Pierre Perrot claims that the termthermodynamicswas coined byJames Joulein 1858 to designate the science of relations between heat and power,however, Joule never used that term, but used instead the termperfect thermo-dynamic enginein reference to Thomson's 1849phraseology.

Branches of thermodynamics

The study of thermodynamical systems has developed into several related branches, each using a different fundamental model as a theoretical or experimental basis, or applying the principles to varying types of systems.

Classical thermodynamics

Classical thermodynamics is the description of the states of thermodynamic systems at near-equilibrium, that uses macroscopic, measurable properties. It is used to model exchanges of energy, work and heat based on thelaws of thermodynamics.The qualifierclassicalreflects the fact that it represents the first level of understanding of the subject as it developed in the 19th century and describes the changes of a system in terms of macroscopic empirical (large scale, and measurable) parameters. A microscopic interpretation of these concepts was later provided by the development ofstatistical mechanics.

Statistical mechanics

Statistical mechanics,also known as statistical thermodynamics, emerged with the development of atomic and molecular theories in the late 19th century and early 20th century, and supplemented classical thermodynamics with an interpretation of the microscopic interactions between individual particles or quantum-mechanical states. This field relates the microscopic properties of individual atoms and molecules to the macroscopic, bulk properties of materials that can be observed on the human scale, thereby explaining classical thermodynamics as a natural result of statistics, classical mechanics, andquantum theoryat the microscopic level.

Chemical thermodynamics

Chemical thermodynamicsis the study of the interrelation ofenergywithchemical reactionsor with a physical change ofstatewithin the confines of thelaws of thermodynamics.The primary objective of chemical thermodynamics is determining the spontaneity of a given transformation.

Equilibrium thermodynamics

Equilibrium thermodynamicsis the study of transfers of matter and energy in systems or bodies that, by agencies in their surroundings, can be driven from one state of thermodynamic equilibrium to another. The term 'thermodynamic equilibrium' indicates a state of balance, in which all macroscopic flows are zero; in the case of the simplest systems or bodies, their intensive properties are homogeneous, and their pressures are perpendicular to their boundaries. In an equilibrium state there are no unbalanced potentials, or driving forces, between macroscopically distinct parts of the system. A central aim in equilibrium thermodynamics is: given a system in a well-defined initial equilibrium state, and given its surroundings, and given its constitutive walls, to calculate what will be the final equilibrium state of the system after a specified thermodynamic operation has changed its walls or surroundings.

Non-equilibrium thermodynamics

Non-equilibrium thermodynamicsis a branch of thermodynamics that deals with systems that are not inthermodynamic equilibrium.Most systems found in nature are not in thermodynamic equilibrium because they are not in stationary states, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics.Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.

Laws of thermodynamics

Main article:Laws of thermodynamics

Annotated color version of the original 1824Carnot heat engineshowing the hot body (boiler), working body (system, steam), and cold body (water), the letters labeled according to the stopping points inCarnot cycle

Thermodynamics is principally based on a set of four laws which are universally valid when applied to systems that fall within the constraints implied by each. In the various theoretical descriptions of thermodynamics these laws may be expressed in seemingly differing forms, but the most prominent formulations are the following.

Zeroth law

Thezeroth law of thermodynamicsstates:If two systems are each in thermal equilibrium with a third, they are also in thermal equilibrium with each other.

This statement implies that thermal equilibrium is anequivalence relationon the set ofthermodynamic systemsunder consideration. Systems are said to be in equilibrium if the small, random exchanges between them (e.g.Brownian motion) do not lead to a net change in energy. This law is tacitly assumed in every measurement of temperature. Thus, if one seeks to decide whether two bodies are at the sametemperature,it is not necessary to bring them into contact and measure any changes of their observable properties in time.The law provides an empirical definition of temperature, and justification for the construction of practical thermometers.

The zeroth law was not initially recognized as a separate law of thermodynamics, as its basis in thermodynamical equilibrium was implied in the other laws. The first, second, and third laws had been explicitly stated already, and found common acceptance in the physics community before the importance of the zeroth law for the definition of temperature was realized. As it was impractical to renumber the other laws, it was named thezeroth law.

First law

Opening a bottle ofsparkling wine(high-speed photography). The sudden drop of pressure causes a huge drop of temperature. The moisture in the air freezes, creating a smoke of tiny ice crystals.

Thefirst law of thermodynamicsstates:In a process without transfer of matter, the change ininternal energy,$\Delta U$,of athermodynamic systemis equal to the energy gained as heat,$Q$,less the thermodynamic work,$W$,done by the system on its surroundings.

$\Delta U=Q-W$.

where$\Delta U$denotes the change in the internal energy of aclosed system(for which heat or work through the system boundary are possible, but matter transfer is not possible),$Q$denotes the quantity of energy suppliedtothe system as heat, and$W$denotes the amount of thermodynamic work donebythe systemonits surroundings. An equivalent statement is thatperpetual motion machinesof the first kind are impossible; work$W$done by a system on its surrounding requires that the system's internal energy$U$decrease or be consumed, so that the amount of internal energy lost by that work must be resupplied as heat$Q$by an external energy source or as work by an external machine acting on the system (so that$U$is recovered) to make the system work continuously.

For processes that include transfer of matter, a further statement is needed:With due account of the respective fiducial reference states of the systems, when two systems, which may be of different chemical compositions, initially separated only by an impermeable wall, and otherwise isolated, are combined into a new system by the thermodynamic operation of removal of the wall, then

$U_{0}=U_{1}+U_{2}$,

whereU₀denotes the internal energy of the combined system, andU₁andU₂denote the internal energies of the respective separated systems.

Adapted for thermodynamics, this law is an expression of the principle ofconservation of energy,which states that energy can be transformed (changed from one form to another), but cannot be created or destroyed.

Internal energy is a principal property of thethermodynamic state,while heat and work are modes of energy transfer by which a process may change this state. A change of internal energy of a system may be achieved by any combination of heat added or removed and work performed on or by the system. As afunction of state,the internal energy does not depend on the manner, or on the path through intermediate steps, by which the system arrived at its state.

Second law

A traditional version of thesecond law of thermodynamicsstates:Heat does not spontaneously flow from a colder body to a hotter body.

The second law refers to a system of matter and radiation, initially with inhomogeneities in temperature, pressure, chemical potential, and otherintensive properties,that are due to internal 'constraints', or impermeable rigid walls, within it, or to externally imposed forces. The law observes that, when the system is isolated from the outside world and from those forces, there is a definite thermodynamic quantity, itsentropy,that increases as the constraints are removed, eventually reaching a maximum value at thermodynamic equilibrium, when the inhomogeneities practically vanish. For systems that are initially far from thermodynamic equilibrium, though several have been proposed, there is known no general physical principle that determines the rates of approach to thermodynamic equilibrium, and thermodynamics does not deal with such rates. The many versions of the second law all express the generalirreversibilityof the transitions involved in systems approaching thermodynamic equilibrium.

In macroscopic thermodynamics, the second law is a basic observation applicable to any actual thermodynamic process; in statistical thermodynamics, the second law is postulated to be a consequence of molecular chaos.

Third law

Thethird law of thermodynamicsstates:As the temperature of a system approaches absolute zero, all processes cease and the entropy of the system approaches a minimum value.

This law of thermodynamics is a statistical law of nature regarding entropy and the impossibility of reachingabsolute zeroof temperature. This law provides an absolute reference point for the determination of entropy. The entropy determined relative to this point is the absolute entropy. Alternate definitions include "the entropy of all systems and of all states of a system is smallest at absolute zero," or equivalently "it is impossible to reach the absolute zero of temperature by any finite number of processes".

Absolute zero, at which all activity would stop if it were possible to achieve, is −273.15 °C (degrees Celsius), or −459.67 °F (degrees Fahrenheit), or 0 K (kelvin), or 0° R (degreesRankine).

System models

A diagram of a generic thermodynamic system

An important concept in thermodynamics is thethermodynamic system,which is a precisely defined region of the universe under study. Everything in the universe except the system is called thesurroundings.A system is separated from the remainder of the universe by aboundarywhich may be a physical or notional, but serve to confine the system to a finite volume. Segments of theboundaryare often described aswalls;they have respective defined 'permeabilities'. Transfers of energy aswork,or asheat,or ofmatter,between the system and the surroundings, take place through the walls, according to their respective permeabilities.

Matter or energy that pass across the boundary so as to effect a change in the internal energy of the system need to be accounted for in the energy balance equation. The volume contained by the walls can be the region surrounding a single atom resonating energy, such as Max Planck defined in 1900; it can be a body of steam or air in asteam engine,such as Sadi Carnot defined in 1824. The system could also be just onenuclide(i.e. a system ofquarks) as hypothesized inquantum thermodynamics.When a looser viewpoint is adopted, and the requirement of thermodynamic equilibrium is dropped, the system can be the body of atropical cyclone,such asKerry Emanueltheorized in 1986 in the field ofatmospheric thermodynamics,or theevent horizonof ablack hole.

Boundaries are of four types: fixed, movable, real, and imaginary. For example, in an engine, a fixed boundary means the piston is locked at its position, within which a constant volume process might occur. If the piston is allowed to move that boundary is movable while the cylinder and cylinder head boundaries are fixed. For closed systems, boundaries are real while for open systems boundaries are often imaginary. In the case of a jet engine, a fixed imaginary boundary might be assumed at the intake of the engine, fixed boundaries along the surface of the case and a second fixed imaginary boundary across the exhaust nozzle.

Generally, thermodynamics distinguishes three classes of systems, defined in terms of what is allowed to cross their boundaries:

Interactions of thermodynamic systems

Type of system	Mass flow	Work	Heat
Open	Y	Y	Y
Closed	N	Y	Y
Thermally isolated	N	Y	N
Mechanically isolated	N	N	Y
Isolated	N	N	N

As time passes in an isolated system, internal differences of pressures, densities, and temperatures tend to even out. A system in which all equalizing processes have gone to completion is said to be in astateofthermodynamic equilibrium.

Once in thermodynamic equilibrium, a system's properties are, by definition, unchanging in time. Systems in equilibrium are much simpler and easier to understand than are systems which are not in equilibrium. Often, when analysing a dynamic thermodynamic process, the simplifying assumption is made that each intermediate state in the process is at equilibrium, producing thermodynamic processes which develop so slowly as to allow each intermediate step to be an equilibrium state and are said to bereversible processes.

States and processes

When a system is at equilibrium under a given set of conditions, it is said to be in a definitethermodynamic state.The state of the system can be described by a number ofstate quantitiesthat do not depend on the process by which the system arrived at its state. They are calledintensive variablesorextensive variablesaccording to how they change when the size of the system changes. The properties of the system can be described by anequation of statewhich specifies the relationship between these variables. State may be thought of as the instantaneous quantitative description of a system with a set number of variables held constant.

Athermodynamic processmay be defined as the energetic evolution of a thermodynamic system proceeding from an initial state to a final state. It can be described byprocess quantities.Typically, each thermodynamic process is distinguished from other processes in energetic character according to what parameters, such as temperature, pressure, or volume, etc., are held fixed; Furthermore, it is useful to group these processes into pairs, in which each variable held constant is one member of aconjugatepair.

Several commonly studied thermodynamic processes are:

• Adiabatic process:occurs without loss or gain of energy byheat
• Isenthalpic process:occurs at a constantenthalpy
• Isentropic process:a reversible adiabatic process, occurs at a constantentropy
• Isobaric process:occurs at constantpressure
• Isochoric process:occurs at constantvolume(also called isometric/isovolumetric)
• Isothermal process:occurs at a constanttemperature
• Steady state process:occurs without a change in theinternal energy

Instrumentation

There are two types ofthermodynamic instruments,the meter and the reservoir. A thermodynamic meter is any device which measures any parameter of athermodynamic system.In some cases, the thermodynamic parameter is actually defined in terms of an idealized measuring instrument. For example, thezeroth lawstates that if two bodies are in thermal equilibrium with a third body, they are also in thermal equilibrium with each other. This principle, as noted byJames Maxwellin 1872, asserts that it is possible to measure temperature. An idealizedthermometeris a sample of an ideal gas at constant pressure. From theideal gas lawpV=nRT,the volume of such a sample can be used as an indicator of temperature; in this manner it defines temperature. Although pressure is defined mechanically, a pressure-measuring device, called abarometermay also be constructed from a sample of an ideal gas held at a constant temperature. Acalorimeteris a device which is used to measure and define the internal energy of a system.

A thermodynamic reservoir is a system which is so large that its state parameters are not appreciably altered when it is brought into contact with the system of interest. When the reservoir is brought into contact with the system, the system is brought into equilibrium with the reservoir. For example, a pressure reservoir is a system at a particular pressure, which imposes that pressure upon the system to which it is mechanically connected. The Earth's atmosphere is often used as a pressure reservoir. The ocean can act as temperature reservoir when used to cool power plants.

Conjugate variables

Main article:Conjugate variables

The central concept of thermodynamics is that ofenergy,the ability to dowork.By theFirst Law,the total energy of a system and its surroundings is conserved. Energy may be transferred into a system by heating, compression, or addition of matter, and extracted from a system by cooling, expansion, or extraction of matter. Inmechanics,for example, energy transfer equals the product of the force applied to a body and the resulting displacement.

Conjugate variablesare pairs of thermodynamic concepts, with the first being akin to a "force" applied to somethermodynamic system,the second being akin to the resulting "displacement", and the product of the two equaling the amount of energy transferred. The common conjugate variables are:

• Pressure-volume(themechanicalparameters);
• Temperature-entropy(thermal parameters);
• Chemical potential-particle number(material parameters).

Potentials

Thermodynamic potentialsare different quantitative measures of the stored energy in a system. Potentials are used to measure the energy changes in systems as they evolve from an initial state to a final state. The potential used depends on the constraints of the system, such as constant temperature or pressure. For example, the Helmholtz and Gibbs energies are the energies available in a system to do useful work when the temperature and volume or the pressure and temperature are fixed, respectively. Thermodynamic potentials cannot be measured in laboratories, but can be computed using molecular thermodynamics.

The five most well known potentials are:

Name	Symbol	Formula	Natural variables
Internal energy	$U$	$\int \left(T\,\mathrm {d} S-p\,\mathrm {d} V+\sum _{i}\mu _{i}\mathrm {d} N_{i}\right)$	$S,V,\{N_{i}\}$
Helmholtz free energy	$F$	$U-TS$	$T,V,\{N_{i}\}$
Enthalpy	$H$	$U+pV$	$S,p,\{N_{i}\}$
Gibbs free energy	$G$	$U+pV-TS$	$T,p,\{N_{i}\}$
Landau potential, or grand potential	$\Omega$,$\Phi _{\text{G}}$	$U-TS-$$\sum _{i}\,$$\mu _{i}N_{i}$	$T,V,\{\mu _{i}\}$

where$T$is thetemperature,$S$theentropy,$p$thepressure,$V$thevolume,$\mu$thechemical potential,$N$the number of particles in the system, and$i$is the count of particles types in the system.

Thermodynamic potentials can be derived from the energy balance equation applied to a thermodynamic system. Other thermodynamic potentials can also be obtained throughLegendre transformation.

Axiomatic thermodynamics

Axiomatic thermodynamics is amathematical disciplinethat aims to describe thermodynamics in terms of rigorousaxioms,for example by finding a mathematically rigorous way to express the familiarlaws of thermodynamics.

The first attempt at an axiomatic theory of thermodynamics wasConstantin Carathéodory's 1909 workInvestigations on the Foundations of Thermodynamics,which made use ofPfaffian systemsand the concept ofadiabatic accessibility,a notion that was introduced by Carathéodory himself.In this formulation, thermodynamic concepts such asheat,entropy,andtemperatureare derived from quantities that are more directly measurable.Theories that came after, differed in the sense that they made assumptions regardingthermodynamic processeswith arbitrary initial and final states, as opposed to considering only neighboring states.

Applied fields

• Atmospheric thermodynamics
• Biological thermodynamics
• Black hole thermodynamics
• Chemical thermodynamics
• Classical thermodynamics
• Equilibrium thermodynamics
• Industrial ecology(re:Exergy)
• Maximum entropy thermodynamics
• Non-equilibrium thermodynamics
• Philosophy of thermal and statistical physics
• Psychrometrics
• Quantum thermodynamics
• Statistical thermodynamics,i.e. Statistical mechanics
• Thermoeconomics
• Polymer chemistry

See also

• Thermodynamic process path

Lists and timelines

• List of important publications in thermodynamics
• List of textbooks on thermodynamics and statistical mechanics
• List of thermal conductivities
• List of thermodynamic properties
• Table of thermodynamic equations
• Timeline of thermodynamics
• Thermodynamic equations

Further reading

• Goldstein, Martin & Inge F. (1993).The Refrigerator and the Universe.Harvard University Press.ISBN978-0-674-75325-9.OCLC32826343.A nontechnical introduction, good on historical and interpretive matters.
• Kazakov, Andrei; Muzny, Chris D.; Chirico, Robert D.; Diky, Vladimir V.; Frenkel, Michael (2008)."Web Thermo Tables – an On-Line Version of the TRC Thermodynamic Tables".Journal of Research of the National Institute of Standards and Technology.113(4): 209–220.doi:10.6028/jres.113.016.ISSN1044-677X.PMC4651616.PMID27096122.
• Gibbs J.W. (1928).The Collected Works of J. Willard Gibbs Thermodynamics.New York: Longmans, Green and Co.Vol. 1, pp. 55–349.
• Guggenheim E.A. (1933).Modern thermodynamics by the methods of Willard Gibbs.London: Methuen & co. ltd.
• Denbigh K. (1981).The Principles of Chemical Equilibrium: With Applications in Chemistry and Chemical Engineering.London: Cambridge University Press.
• Stull, D.R., Westrum Jr., E.F. and Sinke, G.C. (1969).The Chemical Thermodynamics of Organic Compounds.London: John Wiley and Sons, Inc.{{cite book}}:CS1 maint: multiple names: authors list (link)
• Bazarov I.P. (2010).Thermodynamics: Textbook.St. Petersburg: Lan publishing house. p. 384.ISBN978-5-8114-1003-3.5th ed. (in Russian)
• Bawendi Moungi G., Alberty Robert A. and Silbey Robert J. (2004).Physical Chemistry.J. Wiley & Sons, Incorporated.
• Alberty Robert A. (2003).Thermodynamics of Biochemical Reactions.Wiley-Interscience.
• Alberty Robert A. (2006).Biochemical Thermodynamics: Applications of Mathematica.Vol. 48. John Wiley & Sons, Inc. pp. 1–458.ISBN978-0-471-75798-6.PMID16878778.{{cite book}}:|journal=ignored (help)
• Dill Ken A., Bromberg Sarina (2011).Molecular Driving Forces: Statistical Thermodynamics in Biology, Chemistry, Physics, and Nanoscience.Garland Science.ISBN978-0-8153-4430-8.
• M. Scott Shell (2015).Thermodynamics and Statistical Mechanics: An Integrated Approach.Cambridge University Press.ISBN978-1107656789.
• Douglas E. Barrick (2018).Biomolecular Thermodynamics: From Theory to Applications.CRC Press.ISBN978-1-4398-0019-5.

The following titles are more technical:

• Bejan, Adrian (2016).Advanced Engineering Thermodynamics(4 ed.). Wiley.ISBN978-1-119-05209-8.
• Cengel, Yunus A., & Boles, Michael A. (2002).Thermodynamics – an Engineering Approach.McGraw Hill.ISBN978-0-07-238332-4.OCLC45791449.{{cite book}}:CS1 maint: multiple names: authors list (link)
• Dunning-Davies, Jeremy (1997).Concise Thermodynamics: Principles and Applications.Horwood Publishing.ISBN978-1-8985-6315-0.OCLC36025958.
• Kroemer, Herbert & Kittel, Charles (1980).Thermal Physics.W.H. Freeman Company.ISBN978-0-7167-1088-2.OCLC32932988.

External links

• Media related toThermodynamicsat Wikimedia Commons

• Callendar, Hugh Longbourne (1911)."Thermodynamics".Encyclopædia Britannica.Vol. 26 (11th ed.). pp. 808–814.
• Thermodynamics Data & Property Calculation Websites
• Thermodynamics Educational Websites
• Biochemistry Thermodynamics
• Thermodynamics and Statistical Mechanics
• Engineering Thermodynamics – A Graphical Approach
• Thermodynamics and Statistical Mechanicsby Richard Fitzpatrick