Historically, thermodynamics developed out of a desire to increase theefficiency of 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.[1] Scots-Irish physicistLord Kelvin was the first to formulate a concise definition of thermodynamics in 1854[2] which 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 Clausius restated Carnot's principle known as theCarnot cycle and gave thetheory of heat a truer and sounder basis. His most important paper, "On the Moving Force of Heat",[3] 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.[4]
The initial application of thermodynamics tomechanical heat engines was quickly extended to the study of chemical compounds and chemical reactions.Chemical thermodynamics studies the nature of the role of entropy in the process ofchemical reactions and has provided the bulk of expansion and knowledge of the field. Other formulations of thermodynamics emerged.Statistical thermodynamics, or statistical mechanics, concerns itself withstatistical predictions of the collective motion of particles from their microscopic behavior. In 1909,Constantin Carathéodory presented a purely mathematical approach in anaxiomatic formulation, a description often referred to asgeometrical thermodynamics.
A description of any thermodynamic system employs the fourlaws of thermodynamics that form an axiomatic basis.The first law specifies that energy can be transferred between physical systems asheat, aswork, and with the transfer of matter.[5]The second law defines the existence of a quantity calledentropy, which describes the direction, thermodynamically, that a system can evolve and quantifies the state of order of a system and which can be used to quantify the useful work that can be extracted from the system.[6]
In thermodynamics, interactions between large ensembles of objects are studied and categorized. Central to this are the concepts of the thermodynamicsystem and 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 energy andthermodynamic potentials, which are useful for determining conditions forequilibrium andspontaneous processes.
This article is focused mainly on classical thermodynamics which primarily studies systems inthermodynamic equilibrium.Non-equilibrium thermodynamics is often treated as an extension of the classical treatment, but statistical mechanics has brought many advances to that field.
Thehistory of thermodynamics as a scientific discipline generally begins withOtto von Guericke who, in 1650, built and designed the world's firstvacuum pump and demonstrated avacuum using hisMagdeburg hemispheres. Guericke was driven to make a vacuum in order to disproveAristotle's long-held supposition that 'nature abhors a vacuum'. Shortly after Guericke, the Anglo-Irish physicist and chemistRobert Boyle had learned of Guericke's designs and, in 1656, in coordination with English scientistRobert Hooke, built an air pump.[10] Using this pump, Boyle and Hooke noticed a correlation betweenpressure,temperature, andvolume. In time,Boyle's Law was formulated, which states that pressure and volume areinversely proportional. Then, in 1679, based on these concepts, an associate of Boyle's namedDenis Papin built 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 apiston and a cylinder engine. He did not, however, follow through with his design. Nevertheless, in 1697, based on Papin's designs, engineerThomas Savery built the first engine, followed byThomas Newcomen in 1712. Although these early engines were crude and inefficient, they attracted the attention of the leading scientists of the time.
The fundamental concepts ofheat capacity andlatent heat, which were necessary for the development of thermodynamics, were developed by ProfessorJoseph Black at the University of Glasgow, whereJames Watt was employed as an instrument maker. Black and Watt performed experiments together, but it was Watt who conceived the idea of theexternal condenser which resulted in a large increase insteam engine efficiency.[11] 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.[12]
Clausius, who first stated the basic ideas of the second law in his paper "On the Moving Force of Heat",[3] published in 1850, and is called "one of the founding fathers of thermodynamics",[14] introduced the concept ofentropy in 1865.
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]")[22] can be traced back to the rootδύναμιςdynamis, meaning "power".[23][24]
In 1849, the adjectivethermo-dynamic is used by William Thomson.[25][26]
In 1854, the nounthermo-dynamics is used by Thomson and William Rankine to represent the science of generalized heat engines.[26][21]
Pierre Perrot claims that the termthermodynamics was coined byJames Joule in 1858 to designate the science of relations between heat and power,[12] however, Joule never used that term, but used instead the termperfect thermo-dynamic engine in reference to Thomson's 1849[25] phraseology.[21]
The study of thermodynamic 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 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 qualifierclassical reflects 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, 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 theory at the microscopic level.
Equilibrium thermodynamics is 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 is 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.[28] Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.
Annotated color version of the original 1824Carnot heat engine showing 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.
Thezeroth law of thermodynamics states: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 relation on the set ofthermodynamic systems under 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.[29] 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.
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.[30][31][32]
where 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), denotes the quantity of energy suppliedto the system as heat, and denotes the amount of thermodynamic work doneby the systemon its surroundings. An equivalent statement is thatperpetual motion machines of the first kind are impossible; work done by a system on its surrounding requires that the system's internal energy decrease or be consumed, so that the amount of internal energy lost by that work must be resupplied as heat by an external energy source or as work by an external machine acting on the system (so that 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
,
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.[34]
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.
A traditional version of thesecond law of thermodynamics states: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 generalirreversibility of 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.
Thethird law of thermodynamics states: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 zero of temperature. This law provides an absolute reference point for the determination of entropy. The entropy determined relative to this point is the absolute entropy. Alternative 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).
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 aboundary which may be a physical or notional, but serve to confine the system to a finite volume. Segments of theboundary are 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 Emanuel theorized in 1986 in the field ofatmospheric thermodynamics, or theevent horizon of 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:
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 astate ofthermodynamic 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.
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 quantities that do not depend on the process by which the system arrived at its state. They are calledintensive variables orextensive variables according to how they change when the size of the system changes. The properties of the system can be described by anequation of state which 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 process may 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 aconjugate pair.
Several commonly studied thermodynamic processes are:
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 law states 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 Maxwell in 1872, asserts that it is possible to measure temperature. An idealizedthermometer is 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 abarometer may also be constructed from a sample of an ideal gas held at a constant temperature. Acalorimeter is 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.
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 variables are 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:
Thermodynamic potentials are 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.[35][36]
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 is amathematical discipline that 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 systems and the concept ofadiabatic accessibility, a notion that was introduced by Carathéodory himself.[37][38] In this formulation, thermodynamic concepts such asheat,entropy, andtemperature are derived from quantities that are more directly measurable.[39] Theories that came after, differed in the sense that they made assumptions regardingthermodynamic processes with arbitrary initial and final states, as opposed to considering only neighboring states.
^The sign convention (Q is heat suppliedto the system as, W is work doneby the system) is that ofRudolf Clausius. The opposite sign convention is customary in chemical thermodynamics.
^Clausius, Rudolf (1850).On the Motive Power of Heat, and on the Laws which can be deduced from it for the Theory of Heat. Poggendorff's Annalen der Physik, LXXIX (Dover Reprint).ISBN978-0-486-59065-3.{{cite book}}:ISBN / Date incompatibility (help)
^William Thomson, LL.D. D.C.L., F.R.S. (1882).Mathematical and Physical Papers. Vol. 1. London, Cambridge: C.J. Clay, M.A. & Son, Cambridge University Press. p. 232.ISBN978-0-598-96004-7.Archived from the original on 18 April 2021. Retrieved2 November 2020.{{cite book}}:ISBN / Date incompatibility (help)CS1 maint: multiple names: authors list (link)
^The Newcomen engine was improved from 1711 until Watt's work, making the efficiency comparison subject to qualification, but the increase from the 1865 version was on the order of 100%.
^Thompson, Silvanus (1910).The Life of William Thomson, Baron Kelvin of Largs. Vol. 1. MacMillan and Co., Limited. p. 241.the fundamental subject of Natural Philosophy is Dynamics, or thescience of force .... Every phenomenon in nature is a manifestation of force.
^Çengel, Yunus A.; Boles, Michael A.; Kanoğlu, Mehmet (2024).Thermodynamics: An Engineering Approach (Tenth ed.). New York, NY: McGraw Hill.ISBN978-1-266-15211-5.
^abKelvin, William T. (1849) "An Account of Carnot's Theory of the Motive Power of Heat – with Numerical Results Deduced from Regnault's Experiments on Steam."Transactions of the Edinburg Royal Society, XVI. January 2.Scanned CopyArchived 24 July 2017 at theWayback Machine
^Klaus Roth:Sekt, Champagner & Co. So prickelnd kann Chemie sein inChemie unserer Zeit 8. Dezember 2009: Vol. 43, Issue 6, S. 418-432doi:10.1002/ciuz.200900520
^Klaus Roth:Chemische Köstlichkeiten, Wiley-VCH Verlag GmbH & Co. KGaA, 2010, ISBN 978-3527327522, S. 47
^Bailyn, M. (1994).A Survey of Thermodynamics, American Institute of Physics, AIP Press, Woodbury NY,ISBN0883187973, p. 79.
^Callen, H.B. (1960/1985).Thermodynamics and an Introduction to Thermostatistics, second edition, John Wiley & Sons, Hoboken NY,ISBN9780471862567, pp. 11–13.
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.
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