Thermodynamics

Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their
relation to energy, entropy, and the physical properties of matter and radiation. The behavior of
these quantities is governed by the four laws of thermodynamics, which convey a quantitative
description using measurable macroscopic physical quantities but may be explained in terms of
microscopic constituents by statistical mechanics. Thermodynamics applies to various topics in
science and engineering, especially physical chemistry, biochemistry, chemical engineering, and
mechanical engineering, as well as other complex fields such as meteorology.

Historically, thermodynamics developed out of a desire to increase the efficiency of early steam
engines, particularly through the work of French physicist Sadi Carnot (1824) who believed that
engine efficiency was the key that could help France win the Napoleonic Wars.[1] Scots-Irish
physicist Lord 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
mathematician Rudolf Clausius restated Carnot's principle known as the Carnot cycle and gave the
theory of heat a truer and sounder basis. His most important paper, "On the Moving Force of
Heat",[3] published in 1850, first stated the second law of thermodynamics. In 1865 he introduced
the concept of entropy. In 1870 he introduced the virial theorem, which applied to heat.[4]

The initial application of thermodynamics to mechanical 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 of chemical 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 with statistical predictions of the collective
motion of particles from their microscopic behavior. In 1909, Constantin Carathéodory presented a
purely mathematical approach in an axiomatic formulation, a description often referred to as
geometrical thermodynamics.

Introduction

A description of any thermodynamic system employs the four laws of thermodynamics that form an
axiomatic basis. The first law specifies that energy can be transferred between physical systems as
heat, as work, and with transfer of matter.[5] The second law defines the existence of a quantity
called entropy, 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.[6]

In thermodynamics, interactions between large ensembles of objects are studied and categorized.
Central to this are the concepts of the thermodynamic system and its surroundings. A system is
composed of particles, whose average motions define its properties, and those properties are in turn
related to one another through equations of state. Properties can be combined to express internal
energy and thermodynamic potentials, which are useful for determining conditions for equilibrium
and spontaneous 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 in science and engineering, such as
engines, phase transitions, chemical reactions, transport phenomena, and even black holes. The
results of thermodynamics are essential for other fields of physics and for chemistry, chemical
engineering, corrosion engineering, aerospace engineering, mechanical engineering, cell biology,
biomedical engineering, materials science, and economics, to name a few.[7][8]

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

The thermodynamicists of the original eight founding schools of

thermodynamics. The schools with the most-lasting influence on the
modern versions of thermodynamics are the Berlin school,
particularly Rudolf Clausius's 1865 textbook The Mechanical Theory
of Heat, the Vienna school, with the statistical mechanics of Ludwig
Boltzmann, and the Gibbsian school at Yale University of Willard
Gibbs' 1876 and his book On the Equilibrium of Heterogeneous
Substances which launched chemical thermodynamics.[9]

The history of thermodynamics as a scientific discipline generally begins with Otto von Guericke
who, in 1650, built and designed the world's first vacuum pump and demonstrated a vacuum using
his Magdeburg hemispheres. Guericke was driven to make a vacuum in order to disprove Aristotle's
long-held supposition that 'nature abhors a vacuum'. Shortly after Guericke, the Anglo-Irish physicist
and chemist Robert Boyle had learned of Guericke's designs and, in 1656, in coordination with
English scientist Robert Hooke, built an air pump.[10] Using this pump, Boyle and Hooke noticed a
correlation between pressure, temperature, and volume. In time, Boyle's Law was formulated, which
states that pressure and volume are inversely proportional. Then, in 1679, based on these
concepts, an associate of Boyle's named Denis Papin built a steam 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 a piston and a
cylinder engine. He did not, however, follow through with his design. Nevertheless, in 1697, based
on Papin's designs, engineer Thomas Savery built the first engine, followed by Thomas 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 of heat capacity and latent heat, which were necessary for the
development of thermodynamics, were developed by Professor Joseph Black at the University of
Glasgow, where James Watt was employed as an instrument maker. Black and Watt performed
experiments together, but it was Watt who conceived the idea of the external condenser which
resulted in a large increase in steam engine efficiency.[11] Drawing on all the previous work led Sadi
Carnot, the "father of thermodynamics", to publish Reflections on the Motive Power of Fire (1824), a
discourse on heat, power, energy and engine efficiency. The book outlined the basic energetic
relations between the Carnot engine, the Carnot cycle, and motive power. It marked the start of
thermodynamics as a modern science.[12]

The first thermodynamic textbook was written in 1859 by William Rankine, originally trained as a
physicist and a civil and mechanical engineering professor at the University of Glasgow.[13] The first
and second laws of thermodynamics emerged simultaneously in the 1850s, primarily out of the
works of William Rankine, Rudolf Clausius, and William Thomson (Lord Kelvin). The foundations of
statistical thermodynamics were set out by physicists such as James Clerk Maxwell, Ludwig
Boltzmann, Max Planck, Rudolf Clausius and J. Willard Gibbs.

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 of entropy in 1865.

During the years 1873–76 the American mathematical physicist Josiah Willard Gibbs published a
series of three papers, the most famous being On the Equilibrium of Heterogeneous Substances,[15]
in which he showed how thermodynamic processes, including chemical reactions, could be
graphically analyzed, by studying the energy, entropy, volume, temperature and pressure of the
thermodynamic system in such a manner, one can determine if a process would occur
spontaneously.[16] Also Pierre Duhem in the 19th century wrote about chemical thermodynamics.[17]
During the early 20th century, chemists such as Gilbert N. Lewis, Merle Randall,[18] and E. A.
Guggenheim[19][20] applied the mathematical methods of Gibbs to the analysis of chemical
processes.

Etymology

Thermodynamics has an intricate etymology.[21]

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 as thermometer) can be traced back to the root θέρμη
therme, meaning "heat". Secondly, the word dynamics ("science of force [or power]")[22] can be
traced back to the root δύναμις dynamis, meaning "power".[23][24]

In 1849, the adjective thermo-dynamic is used by William Thomson.[25][26]

In 1854, the noun thermo-dynamics is used by Thomson and William Rankine to represent the
science of generalized heat engines.[26][21]

Pierre Perrot claims that the term thermodynamics was coined by James Joule in 1858 to designate
the science of relations between heat and power,[12] however, Joule never used that term, but used
instead the term perfect thermo-dynamic engine in reference to Thomson's 1849[25] phraseology.[21]

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 the laws of thermodynamics. The qualifier classical 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
of statistical 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, and quantum theory at the microscopic level.

Chemical thermodynamics

Chemical thermodynamics is the study of the interrelation of energy with chemical reactions or with
a physical change of state within the confines of the laws of thermodynamics. The primary objective
of chemical thermodynamics is determining the spontaneity of a given transformation.[27]

Equilibrium thermodynamics

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

Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are
not in thermodynamic 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.
Laws of thermodynamics

Annotated color version of the original 1824 Carnot

heat engine showing the hot body (boiler), working
body (system, steam), and cold body (water), the
letters labeled according to the stopping points in
Carnot 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

The zeroth 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 an equivalence relation on the set of
thermodynamic 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 same temperature, 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 the zeroth law.

First law

Opening a bottle of sparkling

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]

The first law of thermodynamics states: In a process without transfer of matter, the change in
internal energy, , of a thermodynamic system is equal to the energy gained as heat, , less the
thermodynamic work, , done by the system on its surroundings.[33][nb 1]

where denotes the change in the internal energy of a closed system (for which heat or work
through the system boundary are possible, but matter transfer is not possible), denotes the
quantity of energy supplied to the system as heat, and denotes the amount of thermodynamic
work done by the system on its surroundings. An equivalent statement is that perpetual 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

where U0 denotes the internal energy of the combined system, and U1 and U2 denote the internal
energies of the respective separated systems.

Adapted for thermodynamics, this law is an expression of the principle of conservation 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 the thermodynamic 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 a function 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 the second 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 other intensive 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, its entropy, 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 general irreversibility 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.

Third law

The third 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
reaching absolute 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 (degrees Rankine).

System models

A diagram of a generic
thermodynamic system

An important concept in thermodynamics is the thermodynamic system, which is a precisely defined

region of the universe under study. Everything in the universe except the system is called the
surroundings. A system is separated from the remainder of the universe by a boundary which may
be a physical or notional, but serve to confine the system to a finite volume. Segments of the
boundary are often described as walls; they have respective defined 'permeabilities'. Transfers of
energy as work, or as heat, or of matter, 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 a steam engine, such as Sadi Carnot defined in 1824. The
system could also be just one nuclide (i.e. a system of quarks) as hypothesized in quantum
thermodynamics. When a looser viewpoint is adopted, and the requirement of thermodynamic
equilibrium is dropped, the system can be the body of a tropical cyclone, such as Kerry Emanuel
theorized in 1986 in the field of atmospheric thermodynamics, or the event horizon of a black 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

Closed

Thermally isolated

Mechanically isolated

Isolated

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 a state of thermodynamic 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 be reversible processes.
States and processes

When a system is at equilibrium under a given set of conditions, it is said to be in a definite

thermodynamic state. The state of the system can be described by a number of state quantities that
do not depend on the process by which the system arrived at its state. They are called intensive
variables or extensive variables according to how they change when the size of the system
changes. The properties of the system can be described by an equation 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.

A thermodynamic 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 by process 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 a conjugate pair.

Several commonly studied thermodynamic processes are:

Adiabatic process: occurs without loss or gain of energy by heat

Isenthalpic process: occurs at a constant enthalpy

Isentropic process: a reversible adiabatic process, occurs at a constant entropy

Isobaric process: occurs at constant pressure

Isochoric process: occurs at constant volume (also called isometric/isovolumetric)

Isothermal process: occurs at a constant temperature

Steady state process: occurs without a change in the internal energy

Instrumentation

There are two types of thermodynamic instruments, the meter and the reservoir. A thermodynamic
meter is any device which measures any parameter of a thermodynamic system. In some cases, the
thermodynamic parameter is actually defined in terms of an idealized measuring instrument. For
example, the zeroth 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 by James Maxwell in 1872,
asserts that it is possible to measure temperature. An idealized thermometer is a sample of an ideal
gas at constant pressure. From the ideal gas law pV=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 a barometer may also be constructed
from a sample of an ideal gas held at a constant temperature. A calorimeter 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.

Conjugate variables

The central concept of thermodynamics is that of energy, the ability to do work. By the First 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. In mechanics, 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 some thermodynamic 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 (the mechanical parameters);

Temperature-entropy (thermal parameters);

Chemical potential-particle number (material parameters).

Potentials

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]

The five most well known potentials are:

Name Symbol Formula Natural variables

Internal energy

Helmholtz free energy

Enthalpy

Gibbs free energy

Landau potential, or
,
grand potential

where is the temperature, the entropy, the pressure, the volume, the chemical potential,
the number of particles in the system, and 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 through Legendre
transformation.

Axiomatic thermodynamics

Axiomatic thermodynamics is a mathematical discipline that aims to describe thermodynamics in

terms of rigorous axioms, for example by finding a mathematically rigorous way to express the
familiar laws of thermodynamics.

The first attempt at an axiomatic theory of thermodynamics was Constantin Carathéodory's 1909
work Investigations on the Foundations of Thermodynamics, which made use of Pfaffian systems
and the concept of adiabatic accessibility, a notion that was introduced by Carathéodory
himself.[37][38] In this formulation, thermodynamic concepts such as heat, entropy, and temperature
are derived from quantities that are more directly measurable.[39] Theories that came after, differed
in the sense that they made assumptions regarding thermodynamic processes with 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

Physics portal
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

Notes

1. The sign convention (Q is heat supplied to the system as, W is work done by the system) is
that of Rudolf Clausius. The opposite sign convention is customary in chemical
thermodynamics.

References

1. 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).
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2. William Thomson, LL.D. D.C.L., F.R.S. (1882). Mathematical and Physical Papers (https://book
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11. The Newcomen engine was improved from 1711 until Watt's work, making the efficiency
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12. Perrot, Pierre (1998). A to Z of Thermodynamics. Oxford University Press. ISBN 978-0-19-
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15. Gibbs, Willard, J. (1874–1878). Transactions of the Connecticut Academy of Arts and Sciences
(https://archive.org/details/transactions03conn) . Vol. III. New Haven. pp. 108 (https://archive.
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Further reading

Goldstein, Martin & Inge F. (1993). The Refrigerator and the Universe (https://archive.org/details/r
efrigeratoruniv0000gold) . Harvard University Press. ISBN 978-0-674-75325-9. OCLC 32826343
(https://search.worldcat.org/oclc/32826343) . 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" (https://www.ncbi.
nlm.nih.gov/pmc/articles/PMC4651616) . Journal of Research of the National Institute of
Standards and Technology. 113 (4): 209–220. doi:10.6028/jres.113.016 (https://doi.org/10.6028%
2Fjres.113.016) . ISSN 1044-677X (https://search.worldcat.org/issn/1044-677X) .
PMC 4651616 (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4651616) . PMID 27096122 (http
s://pubmed.ncbi.nlm.nih.gov/27096122) .

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.

Bazarov I.P. (2010). Thermodynamics: Textbook. St. Petersburg: Lan publishing house. p. 384.
ISBN 978-5-8114-1003-3. 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. ISBN 978-0-471-75798-6. PMID 16878778 (https://pubmed.n
 cbi.nlm.nih.gov/16878778) . {{cite book}}: |journal= ignored (help)

Dill Ken A., Bromberg Sarina (2011). Molecular Driving Forces: Statistical Thermodynamics in
Biology, Chemistry, Physics, and Nanoscience. Garland Science. ISBN 978-0-8153-4430-8.

M. Scott Shell (2015). Thermodynamics and Statistical Mechanics: An Integrated Approach.

Cambridge University Press. ISBN 978-1107656789.

Douglas E. Barrick (2018). Biomolecular Thermodynamics: From Theory to Applications. CRC

Press. ISBN 978-1-4398-0019-5.

The following titles are more technical:

Bejan, Adrian (2016). Advanced Engineering Thermodynamics (4 ed.). Wiley. ISBN 978-1-119-
05209-8.

Cengel, Yunus A., & Boles, Michael A. (2002). Thermodynamics – an Engineering Approach (http
s://archive.org/details/thermodynamicsen00ceng_0) . McGraw Hill. ISBN 978-0-07-238332-4.
OCLC 45791449 (https://search.worldcat.org/oclc/45791449) .

Dunning-Davies, Jeremy (1997). Concise Thermodynamics: Principles and Applications. Horwood

Publishing. ISBN 978-1-8985-6315-0. OCLC 36025958 (https://search.worldcat.org/oclc/3602595
8) .

Kroemer, Herbert & Kittel, Charles (1980). Thermal Physics. W.H. Freeman Company. ISBN 978-
0-7167-1088-2. OCLC 32932988 (https://search.worldcat.org/oclc/32932988) .

External links

Media related to Thermodynamics at Wikimedia Commons

Callendar, Hugh Longbourne (1911). "Thermodynamics" (https://en.wikisource.org/wiki/1911_Enc
yclop%C3%A6dia_Britannica/Thermodynamics) . Encyclopædia Britannica. Vol. 26 (11th ed.).
pp. 808–814.

Thermodynamics Data & Property Calculation Websites (http://tigger.uic.edu/~mansoori/Thermod

ynamic.Data.and.Property_html)

Thermodynamics Educational Websites (http://tigger.uic.edu/~mansoori/Thermodynamics.Educati

onal.Sites_html)

Biochemistry Thermodynamics (http://www.wiley.com/legacy/college/boyer/0470003790/reviews/t

hermo/thermo_intro.htm)

Thermodynamics and Statistical Mechanics (http://farside.ph.utexas.edu/teaching/sm1/lectures/le

ctures.html)
Engineering Thermodynamics – A Graphical Approach (https://web.archive.org/web/20090430200
028/http://www.ent.ohiou.edu/~thermo/)

Thermodynamics and Statistical Mechanics (http://farside.ph.utexas.edu/teaching/sm1/statmech.p

df) by Richard Fitzpatrick