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Thermodynamics is a branch of
physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical science is that depar ...
that deals with
heat In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is al ...
, work, and
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measurement, measured with a thermometer. Thermometers are calibrated in various Conversion of units of temperature, temp ...
, and their relation to
energy In physics, energy (from Ancient Greek: wikt:ἐνέργεια#Ancient_Greek, ἐνέργεια, ''enérgeia'', “activity”) is the physical quantity, quantitative physical property, property that is #Energy transfer, transferred to a phy ...
,
entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...
, and the physical properties of
matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic partic ...
and
radiation In physics, radiation is the emission or transmission of energy in the form of waves or particles through space or through a material medium. This includes: * ''electromagnetic radiation'', such as radio waves, microwaves, infrared, visib ...
. The behavior of these quantities is governed by the four
laws of thermodynamics The laws of thermodynamics are a set of scientific laws which define a group of physical quantities, such as temperature, energy, and entropy, that characterize thermodynamic systems in thermodynamic equilibrium. The laws also use various paramet ...
which convey a quantitative description using measurable macroscopic
physical quantities A physical quantity is a physical property of a material or system that can be quantified by measurement. A physical quantity can be expressed as a ''value'', which is the algebraic multiplication of a ' Numerical value ' and a ' Unit '. For examp ...
, but may be explained in terms of
microscopic The microscopic scale () is the scale of objects and events smaller than those that can easily be seen by the naked eye, requiring a lens (optics), lens or microscope to see them clearly. In physics, the microscopic scale is sometimes regarded a ...
constituents by
statistical mechanics In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical scien ...
. Thermodynamics applies to a wide variety of topics in
science Science is a systematic endeavor that Scientific method, builds and organizes knowledge in the form of Testability, testable explanations and predictions about the universe. Science may be as old as the human species, and some of the earli ...
and
engineering Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range of more specializ ...
, especially
physical chemistry Physical chemistry is the study of macroscopic scale, macroscopic and Microscopic scale, microscopic phenomena in chemistry, chemical systems in terms of the principles, practices, and concepts of physics such as Motion (physics), motion, energy ...
,
biochemistry Biochemistry or biological chemistry is the study of chemical processes within and relating to living organisms. A sub-discipline of both chemistry and biology, biochemistry may be divided into three fields: structural biology, enzymology a ...
,
chemical engineering Chemical engineering is an engineering field which deals with the study of operation and design of chemical plants as well as methods of improving production. Chemical engineers develop economical commercial processes to convert raw materials int ...
and
mechanical engineering Mechanical engineering is the study of physical Machine, machines that may involve force and movement. It is an engineering branch that combines engineering physics and engineering mathematics, mathematics principles with materials science, to d ...
, but also in other complex fields such as
meteorology Meteorology is a branch of the atmospheric sciences (which include atmospheric chemistry and physics) with a major focus on weather forecasting. The study of meteorology dates back millennia, though significant progress in meteorology did not ...
. Historically, thermodynamics developed out of a desire to increase the
efficiency Efficiency is the often measurable ability to avoid wasting materials, energy, efforts, money, and time in doing something or in producing a desired result. In a more general sense, it is the ability to do things well, successfully, and without ...
of early
steam engine A steam engine is a heat engine that performs mechanical work using steam as its working fluid. The steam engine uses the force produced by steam pressure to push a piston back and forth inside a Cylinder (locomotive), cylinder. This pus ...
s, 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 The Napoleonic Wars (1803–1815) were a series of major global conflicts pitting the First French Empire, French Empire and its allies, led by Napoleon, Napoleon I, against a fluctuating array of Coalition forces of the Napoleonic Wars, Europe ...
. Scots-Irish physicist
Lord Kelvin William Thomson, 1st Baron Kelvin, (26 June 182417 December 1907) was a British mathematician, Mathematical physics, mathematical physicist and engineer born in Belfast. Professor of Natural Philosophy (Glasgow), Professor of Natural Philoso ...
was the first to formulate a concise definition of thermodynamics in 1854 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 Rudolf Julius Emanuel Clausius (; 2 January 1822 – 24 August 1888) was a German physicist and mathematician and is considered one of the central founding fathers of the science of thermodynamics. By his restatement of Nicolas Léonard Sadi Ca ...
restated Carnot's principle known as the
Carnot cycle A Carnot cycle is an ideal thermodynamic cycle proposed by French physicist Nicolas Léonard Sadi Carnot, Sadi Carnot in 1824 and expanded upon by others in the 1830s and 1840s. By Carnot's theorem (thermodynamics), Carnot's theorem, it provides ...
and gave so the
theory of heat The history of thermodynamics is a fundamental strand in the history of physics, the history of chemistry, and the history of science in general. Owing to the relevance of thermodynamics in much of science and technology, its history is finely wov ...
a truer and sounder basis. His most important paper, "On the Moving Force of Heat", Contains English translations of many of his other works. published in 1850, first stated the
second law of thermodynamics The second law of thermodynamics is a physical law based on universal experience concerning heat and Energy transformation, energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects ( ...
. In 1865 he introduced the concept of
entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...
. In 1870 he introduced the
virial theorem In mechanics, the virial theorem provides a general equation that relates the average over time of the total kinetic energy In physics Physics is the natural science that studies matter, its Elementary particle, fundamental consti ...
, which applied to
heat In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is al ...
. The initial application of thermodynamics to
mechanical heat engine In thermodynamics and engineering, a heat engine is a system that converts heat to mechanical energy, which can then be used to do work (physics), mechanical work. It does this by bringing a working substance from a higher state temperature to ...
s was quickly extended to the study of chemical compounds and chemical reactions.
Chemical thermodynamics Chemical thermodynamics is the study of the interrelation of heat and Work (thermodynamics), work with chemical reactions or with physical changes of thermodynamic state, state within the confines of the laws of thermodynamics. Chemical thermodynam ...
studies the nature of the role of
entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...
in the process of
chemical reaction A chemical reaction is a process that leads to the IUPAC nomenclature for organic transformations, chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the pos ...
s 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 Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...
predictions of the collective motion of particles from their microscopic behavior. In 1909, Constantin Carathéodory presented a purely mathematical approach in an
axiomatic An axiom, postulate, or assumption is a statement (logic), statement that is taken to be truth, true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word (), meaning 'that whi ...
formulation, a description often referred to as ''geometrical thermodynamics''.

# Introduction

A description of any thermodynamic system employs the four
laws of thermodynamics The laws of thermodynamics are a set of scientific laws which define a group of physical quantities, such as temperature, energy, and entropy, that characterize thermodynamic systems in thermodynamic equilibrium. The laws also use various paramet ...
that form an axiomatic basis. The first law specifies that energy can be transferred between physical systems as
heat In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is al ...
, as work, and with transfer of matter. The second law defines the existence of a quantity called
entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...
, 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 thermodynamic ''
system A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and expres ...
'' 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 The internal energy of a thermodynamic system is the total energy contained within it. It is the energy necessary to create or prepare the system in its given internal state, and includes the contributions of potential energy and internal kinet ...
and
thermodynamic potential A thermodynamic potential (or more accurately, a thermodynamic potential energy)ISO/IEC 80000-5, Quantities an units, Part 5 - Thermodynamics, item 5-20.4 Helmholtz energy, Helmholtz functionISO/IEC 80000-5, Quantities an units, Part 5 - Thermod ...
s, which are useful for determining conditions for equilibrium and
spontaneous process In thermodynamics, a spontaneous process is a process which occurs without any external input to the system. A more technical definition is the time-evolution of a system in which it releases free energy and it moves to a lower, more thermodynami ...
es. 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 Science is a systematic endeavor that Scientific method, builds and organizes knowledge in the form of Testability, testable explanations and predictions about the universe. Science may be as old as the human species, and some of the earli ...
and
engineering Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range of more specializ ...
, such as
engine An engine or motor is a machine designed to convert one or more forms of energy into mechanical energy. Available energy sources include potential energy (e.g. energy of the Earth's gravitational field as exploited in hydroelectric powe ...
s,
phase transition In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic State of ...
s,
chemical reaction A chemical reaction is a process that leads to the IUPAC nomenclature for organic transformations, chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the pos ...
s,
transport phenomena In engineering, physics, and chemistry, the study of transport phenomena concerns the exchange of mass, energy, charge (physics), charge, momentum and angular momentum between observed and studied Physical system, systems. While it draws from fi ...
, and even
black hole A black hole is a region of spacetime where gravitation, gravity is so strong that nothing, including light or other Electromagnetic radiation, electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts t ...
s. The results of thermodynamics are essential for other fields of
physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical science is that depar ...
and for
chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a natural science that covers the elements that make up matter to the compounds made of atoms, molecules and ions: their composition, structure, properties ...
,
chemical engineering Chemical engineering is an engineering field which deals with the study of operation and design of chemical plants as well as methods of improving production. Chemical engineers develop economical commercial processes to convert raw materials int ...
,
corrosion engineering Corrosion engineering is an engineering specialty that applies scientific, technical, engineering skills, and knowledge of natural laws and physical resources to design and implement materials, structures, devices, systems, and procedures to mana ...
,
aerospace engineering Aerospace engineering is the primary field of engineering concerned with the development of aircraft and spacecraft. It has two major and overlapping branches: Aeronautics, aeronautical engineering and Astronautics, astronautical engineering. A ...
,
mechanical engineering Mechanical engineering is the study of physical Machine, machines that may involve force and movement. It is an engineering branch that combines engineering physics and engineering mathematics, mathematics principles with materials science, to d ...
,
cell biology Cell biology (also cellular biology or cytology) is a branch of biology that studies the Anatomy, structure, Physiology, function, and behavior of cell (biology), cells. All living organisms are made of cells. A cell is the basic unit of life th ...
,
biomedical engineering Biomedical engineering (BME) or medical engineering is the application of engineering principles and design concepts to medicine and biology for healthcare purposes (e.g., diagnostic or therapeutic). BME is also traditionally logical sciences ...
,
materials science Materials science is an interdisciplinary Interdisciplinarity or interdisciplinary studies involves the combination of multiple academic disciplines into one activity (e.g., a research project). It draws knowledge from several other field ...
, and
economics Economics () is the social science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and intera ...
thermodynamic equilibrium Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal State variables, state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable ...
.
Non-equilibrium thermodynamics Non-equilibrium thermodynamics is a branch of thermodynamics that deals with physical systems that are not in thermodynamic equilibrium but can be described in terms of macroscopic quantities (non-equilibrium state variables) that represent an ext ...
is often treated as an extension of the classical treatment, but statistical mechanics has brought many advances to that field.

# History

The history of thermodynamics as a scientific discipline generally begins with
Otto von Guericke Otto von Guericke ( , , ; spelled Gericke until 1666; November 20, 1602 – May 11, 1686 ; November 30, 1602 – May 21, 1686 ) was a German scientist, inventor, and politician. His pioneering scientific work, the development of experimental me ...
who, in 1650, built and designed the world's first
vacuum pump A vacuum pump is a device that draws gas molecules from a sealed volume in order to leave behind a partial vacuum. The job of a vacuum pump is to generate a relative vacuum within a capacity. The first vacuum pump was invented in 1650 by Otto vo ...
and demonstrated a
vacuum A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or "Void (astronomy), void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Ph ...
using his
Magdeburg hemispheres The Magdeburg hemispheres are a pair of large copper hemispheres, with mating rims. They were used to demonstrate the power of atmospheric pressure. When the rims were sealed with grease and the air was pumped out, the sphere contained a vacuum a ...
. Guericke was driven to make a vacuum in order to disprove
Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical Greece, Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatet ...
's long-held supposition that 'nature abhors a vacuum'. Shortly after Guericke, the Anglo-Irish physicist and chemist
Robert Boyle Robert Boyle (; 25 January 1627 – 31 December 1691) was an Anglo-Irish natural philosopher, chemist, physicist, Alchemy, alchemist and inventor. Boyle is largely regarded today as the first modern chemist, and therefore one of the foun ...
had learned of Guericke's designs and, in 1656, in coordination with English scientist
Robert Hooke Robert Hooke Fellow of the Royal Society, FRS (; 18 July 16353 March 1703) was an English polymath active as a scientist, natural philosopher and architect, who is credited to be one of two scientists to discover microorganisms in 1665 using ...
, built an air pump. Using this pump, Boyle and Hooke noticed a correlation between
pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...
,
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measurement, measured with a thermometer. Thermometers are calibrated in various Conversion of units of temperature, temp ...
, and
volume Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). ...
. In time,
Boyle's Law Boyle's law, also referred to as the Boyle–Mariotte law, or Mariotte's law (especially in France), is an experimental gas laws, gas law that describes the relationship between pressure and volume of a confined gas. Boyle's law has been stated ...
was formulated, which states that pressure and volume are
inversely proportional In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a Constant (mathematics), constant ratio, which is called the coefficient of proportionality or p ...
. Then, in 1679, based on these concepts, an associate of Boyle's named
Denis Papin Denis Papin Fellow of the Royal Society, FRS (; 22 August 1647 – 26 August 1713) was a French physicist, mathematician and inventor, best known for his pioneering invention of the steam digester, the forerunner of the pressure cooking, press ...
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 A piston is a component of reciprocating engines, reciprocating pumps, gas compressors, hydraulic cylinders and pneumatic cylinders, among other similar mechanisms. It is the moving component that is contained by a cylinder (engine), cylinder a ...
and a cylinder engine. He did not, however, follow through with his design. Nevertheless, in 1697, based on Papin's designs, engineer
Thomas Savery Thomas Savery (; c. 1650 – 15 May 1715) was an English inventor and engineer. He invented the first commercially used Steam engine, steam-powered device, a Pump#Steam pumps, steam pump which is often referred to as the "Savery engine". Savery ...
built the first engine, followed by
Thomas Newcomen Thomas Newcomen (; February 1664 – 5 August 1729) was an English inventor who created the Newcomen atmospheric engine, atmospheric engine, the first practical fuel-burning engine in 1712. He was an ironmonger by trade and a Baptist l ...
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 Heat capacity or thermal capacity is a physical quantity, physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The International System of Units, SI unit of heat ca ...
and
latent heat Latent heat (also known as latent energy or heat of transformation) is energy released or absorbed, by a body or a thermodynamic system, during a constant-temperature process — usually a Phase transition#Modern classifications, first-order phase ...
, which were necessary for the development of thermodynamics, were developed by Professor
Joseph Black Joseph Black (16 April 1728 – 6 December 1799) was a Scottish physicist and chemist, known for his discoveries of magnesium, latent heat, specific heat, and carbon dioxide. He was Professor of Anatomy and Chemistry at the University of Glas ...
at the University of Glasgow, where
James Watt James Watt (; 30 January 1736 (19 January 1736 Old Style and New Style dates, OS) – 25 August 1819) was a Scottish people, Scottish invention, inventor, mechanical engineer, and chemist who improved on Thomas Newcomen's 1712 Newcomen steam ...
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 A steam engine is a heat engine that performs mechanical work using steam as its working fluid. The steam engine uses the force produced by steam pressure to push a piston back and forth inside a Cylinder (locomotive), cylinder. This pus ...
efficiency. Drawing on all the previous work led Sadi Carnot, the "father of thermodynamics", to publish ''
Reflections on the Motive Power of Fire ''Reflections on the Motive Power of Fire and on Machines Fitted to Develop that Power'' is a book published in 1824 by French people, French physicist Nicolas Léonard Sadi Carnot, Sadi Carnot.full text of 1897 ed. ( s:Reflections on the Motive ...
'' (1824), a discourse on heat, power, energy and engine efficiency. The book outlined the basic energetic relations between the Carnot engine, the
Carnot cycle A Carnot cycle is an ideal thermodynamic cycle proposed by French physicist Nicolas Léonard Sadi Carnot, Sadi Carnot in 1824 and expanded upon by others in the 1830s and 1840s. By Carnot's theorem (thermodynamics), Carnot's theorem, it provides ...
, and motive power. It marked the start of thermodynamics as a modern science. The first thermodynamic textbook was written in 1859 by
William Rankine William John Macquorn Rankine (; 5 July 1820 – 24 December 1872) was a Scottish mechanical engineer who also contributed to civil engineering, physics and mathematics. He was a founding contributor, with Rudolf Clausius and William Thomson, 1 ...
, originally trained as a physicist and a civil and mechanical engineering professor at the
University of Glasgow The University of Glasgow (abbreviated as ''Glas.'' in Post-nominal letters, post-nominals; ) is a Public university, public research university in Glasgow, Scotland. Founded by papal bull in , it is the List of oldest universities in continuous ope ...
. The first and second laws of thermodynamics emerged simultaneously in the 1850s, primarily out of the works of
William Rankine William John Macquorn Rankine (; 5 July 1820 – 24 December 1872) was a Scottish mechanical engineer who also contributed to civil engineering, physics and mathematics. He was a founding contributor, with Rudolf Clausius and William Thomson, 1 ...
,
Rudolf Clausius Rudolf Julius Emanuel Clausius (; 2 January 1822 – 24 August 1888) was a German physicist and mathematician and is considered one of the central founding fathers of the science of thermodynamics. By his restatement of Nicolas Léonard Sadi Ca ...
, and William Thomson (Lord Kelvin). The foundations of statistical thermodynamics were set out by physicists such as
James Clerk Maxwell James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish mathematician and scientist responsible for the classical theory of electromagnetic radiation, which was the first theory to describe electricity, magnetism and light ...
,
Ludwig Boltzmann Ludwig Eduard Boltzmann (; 20 February 1844 – 5 September 1906) was an Austrian physicist and philosopher. His greatest achievements were the development of statistical mechanics, and the statistical explanation of the second law of thermodyn ...
,
Max Planck Max Karl Ernst Ludwig Planck (, ; 23 April 1858 – 4 October 1947) was a Germans, German theoretical physicist whose discovery of quantum mechanics, energy quanta won him the Nobel Prize in Physics in 1918. Planck made many substantial con ...
,
Rudolf Clausius Rudolf Julius Emanuel Clausius (; 2 January 1822 – 24 August 1888) was a German physicist and mathematician and is considered one of the central founding fathers of the science of thermodynamics. By his restatement of Nicolas Léonard Sadi Ca ...
and J. 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 of
entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...
in 1865. During the years 1873–76 the American mathematical physicist
Josiah Willard Gibbs Josiah Willard Gibbs (; February 11, 1839 – April 28, 1903) was an American scientist who made significant theoretical contributions to physics, chemistry, and mathematics. His work on the applications of thermodynamics was instrumental in t ...
published a series of three papers, the most famous being '' On the Equilibrium of Heterogeneous Substances'', in which he showed how thermodynamic processes, including
chemical reaction A chemical reaction is a process that leads to the IUPAC nomenclature for organic transformations, chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the pos ...
s, could be graphically analyzed, by studying the
energy In physics, energy (from Ancient Greek: wikt:ἐνέργεια#Ancient_Greek, ἐνέργεια, ''enérgeia'', “activity”) is the physical quantity, quantitative physical property, property that is #Energy transfer, transferred to a phy ...
,
entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...
,
volume Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). ...
,
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measurement, measured with a thermometer. Thermometers are calibrated in various Conversion of units of temperature, temp ...
and
pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...
of the
thermodynamic system A thermodynamic system is a body of matter and/or radiation, confined in space by walls, with defined permeabilities, which separate it from its surroundings. The surroundings may include other thermodynamic systems, or physical systems that are ...
in such a manner, one can determine if a process would occur spontaneously. Also
Pierre Duhem Pierre Maurice Marie Duhem (; 9 June 1861 – 14 September 1916) was a French theoretical physicist who worked on thermodynamics, hydrodynamics, and the theory of Elasticity (physics), elasticity. Duhem was also a history of science, historian ...
in the 19th century wrote about chemical thermodynamics.Duhem, P.M.M. (1886). ''Le Potential Thermodynamique et ses Applications'', Hermann, Paris. During the early 20th century, chemists such as Gilbert N. Lewis, Merle Randall, and E. A. GuggenheimGuggenheim, E.A. (1933). ''Modern Thermodynamics by the Methods of J.W. Gibbs'', Methuen, London.Guggenheim, E.A. (1949/1967). ''Thermodynamics. An Advanced Treatment for Chemists and Physicists'', 1st edition 1949, 5th edition 1967, North-Holland, Amsterdam. applied the mathematical methods of Gibbs to the analysis of chemical processes.

# Etymology

The etymology of ''thermodynamics'' has an intricate history. It was first spelled in a hyphenated form as an adjective (''thermo-dynamic'') and from 1854 to 1868 as the noun ''thermo-dynamics'' to represent the science of generalized heat engines. American
biophysicist Biophysics is an interdisciplinary science that applies approaches and methods traditionally used in physics to study Biology, biological phenomena. Biophysics covers all scales of biological organization, from Molecule, molecular to organismic ...
Donald Haynie claims that ''thermodynamics'' was coined in 1840 from the
Greek Greek may refer to: Greece Anything of, from, or related to Greece, a country in Southern Europe: *Greeks, an ethnic group. *Greek language, a branch of the Indo-European language family. **Proto-Greek language, the assumed last common ancestor ...
root θέρμη ''therme,'' meaning “heat”, and δύναμις ''dynamis,'' meaning “power”. Pierre Perrot claims that the term ''thermodynamics'' was coined by James Joule in 1858 to designate the science of relations between heat and power, however, Joule never used that term, but used instead the term ''perfect thermo-dynamic engine'' in reference to Thomson's 1849 phraseology. By 1858, ''thermo-dynamics'', as a functional term, was used in William Thomson's paper "An Account of Carnot's Theory of the Motive Power of Heat."Kelvin, 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 Copy

# 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 laws of thermodynamics are a set of scientific laws which define a group of physical quantities, such as temperature, energy, and entropy, that characterize thermodynamic systems in thermodynamic equilibrium. The laws also use various paramet ...
. 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 In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical scien ...
, 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 Chemical thermodynamics is the study of the interrelation of heat and Work (thermodynamics), work with chemical reactions or with physical changes of thermodynamic state, state within the confines of the laws of thermodynamics. Chemical thermodynam ...
is the study of the interrelation of
energy In physics, energy (from Ancient Greek: wikt:ἐνέργεια#Ancient_Greek, ἐνέργεια, ''enérgeia'', “activity”) is the physical quantity, quantitative physical property, property that is #Energy transfer, transferred to a phy ...
with
chemical reactions A chemical reaction is a process that leads to the chemical transformation of one set of chemical substance A chemical substance is a form of matter having constant chemical composition and characteristic properties. Some references add th ...
or with a physical change of
state State may refer to: Arts, entertainment, and media Literature * ''State Magazine'', a monthly magazine published by the U.S. Department of State * The State (newspaper), ''The State'' (newspaper), a daily newspaper in Columbia, South Carolina, U ...
within the confines of the
laws of thermodynamics The laws of thermodynamics are a set of scientific laws which define a group of physical quantities, such as temperature, energy, and entropy, that characterize thermodynamic systems in thermodynamic equilibrium. The laws also use various paramet ...
. The primary objective of chemical thermodynamics is determining the spontaneity of a given transformation.

## 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 Non-equilibrium thermodynamics is a branch of thermodynamics that deals with physical systems that are not in thermodynamic equilibrium but can be described in terms of macroscopic quantities (non-equilibrium state variables) that represent an ext ...
is a branch of thermodynamics that deals with systems that are not in
thermodynamic equilibrium Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal State variables, state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable ...
. 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

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 The zeroth law of thermodynamics is one of the four principal laws of thermodynamics. It provides an independent definition of temperature without reference to entropy, which is defined in the second law. The law was established by Ralph H. Fowle ...
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 In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented i ...
on the set of
thermodynamic system A thermodynamic system is a body of matter and/or radiation, confined in space by walls, with defined permeabilities, which separate it from its surroundings. The surroundings may include other thermodynamic systems, or physical systems that are ...
s under consideration. Systems are said to be in equilibrium if the small, random exchanges between them (e.g.
Brownian motion Brownian motion, or pedesis (from grc, πήδησις "leaping"), is the random motion of particles suspended in a medium (a liquid or a gas). This pattern of motion typically consists of Randomness, random fluctuations in a particle's po ...
) 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 Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measurement, measured with a thermometer. Thermometers are calibrated in various Conversion of units of temperature, temp ...
, 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 the ''zeroth law''.

## First law

The
first law of thermodynamics The first law of thermodynamics is a formulation of the law of conservation of energy, adapted for thermodynamic processes. It distinguishes in principle two forms of energy transfer, heat and Work (thermodynamics), thermodynamic work for a syst ...
states: ''In a process without transfer of matter, the change in
internal energy The internal energy of a thermodynamic system is the total energy contained within it. It is the energy necessary to create or prepare the system in its given internal state, and includes the contributions of potential energy and internal kinet ...
,'' $\Delta U$'', of a
thermodynamic system A thermodynamic system is a body of matter and/or radiation, confined in space by walls, with defined permeabilities, which separate it from its surroundings. The surroundings may include other thermodynamic systems, or physical systems that are ...
is equal to the energy gained as heat,'' $Q$'', less the thermodynamic work,'' $W$'', done by the system on its surroundings.''The sign convention (Q is heat supplied ''to'' the system as, W is work done ''by'' the system) is that of
Rudolf Clausius Rudolf Julius Emanuel Clausius (; 2 January 1822 – 24 August 1888) was a German physicist and mathematician and is considered one of the central founding fathers of the science of thermodynamics. By his restatement of Nicolas Léonard Sadi Ca ...
. The opposite sign convention is customary in chemical thermodynamics.
:$\Delta U = Q - W$. where $\Delta U$ denotes the change in the internal energy of a
closed system A closed system is a natural physical system that does not allow transfer of matter in or out of the system, although — in contexts such as physics, chemistry or engineering — the transfer of energy (''e.g.'' as work or heat) is allowed. In ...
(for which heat or work through the system boundary are possible, but matter transfer is not possible), $Q$ denotes the quantity of energy supplied ''to'' the system as heat, and $W$ 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 $W$ 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'' :$U_0 = U_1 + U_2$, ''where'' ''denotes the internal energy of the combined system, and'' ''and'' ''denote the internal energies of the respective separated systems.'' Adapted for thermodynamics, this law is an expression of the principle of
conservation of energy In physics and chemistry, the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be Conservation law, ''conserved'' over time. This law, first proposed and tested by Émilie du Chât ...
, 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 the
thermodynamic state In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these qua ...
, 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

second law of thermodynamics The second law of thermodynamics is a physical law based on universal experience concerning heat and Energy transformation, energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects ( ...
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 Physical properties of materials and systems can often be categorized as being either intensive or extensive, according to how the property changes when the size (or extent) of the system changes. According to International Union of Pure and Appl ...
, 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 Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...
, 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
irreversibility In science, a process that is not reversible is called irreversible. This concept arises frequently in thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relat ...
of such approach to 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 The third law of thermodynamics states, regarding the properties of closed systems in thermodynamic equilibrium: This constant value cannot depend on any other parameters characterizing the closed system, such as pressure or applied magnetic fiel ...
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 Absolute zero is the lowest limit of the thermodynamic temperature scale, a state at which the enthalpy and entropy of a cooled ideal gas reach their minimum value, taken as zero kelvin. The fundamental particles of nature have minimum vibration ...
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. 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 (degrees Rankine).

# System models

An important concept in thermodynamics is the
thermodynamic system A thermodynamic system is a body of matter and/or radiation, confined in space by walls, with defined permeabilities, which separate it from its surroundings. The surroundings may include other thermodynamic systems, or physical systems that are ...
, 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 In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is al ...
, or of
matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic partic ...
, 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 Max Karl Ernst Ludwig Planck (, ; 23 April 1858 – 4 October 1947) was a Germans, German theoretical physicist whose discovery of quantum mechanics, energy quanta won him the Nobel Prize in Physics in 1918. Planck made many substantial con ...
defined in 1900; it can be a body of steam or air in a
steam engine A steam engine is a heat engine that performs mechanical work using steam as its working fluid. The steam engine uses the force produced by steam pressure to push a piston back and forth inside a Cylinder (locomotive), cylinder. This pus ...
, such as Sadi Carnot defined in 1824. The system could also be just one
nuclide A nuclide (or nucleide, from atomic nucleus, nucleus, also known as nuclear species) is a class of atoms characterized by their number of protons, ''Z'', their number of neutrons, ''N'', and their nuclear energy state. The word ''nuclide'' was co ...
(i.e. a system of
quark A quark () is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nucleus, atomic nuclei ...
s) as hypothesized in
quantum thermodynamics Quantum thermodynamics is the study of the relations between two independent physical theories: thermodynamics and quantum mechanics. The two independent theories address the physical phenomena of light and matter. In 1905, Albert Einstein argued ...
. When a looser viewpoint is adopted, and the requirement of thermodynamic equilibrium is dropped, the system can be the body of a
tropical cyclone A tropical cyclone is a rapidly rotating storm, storm system characterized by a Low-pressure area, low-pressure center, a closed low-level atmospheric circulation, Beaufort scale, strong winds, and a spiral arrangement of thunderstorms tha ...
, such as Kerry Emanuel theorized in 1986 in the field of
atmospheric thermodynamics Atmospheric thermodynamics is the study of heat-to-Work (physics), work transformations (and their reverse) that take place in the earth's atmosphere and manifest as weather or climate. Atmospheric thermodynamics use the laws of classical thermodyn ...
, or the
event horizon In astrophysics, an event horizon is a boundary beyond which events cannot affect an observer. Wolfgang Rindler coined the term in the 1950s. In 1784, John Michell proposed that gravity can be strong enough in the vicinity of massive compact obj ...
of a
black hole A black hole is a region of spacetime where gravitation, gravity is so strong that nothing, including light or other Electromagnetic radiation, electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts t ...
. 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 a
state State may refer to: Arts, entertainment, and media Literature * ''State Magazine'', a monthly magazine published by the U.S. Department of State * The State (newspaper), ''The State'' (newspaper), a daily newspaper in Columbia, South Carolina, U ...
of
thermodynamic equilibrium Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal State variables, state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable ...
. 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 In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these qua ...
. 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 In physics, chemistry, and thermodynamics, an equation of state is a thermodynamic equations, thermodynamic equation relating state variables, which describe the state of matter under a given set of physical conditions, such as pressure, Volume ( ...
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 Classical thermodynamics considers three main kinds of thermodynamic process: (1) changes in a system, (2) cycles in a system, and (3) flow processes. (1)A Thermodynamic process is a process in which the thermodynamic state of a system is change ...
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 In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these qu ...
: occurs without loss or gain of energy by
heat In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is al ...
*
Isenthalpic process An isenthalpic process or isoenthalpic process is a process that proceeds without any change in enthalpy, ''H''; or Enthalpy#Specific enthalpy, specific enthalpy, ''h''. Overview If a steady-state, steady-flow process is analysed using a control ...
: occurs at a constant
enthalpy Enthalpy , a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It is a state function used in many measurements in chemical, biological, and physical systems at a constant p ...
*
Isentropic process In thermodynamics, an isentropic process is an idealized thermodynamic process that is both Adiabatic process, adiabatic and Reversible process (thermodynamics), reversible. The work (physics), work transfers of the system are frictionless, and th ...
: a reversible adiabatic process, occurs at a constant
entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...
*
Isobaric process In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these qu ...
: occurs at constant
pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...
*
Isochoric process In thermodynamics, an isochoric process, also called a constant-volume process, an isovolumetric process, or an isometric process, is a thermodynamic process during which the volume (thermodynamics), volume of the closed system undergoing such a ...
: occurs at constant
volume Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). ...
(also called isometric/isovolumetric) *
Isothermal process In thermodynamics, an isothermal process is a type of thermodynamic process in which the temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measurement, mea ...
: occurs at a constant
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measurement, measured with a thermometer. Thermometers are calibrated in various Conversion of units of temperature, temp ...
* Steady state process: occurs without a change in the
internal energy The internal energy of a thermodynamic system is the total energy contained within it. It is the energy necessary to create or prepare the system in its given internal state, and includes the contributions of potential energy and internal kinet ...

# 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 A thermodynamic system is a body of matter and/or radiation, confined in space by walls, with defined permeabilities, which separate it from its surroundings. The surroundings may include other thermodynamic systems, or physical systems that are ...
. 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 A thermometer is a device that temperature measurement, measures temperature or a temperature gradient (the degree of hotness or coldness of an object). A thermometer has two important elements: (1) a temperature sensor (e.g. the bulb of a merc ...
is a sample of an ideal gas at constant pressure. From the
ideal gas law The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions, although it has several limitations. It was first s ...
''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 A barometer is a scientific instrument that is used to measure air pressure in a certain environment. Pressure tendency can forecast short term changes in the weather. Many measurements of air pressure are used within surface weather analysis ...
may also be constructed from a sample of an ideal gas held at a constant temperature. A
calorimeter A calorimeter is an object used for calorimetry, or the process of measuring the heat of chemical reactions or physical changes as well as heat capacity. Differential scanning calorimeters, isothermal micro calorimeters, titration 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 In physics, energy (from Ancient Greek: wikt:ἐνέργεια#Ancient_Greek, ἐνέργεια, ''enérgeia'', “activity”) is the physical quantity, quantitative physical property, property that is #Energy transfer, transferred to a phy ...
, 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 Mechanics (from Ancient Greek: wikt:μηχανική#Ancient_Greek, μηχανική, ''mēkhanikḗ'', "of machine, machines") is the area of mathematics and physics concerned with the relationships between force, matter, and motion among Ph ...
, for example, energy transfer equals the product of the force applied to a body and the resulting displacement.
Conjugate variables Conjugate variables are pairs of variables mathematically defined in such a way that they become Fourier transform dual (mathematics), duals, or more generally are related through Pontryagin duality. The duality relations lead naturally to an unc ...
are pairs of thermodynamic concepts, with the first being akin to a "force" applied to some
thermodynamic system A thermodynamic system is a body of matter and/or radiation, confined in space by walls, with defined permeabilities, which separate it from its surroundings. The surroundings may include other thermodynamic systems, or physical systems that are ...
, 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 Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...
-
volume Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). ...
(the mechanical parameters); *
Temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measurement, measured with a thermometer. Thermometers are calibrated in various Conversion of units of temperature, temp ...
-
entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...
(thermal parameters); *
Chemical potential In thermodynamics, the chemical potential of a Chemical specie, species is the energy that can be absorbed or released due to a change of the particle number of the given species, e.g. in a chemical reaction or phase transition. The chemical potent ...
-
particle number The particle number (or number of particles) of a thermodynamic system, conventionally indicated with the letter ''N'', is the number of constituent particles in that system. The particle number is a fundamental parameter in thermodynamics which is ...
(material parameters).

# Potentials

Thermodynamic potential A thermodynamic potential (or more accurately, a thermodynamic potential energy)ISO/IEC 80000-5, Quantities an units, Part 5 - Thermodynamics, item 5-20.4 Helmholtz energy, Helmholtz functionISO/IEC 80000-5, Quantities an units, Part 5 - Thermod ...
s 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. The five most well known potentials are: where $T$ is the
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measurement, measured with a thermometer. Thermometers are calibrated in various Conversion of units of temperature, temp ...
, $S$ the
entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...
, $p$ the
pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...
, $V$ the
volume Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). ...
, $\mu$ the
chemical potential In thermodynamics, the chemical potential of a Chemical specie, species is the energy that can be absorbed or released due to a change of the particle number of the given species, e.g. in a chemical reaction or phase transition. The chemical potent ...
, $N$ 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 through
Legendre transformation In mathematics, the Legendre transformation (or Legendre transform), named after Adrien-Marie Legendre, is an involution (mathematics), involutive List of transforms, transformation on real number, real-valued convex functions of one real variable ...
.

# Axiomatic thermodynamics

Axiomatic thermodynamics is a mathematical discipline that aims to describe thermodynamics in terms of rigorous
axiom An axiom, postulate, or assumption is a statement (logic), statement that is taken to be truth, true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word (), meaning 'that whi ...
s, for example by finding a mathematically rigorous way to express the familiar
laws of thermodynamics The laws of thermodynamics are a set of scientific laws which define a group of physical quantities, such as temperature, energy, and entropy, that characterize thermodynamic systems in thermodynamic equilibrium. The laws also use various paramet ...
. 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. In this formulation, thermodynamic concepts such as
heat In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is al ...
,
entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...
, and
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measurement, measured with a thermometer. Thermometers are calibrated in various Conversion of units of temperature, temp ...
are derived from quantities that are more directly measurable. Theories that came after, differed in the sense that they made assumptions regarding
thermodynamic process Classical thermodynamics considers three main kinds of thermodynamic process: (1) changes in a system, (2) cycles in a system, and (3) flow processes. (1)A Thermodynamic process is a process in which the thermodynamic state of a system is change ...
es with arbitrary initial and final states, as opposed to considering only neighboring states.

# Applied fields

* 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 In thermodynamics, a physical property is any property that is measurable, and whose value describes a state of a physical system. Thermodynamic properties are defined as characteristic features of a system, capable of specifying the system's stat ...
* Table of thermodynamic equations * Timeline of thermodynamics * Thermodynamic equations

# References

* A nontechnical introduction, good on historical and interpretive matters. * * Vol. 1, pp. 55–349. * * * * 5th ed. (in Russian) * * * * * * The following titles are more technical: * * * *

* *
Thermodynamics Data & Property Calculation Websites

Thermodynamics Educational Websites

Engineering Thermodynamics – A Graphical Approach

Thermodynamics and Statistical Mechanics
by Richard Fitzpatrick {{Authority control Energy Chemical engineering