# Thermodynamics

Last updated

Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, radiation, and physical properties of matter. 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 a wide variety of topics in science and engineering, especially physical chemistry, biochemistry, chemical engineering and mechanical engineering, but also in other complex fields such as meteorology.

## Contents

Historically, thermodynamics developed out of a desire to increase the efficiency of early steam engines, particularly through the work of French physicist Nicolas Léonard 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."

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. [3] [4] [5] [6] [7] [8] [9] [10] [11] 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. [12] 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. [13]

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. [14] [15]

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 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. [17] 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. [18] 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. [10]

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. [19] 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.

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 , [3] 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. [20] Also Pierre Duhem in the 19th century wrote about chemical thermodynamics. [4] During the early 20th century, chemists such as Gilbert N. Lewis, Merle Randall, [5] and E. A. Guggenheim [6] [7] applied the mathematical methods of Gibbs to the analysis of chemical processes.

## Etymology

The etymology of thermodynamics has an intricate history. [21] 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. [21]

American biophysicist Donald Haynie claims that thermodynamics was coined in 1840 from the Greek root θέρμη therme, meaning “heat”, and δύναμις dynamis, meaning “power”. [22]

Pierre Perrot claims that the term thermodynamics was coined by James Joule in 1858 to designate the science of relations between heat and power, [10] however, Joule never used that term, but used instead the term perfect thermo-dynamic engine in reference to Thomson's 1849 [23] phraseology. [21]

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." [23]

## 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.

### 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 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. 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 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. [24] 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 states: In a process without transfer of matter, the change in internal energy,${\displaystyle \Delta U}$, of a thermodynamic system is equal to the energy gained as heat,${\displaystyle Q}$, less the thermodynamic work,${\displaystyle W}$, done by the system on its surroundings. [25] [nb 1]

${\displaystyle \Delta U=Q-W}$.

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

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

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

Adapted for thermodynamics, this law is an expression of the principle of conservation of energy, which states that energy can be transformed (changed from one form to another), but cannot be created or destroyed. [26]

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.

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 irreversibility 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 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. 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, 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 N
Thermally isolated NN
Mechanically isolated NN
Isolated NNN

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:

## 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:

## 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.

The five most well known potentials are:

NameSymbolFormulaNatural variables
Internal energy ${\displaystyle U}$${\displaystyle \int \left(T\,dS-p\,dV+\sum _{i}\mu _{i}dN_{i}\right)}$${\displaystyle S,V,\{N_{i}\}}$
Helmholtz free energy ${\displaystyle F}$${\displaystyle U-TS}$${\displaystyle T,V,\{N_{i}\}}$
Enthalpy ${\displaystyle H}$${\displaystyle U+pV}$${\displaystyle S,p,\{N_{i}\}}$
Gibbs free energy ${\displaystyle G}$${\displaystyle U+pV-TS}$${\displaystyle T,p,\{N_{i}\}}$
Landau potential, or
grand potential
${\displaystyle \Omega }$, ${\displaystyle \Phi _{\text{G}}}$${\displaystyle U-TS-}$${\displaystyle \sum _{i}\,}$${\displaystyle \mu _{i}N_{i}}$${\displaystyle T,V,\{\mu _{i}\}}$

where ${\displaystyle T}$ is the temperature, ${\displaystyle S}$ the entropy, ${\displaystyle p}$ the pressure, ${\displaystyle V}$ the volume, ${\displaystyle \mu }$ the chemical potential, ${\displaystyle N}$ the number of particles in the system, and ${\displaystyle i}$ 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.

## 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.

## Related Research Articles

Chemical thermodynamics is the study of the interrelation of heat and work with chemical reactions or with physical changes of state within the confines of the laws of thermodynamics. Chemical thermodynamics involves not only laboratory measurements of various thermodynamic properties, but also the application of mathematical methods to the study of chemical questions and the spontaneity of processes.

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 thermodynamics, where it was first recognized, to the microscopic description of nature in statistical physics, and to the principles of information theory. It has found far-ranging applications in chemistry and physics, in biological systems and their relation to life, in cosmology, economics, sociology, weather science, climate change, and information systems including the transmission of information in telecommunication.

The thermodynamic free energy is a concept useful in the thermodynamics of chemical or thermal processes in engineering and science. The change in the free energy is the maximum amount of work that a thermodynamic system can perform in a process at constant temperature, and its sign indicates whether a process is thermodynamically favorable or forbidden. Since free energy usually contains potential energy, it is not absolute but depends on the choice of a zero point. Therefore, only relative free energy values, or changes in free energy, are physically meaningful.

The second law of thermodynamics establishes the concept of entropy as a physical property of a thermodynamic system. Entropy predicts the direction of spontaneous processes, and determines whether they are irreversible or impossible, despite obeying the requirement of conservation of energy, which is established in the first law of thermodynamics. The second law may be formulated by the observation that the entropy of isolated systems left to spontaneous evolution cannot decrease, as they always arrive at a state of thermodynamic equilibrium, where the entropy is highest. If all processes in the system are reversible, the entropy is constant. An increase in entropy accounts for the irreversibility of natural processes, often referred to in the concept of the arrow of time.

In thermodynamics, the Gibbs free energy is a thermodynamic potential that can be used to calculate the maximum reversible work that may be performed by a thermodynamic system at a constant temperature and pressure. The Gibbs free energy (, measured in joules in SI) is the maximum amount of non-expansion work that can be extracted from a thermodynamically closed system. This maximum can be attained only in a completely reversible process. When a system transforms reversibly from an initial state to a final state, the decrease in Gibbs free energy equals the work done by the system to its surroundings, minus the work of the pressure forces.

Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermodynamic equilibrium there are no net macroscopic flows of matter or of energy, either within a system or between systems.

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 not thermodynamic systems. A wall of a thermodynamic system may be purely notional, when it is described as being 'permeable' to all matter, all radiation, and all forces. A thermodynamic system can be fully described by a definite set of thermodynamic state variables, which always covers both intensive and extensive properties.

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 variables that represent an extrapolation of the variables used to specify the system in thermodynamic equilibrium. Non-equilibrium thermodynamics is concerned with transport processes and with the rates of chemical reactions. It relies on what may be thought of as more or less nearness to thermodynamic equilibrium.

The laws of thermodynamics define a group of physical quantities, such as temperature, energy, and entropy, that characterize thermodynamic systems in thermodynamic equilibrium. The laws also use various parameters for thermodynamic processes, such as thermodynamic work and heat, and establish relationships between them. They state empirical facts that form a basis of precluding the possibility of certain phenomena, such as perpetual motion. In addition to their use in thermodynamics, they are important fundamental laws of physics in general, and are applicable in other natural sciences.

In thermodynamics, the exergy of a system is the maximum useful work possible during a process that brings the system into equilibrium with a heat reservoir, reaching maximum entropy. When the surroundings are the reservoir, exergy is the potential of a system to cause a change as it achieves equilibrium with its environment. Exergy is the energy that is available to be used. After the system and surroundings reach equilibrium, the exergy is zero. Determining exergy was also the first goal of thermodynamics. The term "exergy" was coined in 1956 by Zoran Rant (1904–1972) by using the Greek ex and ergon meaning "from work", but the concept had been earlier developed by J Willard Gibbs in 1873.

Thermodynamics is expressed by a mathematical framework of thermodynamic equations which relate various thermodynamic quantities and physical properties measured in a laboratory or production process. Thermodynamics is based on a fundamental set of postulates, that became the laws of thermodynamics.

Equilibrium Thermodynamics is the systematic study of transformations of matter and energy in systems in terms of a concept called thermodynamic equilibrium. The word equilibrium implies a state of balance. Equilibrium thermodynamics, in origins, derives from analysis of the Carnot cycle. Here, typically a system, as cylinder of gas, initially in its own state of internal thermodynamic equilibrium, is set out of balance via heat input from a combustion reaction. Then, through a series of steps, as the system settles into its final equilibrium state, work is extracted.

The mathematical expressions for thermodynamic entropy in the statistical thermodynamics formulation established by Ludwig Boltzmann and J. Willard Gibbs in the 1870s are similar to the information entropy by Claude Shannon and Ralph Hartley, developed in the 1940s.

In thermodynamics, work performed by a system is energy transferred by the system to its surroundings, by a mechanism through which the system can spontaneously exert macroscopic forces on its surroundings. In the surroundings, through suitable passive linkages, the work can lift a weight, for example. Energy can also transfer from the surroundings to the system; in a sign convention used in physics, such work has a negative magnitude.

The concept of entropy developed in response to the observation that a certain amount of functional energy released from combustion reactions is always lost to dissipation or friction and is thus not transformed into useful work. Early heat-powered engines such as Thomas Savery's (1698), the Newcomen engine (1712) and the Cugnot steam tricycle (1769) were inefficient, converting less than two percent of the input energy into useful work output; a great deal of useful energy was dissipated or lost. Over the next two centuries, physicists investigated this puzzle of lost energy; the result was the concept of entropy.

In classical thermodynamics, entropy is a property of a thermodynamic system that expresses the direction or outcome of spontaneous changes in the system. The term was introduced by Rudolf Clausius in the mid-nineteenth century from the Greek word τρoπή (transformation) to explain the relationship of the internal energy that is available or unavailable for transformations in form of heat and work. Entropy predicts that certain processes are irreversible or impossible, despite not violating the conservation of energy. The definition of entropy is central to the establishment of the second law of thermodynamics, which states that the entropy of isolated systems cannot decrease with time, as they always tend to arrive at a state of thermodynamic equilibrium, where the entropy is highest. Entropy is therefore also considered to be a measure of disorder in the system.

The concept entropy was first developed by German physicist Rudolf Clausius in the mid-nineteenth century as a thermodynamic property that predicts that certain spontaneous processes are irreversible or impossible. In statistical mechanics, entropy is formulated as a statistical property using probability theory. The statistical entropy perspective was introduced in 1870 by Austrian physicist Ludwig Boltzmann, who established a new field of physics that provided the descriptive linkage between the macroscopic observation of nature and the microscopic view based on the rigorous treatment of a large ensembles of microstates that constitute thermodynamic systems.

In thermodynamics, entropy is a numerical quantity that shows that many physical processes can go in only one direction in time. For example, you can pour cream into coffee and mix it, but you cannot "unmix" it; you can burn a piece of wood, but you can't "unburn" it. The word 'entropy' has entered popular usage to refer a lack of order or predictability, or of a gradual decline into disorder. A more physical interpretation of thermodynamic entropy refers to spread of energy or matter, or to extent and diversity of microscopic motion.

In thermodynamics, heat is energy in transfer to or from a thermodynamic system, by mechanisms other than thermodynamic work or transfer of matter. The various mechanisms of energy transfer that define heat are stated in the next section of this article.

Temperature is a physical quantity that expresses hot and cold. It is the manifestation of thermal energy, present in all matter, which is the source of the occurrence of heat, a flow of energy, when a body is in contact with another that is colder or hotter.

## 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). ISBN   978-0-486-59065-3.
2. William Thomson, LL.D. D.C.L., F.R.S. (1882). Mathematical and Physical Papers. 1. London, Cambridge: C.J. Clay, M.A. & Son, Cambridge University Press. p. 232. Archived from the original on 18 April 2021. Retrieved 2 November 2020.CS1 maint: multiple names: authors list (link)
3. Gibbs, Willard, J. (1874–1878). Transactions of the Connecticut Academy of Arts and Sciences. III. New Haven. pp.  108–248, 343–524.CS1 maint: multiple names: authors list (link)
4. Duhem, P.M.M. (1886). Le Potential Thermodynamique et ses Applications, Hermann, Paris.
5. Lewis, Gilbert N.; Randall, Merle (1923). Thermodynamics and the Free Energy of Chemical Substances. McGraw-Hill Book Co. Inc.
6. Guggenheim, E.A. (1933). Modern Thermodynamics by the Methods of J.W. Gibbs, Methuen, London.
7. Guggenheim, E.A. (1949/1967). Thermodynamics. An Advanced Treatment for Chemists and Physicists, 1st edition 1949, 5th edition 1967, North-Holland, Amsterdam.
8. Ilya Prigogine, I. & Defay, R., translated by D.H. Everett (1954). Chemical Thermodynamics. Longmans, Green & Co., London. Includes classical non-equilibrium thermodynamics.CS1 maint: multiple names: authors list (link)
9. Enrico Fermi (1956). Thermodynamics. Courier Dover Publications. p. ix. ISBN   978-0486603612. OCLC   230763036. Archived from the original on 18 April 2021. Retrieved 2 November 2020.
10. Perrot, Pierre (1998). A to Z of Thermodynamics. Oxford University Press. ISBN   978-0-19-856552-9. OCLC   123283342.
11. Clark, John, O.E. (2004). The Essential Dictionary of Science. Barnes & Noble Books. ISBN   978-0-7607-4616-5. OCLC   58732844.CS1 maint: multiple names: authors list (link)
12. Van Ness, H.C. (1983) [1969]. . Dover Publications, Inc. ISBN   9780486632773. OCLC   8846081.
13. Dugdale, J.S. (1998). Entropy and its Physical Meaning. Taylor and Francis. ISBN   978-0-7484-0569-5. OCLC   36457809.
14. Smith, J.M.; Van Ness, H.C.; Abbott, M.M. (2005). Introduction to Chemical Engineering Thermodynamics (7th ed.). p. 584. Bibcode:1950JChEd..27..584S. ISBN   978-0-07-310445-4. OCLC   56491111.
15. Haynie, Donald, T. (2001). Biological Thermodynamics. Cambridge University Press. ISBN   978-0-521-79549-4. OCLC   43993556.CS1 maint: multiple names: authors list (link)
16. Schools of thermodynamics Archived 7 December 2017 at the Wayback Machine – EoHT.info.
17. Partington, J.R. (1989). . Dover. OCLC   19353301.
18. The Newcomen engine was improved from 1711 until Watt's work, making the efficiency comparison subject to qualification, but the increase from the 1865 version was on the order of 100%.
19. Cengel, Yunus A.; Boles, Michael A. (2005). Thermodynamics – an Engineering Approach. McGraw-Hill. ISBN   978-0-07-310768-4.
20. Gibbs, Willard (1993). The Scientific Papers of J. Willard Gibbs, Volume One: Thermodynamics. Ox Bow Press. ISBN   978-0-918024-77-0. OCLC   27974820.
21. "Thermodynamics (etymology)". EoHT.info. Archived from the original on 25 May 2010. Retrieved 24 July 2010.
22. Donald T. Haynie (2008). (2 ed.). Cambridge University Press. p.  26.
23. 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 Archived 24 July 2017 at the Wayback Machine
24. Moran, Michael J. and Howard N. Shapiro, 2008. Fundamentals of Engineering Thermodynamics. 6th ed. Wiley and Sons: 16.
25. Bailyn, M. (1994). A Survey of Thermodynamics, American Institute of Physics, AIP Press, Woodbury NY, ISBN   0883187973, p. 79.
26. Callen, H.B. (1960/1985).Thermodynamics and an Introduction to Thermostatistics, second edition, John Wiley & Sons, Hoboken NY, ISBN   9780471862567, pp. 11–13.
• Goldstein, Martin & Inge F. (1993). . Harvard University Press. ISBN   978-0-674-75325-9. 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". Journal of Research of the National Institute of Standards and Technology. 113 (4): 209–220. doi:10.6028/jres.113.016. ISSN   1044-677X. PMC  . PMID   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.CS1 maint: multiple names: authors list (link)
• 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. Methods of Biochemical Analysis. 48. John Wiley & Sons, Inc. pp. 1–458. ISBN   978-0-471-75798-6. PMID   16878778.
• 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: