TheInfoList

OR:

In
thermodynamics Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of the ...
, heat is defined as the form of
energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat ...
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 also often used to refer to the
thermal energy The term "thermal energy" is used loosely in various contexts in physics and engineering. It can refer to several different well-defined physical concepts. These include the internal energy or enthalpy of a body of matter and radiation; heat, d ...
contained in a system as a component of its internal energy and that is reflected in the temperature of the system. For both uses of the term, heat is a form of energy. An example of formal vs. informal usage may be obtained from the right-hand photo, in which the metal bar is "conducting heat" from its hot end to its cold end, but if the metal bar is considered a thermodynamic system, then the energy flowing within the metal bar is called internal energy, not heat. The hot metal bar is also transferring heat to its surroundings, a correct statement for both the strict and loose meanings of ''heat''. Another example of informal usage is the term '' heat content'', used despite the fact that physics defines heat as energy transfer. More accurately, it is ''thermal energy'' that is ''contained'' in the system or body, as it is stored in the microscopic degrees of freedom of the modes of vibration. Heat is
energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat ...
in transfer to or from a thermodynamic system, by a mechanism that involves the microscopic atomic modes of motion or the corresponding macroscopic properties. This descriptive characterization excludes the transfers of energy by
thermodynamic work In thermodynamics, work is one of the principal processes by which a thermodynamic system can interact with its surroundings and exchange energy. An exchange of energy is facilitated by a mechanism through which the system can spontaneously exer ...
or mass transfer. Defined quantitatively, the heat involved in a process is the difference in internal energy between the final and initial states of a system, and subtracting the work done in the process. This is the formulation of 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 thermodynamic work for a system of a constant amoun ...
. The measurement of energy transferred as heat is called
calorimetry In chemistry and thermodynamics, calorimetry () is the science or act of measuring changes in '' state variables'' of a body for the purpose of deriving the heat transfer associated with changes of its state due, for example, to chemical rea ...
, performed by measuring its effect on the states of interacting bodies. For example, heat can be measured by the amount of ice melted, or by change in temperature of a body in the surroundings of the system. In the
International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...
(SI) the unit of measurement for heat, as a form of energy, is the
joule The joule ( , ; symbol: J) is the unit of energy in the International System of Units (SI). It is equal to the amount of work done when a force of 1 newton displaces a mass through a distance of 1 metre in the direction of the force applied ...
(J).

# Notation and units

As a form of energy, heat has the unit
joule The joule ( , ; symbol: J) is the unit of energy in the International System of Units (SI). It is equal to the amount of work done when a force of 1 newton displaces a mass through a distance of 1 metre in the direction of the force applied ...
(J) in the
International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...
(SI). In addition, many applied branches of engineering use other, traditional units, such as the British thermal unit (BTU) and the
calorie The calorie is a unit of energy. For historical reasons, two main definitions of "calorie" are in wide use. The large calorie, food calorie, or kilogram calorie was originally defined as the amount of heat needed to raise the temperature of o ...
. The standard unit for the rate of heating is the
watt The watt (symbol: W) is the unit of power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m2⋅s−3. It is used to quantify the rate of energy transfer. The watt is named after James Wat ...
(W), defined as one joule per second. The symbol for heat was introduced by
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 Sadi Carnot's principle ...
and Macquorn Rankine in c. 1859. Heat released by a system into its surroundings is by convention a negative quantity (); when a system absorbs heat from its surroundings, it is positive (). Heat transfer rate, or heat flow per unit time, is denoted by $\dot$, but it is not a time derivative of a function of state (which can also be written with the dot notation) since heat is not a function of state.Baierlein, R. (1999), p. 21. Heat flux is defined as rate of heat transfer per unit cross-sectional area (watts per square metre).

# Classical thermodynamics

## Heat and entropy

In 1856,
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 Sadi Carnot's principle ...
, referring to closed systems, in which transfers of matter do not occur, defined the ''second fundamental theorem'' (the
second law of thermodynamics The second law of thermodynamics is a physical law based on universal experience concerning heat and energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects (or "downhill"), unless ...
) in the mechanical
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 ...
(
thermodynamics Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of the ...
): "if two transformations which, without necessitating any other permanent change, can mutually replace one another, be called equivalent, then the generations of the quantity of heat ''Q'' from
work Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical work done by humans ** House work, housework, or homemaking ** Working animal, an animal ...
at the temperature ''T'', has the ''equivalence-value'':" :$\frac .$ In 1865, he came to define 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 thermodyna ...
symbolized by ''S'', such that, due to the supply of the amount of heat ''Q'' at temperature ''T'' the entropy of the system is increased by In a transfer of energy as heat without work being done, there are changes of entropy in both the surroundings which lose heat and the system which gains it. The increase, , of entropy in the system may be considered to consist of two parts, an increment, that matches, or 'compensates', the change, , of entropy in the surroundings, and a further increment, that may be considered to be 'generated' or 'produced' in the system, and is said therefore to be 'uncompensated'. Thus :$\Delta S = \Delta S\text{'} +\Delta S\text{'}\text{'} .$ This may also be written :$\Delta S_ = \Delta S_+\Delta S_\,\,\,\,\text\,\,\,\,\Delta S_=-\Delta S_.$ The total change of entropy in the system and surroundings is thus :$\Delta S_ = \Delta S^\prime+\Delta S^-\Delta S^\prime=\Delta S^ .$ This may also be written :$\Delta S_ = \Delta S_+\Delta S_+\Delta S_=\Delta S_ .$ It is then said that an amount of entropy has been transferred from the surroundings to the system. Because entropy is not a conserved quantity, this is an exception to the general way of speaking, in which an amount transferred is of a conserved quantity. From the second law of thermodynamics it follows that in a spontaneous transfer of heat, in which the temperature of the system is different from that of the surroundings: :$\Delta S_ > 0 .$ For purposes of mathematical analysis of transfers, one thinks of fictive processes that are called ''reversible'', with the temperature of the system being hardly less than that of the surroundings, and the transfer taking place at an imperceptibly slow rate. Following the definition above in formula (), for such a fictive reversible process, a quantity of transferred heat (an inexact differential) is analyzed as a quantity , with (an exact differential): :$T\,\mathrmS=\delta Q .$ This equality is only valid for a fictive transfer in which there is no production of entropy, that is to say, in which there is no uncompensated entropy. If, in contrast, the process is natural, and can really occur, with irreversibility, then there is entropy production, with . The quantity was termed by Clausius the "uncompensated heat", though that does not accord with present-day terminology. Then one has :$T_\,\mathrmS=\delta Q+T\,\mathrmS_ > \delta Q .$ This leads to the statement :$T_\,\mathrmS \geq \delta Q \quad \text\,.$ which is the
second law of thermodynamics The second law of thermodynamics is a physical law based on universal experience concerning heat and energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects (or "downhill"), unless ...
for closed systems. In non-equilibrium thermodynamics that makes the approximation of assuming the hypothesis of local thermodynamic equilibrium, there is a special notation for this. The transfer of energy as heat is assumed to take place across an infinitesimal temperature difference, so that the system element and its surroundings have near enough the same temperature . Then one writes :$\mathrmS = \mathrmS_ + \mathrmS_\,,$ where by definition :$\delta Q = T\,\mathrmS_\,\,\,\,\,\text\,\,\,\,\,\mathrmS_\equiv\mathrmS_.$ The second law for a natural process asserts that :$\mathrm d S_ > 0 .$

## Heat and enthalpy

For a closed system (a system from which no matter can enter or exit), one version of 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 thermodynamic work for a system of a constant amoun ...
states that the change in internal energy of the system is equal to the amount of heat supplied to the system minus the amount of
thermodynamic work In thermodynamics, work is one of the principal processes by which a thermodynamic system can interact with its surroundings and exchange energy. An exchange of energy is facilitated by a mechanism through which the system can spontaneously exer ...
done by system on its surroundings. The foregoing sign convention for work is used in the present article, but an alternate sign convention, followed by IUPAC, for work, is to consider the work performed on the system by its surroundings as positive. This is the convention adopted by many modern textbooks of physical chemistry, such as those by Peter Atkins and Ira Levine, but many textbooks on physics define work as work done by the system. :$\Delta U = Q - W \, .$ This formula can be re-written so as to express a definition of quantity of energy transferred as heat, based purely on the concept of adiabatic work, if it is supposed that is defined and measured solely by processes of adiabatic work: :$Q = \Delta U + W.$ The thermodynamic work done by the system is through mechanisms defined by its thermodynamic state variables, for example, its volume , not through variables that necessarily involve mechanisms in the surroundings. The latter are such as shaft work, and include isochoric work. The internal energy, , is a
state function In the thermodynamics of equilibrium, a state function, function of state, or point function for a thermodynamic system is a mathematical function relating several state variables or state quantities (that describe equilibrium states of a sys ...
. In cyclical processes, such as the operation of a heat engine, state functions of the working substance return to their initial values upon completion of a cycle. The differential, or infinitesimal increment, for the internal energy in an infinitesimal process is an exact differential . The symbol for exact differentials is the lowercase letter . In contrast, neither of the infinitesimal increments nor in an infinitesimal process represents the change in a state function of the system. Thus, infinitesimal increments of heat and work are inexact differentials. The lowercase Greek letter delta, , is the symbol for inexact differentials. The integral of any inexact differential in a process where the system leaves and then returns to the same thermodynamic state does not necessarily equal zero. As recounted above, in the section headed ''heat and entropy'', the second law of thermodynamics observes that if heat is supplied to a system in a reversible process, the increment of heat and the temperature form the exact differential :$\mathrmS =\frac,$ and that , the entropy of the working body, is a state function. Likewise, with a well-defined pressure, , behind a slowly moving (quasistatic) boundary, the work differential, , and the pressure, , combine to form the exact differential :$\mathrmV =\frac,$ with the volume of the system, which is a state variable. In general, for systems of uniform pressure and temperature without composition change, :$\mathrmU = T\mathrmS - P\mathrmV.$ Associated with this differential equation is the concept that the internal energy may be considered to be a function of its natural variables and . The internal energy representation of the fundamental thermodynamic relation is written asAdkins, C.J. (1983), p. 101. :$U=U\left(S,V\right).$ If is constant :$T\mathrmS=\mathrmU\,\,\,\,\,\,\,\,\,\,\,\,\left(V\,\, \text$ and if is constant :$T\mathrmS=\mathrmH\,\,\,\,\,\,\,\,\,\,\,\,\left(P\,\, \text$ with the enthalpy defined by :$H=U+PV.$ The enthalpy may be considered to be a function of its natural variables and . The enthalpy representation of the fundamental thermodynamic relation is written Callen, H.B. (1985), p. 147. :$H=H\left(S,P\right).$ The internal energy representation and the enthalpy representation are partial Legendre transforms of one another. They contain the same physical information, written in different ways. Like the internal energy, the enthalpy stated as a function of its natural variables is a thermodynamic potential and contains all thermodynamic information about a body. If a quantity of heat is added to a body while it does only expansion work on its surroundings, one has :$\Delta H=\Delta U + \Delta\left(PV\right)\,.$ If this is constrained to happen at constant pressure, i.e. with , the expansion work done by the body is given by ; recalling the first law of thermodynamics, one has :$\Delta U=Q - W=Q - P\, \Delta V \text\Delta \left(PV\right) = P\, \Delta V \,.$ Consequently, by substitution one has :$\begin \Delta H &= Q - P\, \Delta V + P\, \Delta V \\ &=Q\qquad\qquad\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \text \end$ In this scenario, the increase in enthalpy is equal to the quantity of heat added to the system. This is the basis of the determination of enthalpy changes in chemical reactions by calorimetry. Since many processes do take place at constant atmospheric pressure, the enthalpy is sometimes given the misleading name of 'heat content' or heat function, while it actually depends strongly on the energies of covalent bonds and intermolecular forces. In terms of the natural variables of the state function , this process of change of state from state 1 to state 2 can be expressed as :$\begin \Delta H &= \int_^ \left\left(\frac\right\right)_P \mathrm dS +\int_^ \left\left(\frac\right\right)_S \mathrm dP \\ &=\int_^ \left\left(\frac\right\right)_P \mathrm dS\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \text \end$ It is known that the temperature is identically stated by :$\left\left(\frac\right\right)_P \equiv T\left(S,P\right)\,.$ Consequently, :$\Delta H=\int_^ T\left(S,P\right) \mathrm dS\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \text$ In this case, the integral specifies a quantity of heat transferred at constant pressure.

# History

As a common noun, English ''heat'' or ''warmth'' (just as French ''chaleur'', German ''Wärme'', Latin ''calor'', Greek θάλπος, etc.) refers to (the human perception of) either
thermal energy The term "thermal energy" is used loosely in various contexts in physics and engineering. It can refer to several different well-defined physical concepts. These include the internal energy or enthalpy of a body of matter and radiation; heat, d ...
or temperature. Speculation on thermal energy or "heat" as a separate form of matter has a long history, identified as
caloric theory The caloric theory is an obsolete scientific theory that heat consists of a self-repellent fluid called caloric that flows from hotter bodies to colder bodies. Caloric was also thought of as a weightless gas that could pass in and out of pores ...
,
phlogiston The phlogiston theory is a superseded scientific theory that postulated the existence of a fire-like element called phlogiston () contained within combustible bodies and released during combustion. The name comes from the Ancient Greek (''burn ...
theory, and fire. The modern understanding of thermal energy originates with Thompson's 1798 mechanical theory of heat ('' An Experimental Enquiry Concerning the Source of the Heat which is Excited by Friction''), postulating a mechanical equivalent of heat. A collaboration between Nicolas Clément and Sadi Carnot ('' Reflections on the Motive Power of Fire'') in the 1820s had some related thinking along similar lines. In 1845, Joule published a paper entitled ''The Mechanical Equivalent of Heat'', in which he specified a numerical value for the amount of mechanical work required to "produce a unit of heat". The theory of classical thermodynamics matured in the 1850s to 1860s.
John Tyndall John Tyndall FRS (; 2 August 1820 – 4 December 1893) was a prominent 19th-century Irish physicist. His scientific fame arose in the 1850s from his study of diamagnetism. Later he made discoveries in the realms of infrared radiation and the ...
's ''Heat Considered as Mode of Motion'' (1863) was instrumental in popularizing the idea of heat as motion to the English-speaking public. The theory was developed in academic publications in French, English and German. From an early time, the French technical term ''chaleur'' used by Carnot was taken as equivalent to the English ''heat'' and German ''Wärme'' (lit. "warmth", while the equivalent of ''heat'' would be German ''Hitze''). The process function was introduced by
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 Sadi Carnot's principle ...
in 1850. Clausius described it with the German compound ''Wärmemenge'', translated as "amount of heat". '' Die Wärmemenge, welche dem Gase mitgetheilt werden muss, während es aus irgend einem früheren Zustande auf einem bestimmten Wege in den Zustand übergeführt wird, in welchem sein Volumen = ''v'' und seine Temperatur = ''t'' ist, möge ''Q'' heissen'' (R. Clausius
''Ueber die bewegende Kraft der Wärme und die Gesetze, welche sich daraus für die Wärmelehre selbst ableiten lassen''
, communication to the Academy of Berlin, February 1850, published in Pogendorff's Annalen vol. 79, March/April 1850, first translated in Philosophical Magazine vol. 2, July 1851, as "First Memoir" in: ''The Mechanical Theory of Heat, with its Applications to the Steam-Engine and to the Physical Properties of Bodies'', trans. John Tyndall, London, 1867
p. 25
.
James Clerk Maxwell in his 1871 ''Theory of Heat'' outlines four stipulations for the definition of heat: * It is ''something which may be transferred from one body to another'', according to the
second law of thermodynamics The second law of thermodynamics is a physical law based on universal experience concerning heat and energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects (or "downhill"), unless ...
. * It is a ''measurable quantity'', and so can be treated mathematically. * It ''cannot be treated as a material substance'', because it may be transformed into something that is not a material substance, e.g., mechanical work. * Heat is ''one of the forms of energy''. The process function is referred to as ''Wärmemenge'' by Clausius, or as "amount of heat" in translation. Use of "heat" as an abbreviated form of the specific concept of "quantity of energy transferred as heat" led to some terminological confusion by the early 20th century. The generic meaning of "heat", even in classical thermodynamics, is just "thermal energy". Since the 1920s, it has been recommended practice to use enthalpy to refer to the "heat content at constant volume", and to
thermal energy The term "thermal energy" is used loosely in various contexts in physics and engineering. It can refer to several different well-defined physical concepts. These include the internal energy or enthalpy of a body of matter and radiation; heat, d ...
when "heat" in the general sense is intended, while "heat" is reserved for the very specific context of the transfer of thermal energy between two systems. Leonard Benedict Loeb in his ''Kinetic Theory of Gases'' (1927) makes a point of using "quantity of heat" or "heat–quantity" when referring to : :After the perfection of thermometry ..the next great advance made in the field of heat was the definition of a term which is called the quantity of heat. [... after the abandonment of
caloric theory The caloric theory is an obsolete scientific theory that heat consists of a self-repellent fluid called caloric that flows from hotter bodies to colder bodies. Caloric was also thought of as a weightless gas that could pass in and out of pores ...
,] It still remains to interpret this very definite concept, the quantity of heat, in terms of a theory ascribing all heat to the kinetics of gas molecules. Today's narrow definition of ''heat'' in physics contrasts with its use in common language, in some engineering disciplines, and in the historical scientific development of thermodynamics in the caloric theory. The terminology of ''heat'' in these instances may be replaced accurately with ''
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 thermodyna ...
''. Richard Feynman introduced ''heat'' with a physical depiction, as associated with the jiggling motion of atoms and molecules, with faster motion corresponding to increased temperature. To explain physics further, he used the term "heat energy," along with "heat".

## Carathéodory (1909)

primitive notion In mathematics, logic, philosophy, and formal systems, a primitive notion is a concept that is not defined in terms of previously-defined concepts. It is often motivated informally, usually by an appeal to intuition and everyday experience. In an ...

# Heat transfer

## Heat transfer between two bodies

Referring to conduction, Partington writes: "If a hot body is brought in conducting contact with a cold body, the temperature of the hot body falls and that of the cold body rises, and it is said that a ''quantity of heat'' has passed from the hot body to the cold body." Referring to radiation,
Maxwell Maxwell may refer to: People * Maxwell (surname), including a list of people and fictional characters with the name ** James Clerk Maxwell, mathematician and physicist * Justice Maxwell (disambiguation) * Maxwell baronets, in the Baronetage of ...
writes: "In Radiation, the hotter body loses heat, and the colder body receives heat by means of a process occurring in some intervening medium which does not itself thereby become hot." Maxwell writes that convection as such "is not a purely thermal phenomenon". In thermodynamics, convection in general is regarded as transport of internal energy. If, however, the convection is enclosed and circulatory, then it may be regarded as an intermediary that transfers energy as heat between source and destination bodies, because it transfers only energy and not matter from the source to the destination body. Chandrasekhar, S. (1961). In accordance with the first law for closed systems, energy transferred solely as heat leaves one body and enters another, changing the internal energies of each. Transfer, between bodies, of energy as work is a complementary way of changing internal energies. Though it is not logically rigorous from the viewpoint of strict physical concepts, a common form of words that expresses this is to say that heat and work are interconvertible. Cyclically operating engines that use only heat and work transfers have two thermal reservoirs, a hot and a cold one. They may be classified by the range of operating temperatures of the working body, relative to those reservoirs. In a heat engine, the working body is at all times colder than the hot reservoir and hotter than the cold reservoir. In a sense, it uses heat transfer to produce work. In a heat pump, the working body, at stages of the cycle, goes both hotter than the hot reservoir, and colder than the cold reservoir. In a sense, it uses work to produce heat transfer.

## Heat engine

In classical thermodynamics, a commonly considered model is the heat engine. It consists of four bodies: the working body, the hot reservoir, the cold reservoir, and the work reservoir. A cyclic process leaves the working body in an unchanged state, and is envisaged as being repeated indefinitely often. Work transfers between the working body and the work reservoir are envisaged as reversible, and thus only one work reservoir is needed. But two thermal reservoirs are needed, because transfer of energy as heat is irreversible. A single cycle sees energy taken by the working body from the hot reservoir and sent to the two other reservoirs, the work reservoir and the cold reservoir. The hot reservoir always and only supplies energy and the cold reservoir always and only receives energy. The second law of thermodynamics requires that no cycle can occur in which no energy is received by the cold reservoir. Heat engines achieve higher efficiency when the ratio of the initial and final temperature is greater.

## Heat pump or refrigerator

Another commonly considered model is the heat pump or refrigerator. Again there are four bodies: the working body, the hot reservoir, the cold reservoir, and the work reservoir. A single cycle starts with the working body colder than the cold reservoir, and then energy is taken in as heat by the working body from the cold reservoir. Then the work reservoir does work on the working body, adding more to its internal energy, making it hotter than the hot reservoir. The hot working body passes heat to the hot reservoir, but still remains hotter than the cold reservoir. Then, by allowing it to expand without passing heat to another body, the working body is made colder than the cold reservoir. It can now accept heat transfer from the cold reservoir to start another cycle. The device has transported energy from a colder to a hotter reservoir, but this is not regarded as by an inanimate agency; rather, it is regarded as by the harnessing of work . This is because work is supplied from the work reservoir, not just by a simple thermodynamic process, but by a cycle of thermodynamic operations and processes, which may be regarded as directed by an animate or harnessing agency. Accordingly, the cycle is still in accord with the second law of thermodynamics. The 'efficiency' of a heat pump (which exceeds unity) is best when the temperature difference between the hot and cold reservoirs is least. Functionally, such engines are used in two ways, distinguishing a target reservoir and a resource or surrounding reservoir. A heat pump transfers heat to the hot reservoir as the target from the resource or surrounding reservoir. A refrigerator transfers heat, from the cold reservoir as the target, to the resource or surrounding reservoir. The target reservoir may be regarded as leaking: when the target leaks heat to the surroundings, heat pumping is used; when the target leaks coldness to the surroundings, refrigeration is used. The engines harness work to overcome the leaks.

## Macroscopic view

According to
Planck Max Karl Ernst Ludwig Planck (, ; 23 April 1858 – 4 October 1947) was a German theoretical physicist whose discovery of energy quanta won him the Nobel Prize in Physics in 1918. Planck made many substantial contributions to theoretical ...
, there are three main conceptual approaches to heat. One is the microscopic or kinetic theory approach. The other two are macroscopic approaches. One is the approach through the law of conservation of energy taken as prior to thermodynamics, with a mechanical analysis of processes, for example in the work of Helmholtz. This mechanical view is taken in this article as currently customary for thermodynamic theory. The other macroscopic approach is the thermodynamic one, which admits heat as a primitive concept, which contributes, by scientific induction to knowledge of the law of conservation of energy. This view is widely taken as the practical one, quantity of heat being measured by calorimetry. Bailyn also distinguishes the two macroscopic approaches as the mechanical and the thermodynamic. The thermodynamic view was taken by the founders of thermodynamics in the nineteenth century. It regards quantity of energy transferred as heat as a primitive concept coherent with a primitive concept of temperature, measured primarily by calorimetry. A calorimeter is a body in the surroundings of the system, with its own temperature and internal energy; when it is connected to the system by a path for heat transfer, changes in it measure heat transfer. The mechanical view was pioneered by Helmholtz and developed and used in the twentieth century, largely through the influence of
Max Born Max Born (; 11 December 1882 – 5 January 1970) was a German physicist and mathematician who was instrumental in the development of quantum mechanics. He also made contributions to solid-state physics and optics and supervised the work of a n ...

## Microscopic view

In the
kinetic theory Kinetic (Ancient Greek: κίνησις “kinesis”, movement or to move) may refer to: * Kinetic theory, describing a gas as particles in random motion * Kinetic energy, the energy of an object that it possesses due to its motion Art and ente ...
, heat is explained in terms of the microscopic motions and interactions of constituent particles, such as electrons, atoms, and molecules.Kittel, C. Kroemer, H. (1980). The immediate meaning of the kinetic energy of the constituent particles is not as heat. It is as a component of internal energy. In microscopic terms, heat is a transfer quantity, and is described by a transport theory, not as steadily localized kinetic energy of particles. Heat transfer arises from temperature gradients or differences, through the diffuse exchange of microscopic kinetic and potential particle energy, by particle collisions and other interactions. An early and vague expression of this was made by
Francis Bacon Francis Bacon, 1st Viscount St Alban (; 22 January 1561 – 9 April 1626), also known as Lord Verulam, was an English philosopher and statesman who served as Attorney General and Lord Chancellor of England. Bacon led the advancement of both ...
. Precise and detailed versions of it were developed in the nineteenth century. In
statistical mechanics In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic b ...
, for a closed system (no transfer of matter), heat is the energy transfer associated with a disordered, microscopic action on the system, associated with jumps in occupation numbers of the energy levels of the system, without change in the values of the energy levels themselves. It is possible for macroscopic thermodynamic work to alter the occupation numbers without change in the values of the system energy levels themselves, but what distinguishes transfer as heat is that the transfer is entirely due to disordered, microscopic action, including radiative transfer. A mathematical definition can be formulated for small increments of quasi-static adiabatic work in terms of the statistical distribution of an ensemble of microstates.

## Calorimetry

Quantity of heat transferred can be measured by calorimetry, or determined through calculations based on other quantities. Calorimetry is the empirical basis of the idea of quantity of heat transferred in a process. The transferred heat is measured by changes in a body of known properties, for example, temperature rise, change in volume or length, or phase change, such as melting of ice. A calculation of quantity of heat transferred can rely on a hypothetical quantity of energy transferred as adiabatic work and on 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 thermodynamic work for a system of a constant amoun ...
. Such calculation is the primary approach of many theoretical studies of quantity of heat transferred. Carathéodory, C. (1909).Bryan, G.H. (1907), p. 47.

## Engineering

The discipline of
heat transfer Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, ...
, typically considered an aspect of mechanical engineering and chemical engineering, deals with specific applied methods by which thermal energy in a system is generated, or converted, or transferred to another system. Although the definition of heat implicitly means the transfer of energy, the term ''heat transfer'' encompasses this traditional usage in many engineering disciplines and laymen language. ''Heat transfer'' is generally described as including the mechanisms of heat conduction,
heat convection Convection (or convective heat transfer) is the transfer of heat from one place to another due to the movement of fluid. Although often discussed as a distinct method of heat transfer, convective heat transfer involves the combined processes o ...
,
thermal radiation Thermal radiation is electromagnetic radiation generated by the thermal motion of particles in matter. Thermal radiation is generated when heat from the movement of charges in the material (electrons and protons in common forms of matter) is ...
, but may include mass transfer and heat in processes of phase changes. Convection may be described as the combined effects of conduction and fluid flow. From the thermodynamic point of view, heat flows into a fluid by diffusion to increase its energy, the fluid then transfers ( advects) this increased internal energy (not heat) from one location to another, and this is then followed by a second thermal interaction which transfers heat to a second body or system, again by diffusion. This entire process is often regarded as an additional mechanism of heat transfer, although technically, "heat transfer" and thus heating and cooling occurs only on either end of such a conductive flow, but not as a result of flow. Thus, conduction can be said to "transfer" heat only as a net result of the process, but may not do so at every time within the complicated convective process.

# Latent and sensible heat

In an 1847 lecture entitled ''On Matter, Living Force, and Heat'',
James Prescott Joule James Prescott Joule (; 24 December 1818 11 October 1889) was an English physicist, mathematician and brewer, born in Salford, Lancashire. Joule studied the nature of heat, and discovered its relationship to mechanical work (see energy). Th ...
characterized the terms
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 first-order phase transition. Latent heat can be underst ...
and
sensible heat Sensible heat is heat exchanged by a body or thermodynamic system in which the exchange of heat changes the temperature of the body or system, and some macroscopic variables of the body or system, but leaves unchanged certain other macroscopic vari ...
as components of heat each affecting distinct physical phenomena, namely the potential and kinetic energy of particles, respectively."Heat must therefore consist of either living force or of attraction through space. In the former case we can conceive the constituent particles of heated bodies to be, either in whole or in part, in a state of motion. In the latter we may suppose the particles to be removed by the process of heating, so as to exert attraction through greater space. I am inclined to believe that both of these hypotheses will be found to hold good,—that in some instances, particularly in the case of sensible heat, or such as is indicated by the thermometer, heat will be found to consist in the living force of the particles of the bodies in which it is induced; whilst in others, particularly in the case of latent heat, the phenomena are produced by the separation of particle from particle, so as to cause them to attract one another through a greater space." Joule, J.P. (1884). He described latent energy as the energy possessed via a distancing of particles where attraction was over a greater distance, i.e. a form of
potential energy In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors. Common types of potential energy include the gravitational potenti ...
, and the sensible heat as an energy involving the motion of particles, i.e.
kinetic energy In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its accel ...
. Latent heat is the heat released or absorbed by a chemical substance or 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 ...
during a 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), a daily newspaper in Columbia, South Carolina, United States * ''Our S ...
that occurs without a change in temperature. Such a process may be a
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 states ...
, such as the melting of ice or the boiling of water.Perrot, P. (1998).

# Heat capacity

Heat capacity is a
measurable In mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notions, such as mass and probability of events. These seemingly distinct concepts have many simila ...
physical quantity equal to the ratio of the heat added to an object to the resulting temperature change. The ''molar heat capacity'' is the heat capacity per unit amount (SI unit:
mole Mole (or Molé) may refer to: Animals * Mole (animal) or "true mole", mammals in the family Talpidae, found in Eurasia and North America * Golden moles, southern African mammals in the family Chrysochloridae, similar to but unrelated to Talpida ...
) of a pure substance, and the ''specific heat capacity'', often called simply ''specific heat'', is the heat capacity per unit mass of a material. Heat capacity is a physical property of a substance, which means that it depends on the state and properties of the substance under consideration. The specific heats of monatomic gases, such as helium, are nearly constant with temperature. Diatomic gases such as hydrogen display some temperature dependence, and triatomic gases (e.g., carbon dioxide) still more. Before the development of the laws of thermodynamics, heat was measured by changes in the states of the participating bodies. Some general rules, with important exceptions, can be stated as follows. In general, most bodies expand on heating. In this circumstance, heating a body at a constant volume increases the pressure it exerts on its constraining walls, while heating at a constant pressure increases its volume. Beyond this, most substances have three ordinarily recognized
states of matter In physics, a state of matter is one of the distinct forms in which matter can exist. Four states of matter are observable in everyday life: solid, liquid, gas, and plasma. Many intermediate states are known to exist, such as liquid crystal, ...
, solid, liquid, and gas. Some can also exist in a plasma. Many have further, more finely differentiated, states of matter, such as glass and
liquid crystal Liquid crystal (LC) is a state of matter whose properties are between those of conventional liquids and those of solid crystals. For example, a liquid crystal may flow like a liquid, but its molecules may be oriented in a crystal-like way. The ...
. In many cases, at fixed temperature and pressure, a substance can exist in several distinct states of matter in what might be viewed as the same 'body'. For example, ice may float in a glass of water. Then the ice and the water are said to constitute two phases within the 'body'. Definite
rules Rule or ruling may refer to: Education * Royal University of Law and Economics (RULE), a university in Cambodia Human activity * The exercise of political or personal control by someone with authority or power * Business rule, a rule pert ...
are known, telling how distinct phases may coexist in a 'body'. Mostly, at a fixed pressure, there is a definite temperature at which heating causes a solid to melt or evaporate, and a definite temperature at which heating causes a liquid to evaporate. In such cases, cooling has the reverse effects. All of these, the commonest cases, fit with a rule that heating can be measured by changes of state of a body. Such cases supply what are called ''thermometric bodies'', that allow the definition of empirical temperatures. Before 1848, all temperatures were defined in this way. There was thus a tight link, apparently logically determined, between heat and temperature, though they were recognized as conceptually thoroughly distinct, especially by Joseph Black in the later eighteenth century. There are important exceptions. They break the obviously apparent link between heat and temperature. They make it clear that empirical definitions of temperature are contingent on the peculiar properties of particular thermometric substances, and are thus precluded from the title 'absolute'. For example, water contracts on being heated near 277 K. It cannot be used as a thermometric substance near that temperature. Also, over a certain temperature range, ice contracts on heating. Moreover, many substances can exist in metastable states, such as with negative pressure, that survive only transiently and in very special conditions. Such facts, sometimes called 'anomalous', are some of the reasons for the thermodynamic definition of absolute temperature. In the early days of measurement of high temperatures, another factor was important, and used by Josiah Wedgwood in his
pyrometer A pyrometer is a type of remote-sensing thermometer used to measure the temperature of distant objects. Various forms of pyrometers have historically existed. In the modern usage, it is a device that from a distance determines the temperature of ...
. The temperature reached in a process was estimated by the shrinkage of a sample of clay. The higher the temperature, the more the shrinkage. This was the only available more or less reliable method of measurement of temperatures above 1000 °C (1,832 °F). But such shrinkage is irreversible. The clay does not expand again on cooling. That is why it could be used for the measurement. But only once. It is not a thermometric material in the usual sense of the word. Nevertheless, the thermodynamic definition of absolute temperature does make essential use of the concept of heat, with proper circumspection.

# "Hotness"

The property of hotness is a concern of thermodynamics that should be defined without reference to the concept of heat. Consideration of hotness leads to the concept of empirical temperature. All physical systems are capable of heating or cooling others. With reference to hotness, the comparative terms hotter and colder are defined by the rule that heat flows from the hotter body to the colder. If a physical system is inhomogeneous or very rapidly or irregularly changing, for example by turbulence, it may be impossible to characterize it by a temperature, but still there can be transfer of energy as heat between it and another system. If a system has a physical state that is regular enough, and persists long enough to allow it to reach thermal equilibrium with a specified thermometer, then it has a temperature according to that thermometer. An empirical thermometer registers degree of hotness for such a system. Such a temperature is called empirical. For example, Truesdell writes about classical thermodynamics: "At each time, the body is assigned a real number called the ''temperature''. This number is a measure of how hot the body is." Physical systems that are too turbulent to have temperatures may still differ in hotness. A physical system that passes heat to another physical system is said to be the hotter of the two. More is required for the system to have a thermodynamic temperature. Its behavior must be so regular that its empirical temperature is the same for all suitably calibrated and scaled thermometers, and then its hotness is said to lie on the one-dimensional hotness manifold. This is part of the reason why heat is defined following Carathéodory and Born, solely as occurring other than by work or transfer of matter; temperature is advisedly and deliberately not mentioned in this now widely accepted definition. This is also the reason that the zeroth law of thermodynamics is stated explicitly. If three physical systems, ''A'', ''B'', and ''C'' are each not in their own states of internal thermodynamic equilibrium, it is possible that, with suitable physical connections being made between them, ''A'' can heat ''B'' and ''B'' can heat ''C'' and ''C'' can heat ''A''. In non-equilibrium situations, cycles of flow are possible. It is the special and uniquely distinguishing characteristic of internal thermodynamic equilibrium that this possibility is not open to thermodynamic systems (as distinguished amongst physical systems) which are in their own states of internal thermodynamic equilibrium; this is the reason why the zeroth law of thermodynamics needs explicit statement. That is to say, the relation 'is not colder than' between general non-equilibrium physical systems is not transitive, whereas, in contrast, the relation 'has no lower a temperature than' between thermodynamic systems in their own states of internal thermodynamic equilibrium is transitive. It follows from this that the relation 'is in thermal equilibrium with' is transitive, which is one way of stating the zeroth law. Just as temperature may be undefined for a sufficiently inhomogeneous system, so also may entropy be undefined for a system not in its own state of internal thermodynamic equilibrium. For example, 'the temperature of the solar system' is not a defined quantity. Likewise, 'the entropy of the solar system' is not defined in classical thermodynamics. It has not been possible to define non-equilibrium entropy, as a simple number for a whole system, in a clearly satisfactory way.Lieb, E.H., Yngvason, J. (2003), p. 190.

*
Effect of sun angle on climate The amount of heat energy received at any location on the globe is a direct effect of Sun angle on climate, as the angle at which sunlight strikes Earth varies by location, time of day, and season due to Earth's orbit around the Sun and Earth's rot ...
*
Heat death of the Universe The heat death of the universe (also known as the Big Chill or Big Freeze) is a hypothesis on the ultimate fate of the universe, which suggests the universe will evolve to a state of no thermodynamic free energy, and will therefore be unabl ...
* Heat diffusion *
Heat equation In mathematics and physics, the heat equation is a certain partial differential equation. Solutions of the heat equation are sometimes known as caloric functions. The theory of the heat equation was first developed by Joseph Fourier in 1822 for ...
* Heat exchanger *
Heat wave A heat wave, or heatwave, is a period of excessively hot weather, which may be accompanied by high humidity, especially in oceanic climate countries. While definitions vary, a heat wave is usually measured relative to the usual climate in the ...
* Heat flux sensor * Heat transfer coefficient * History of heat * Orders of magnitude (temperature) * Sigma heat * Shock heating * Thermal management of electronic devices and systems *
Thermometer A thermometer is a device that 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 mercury-in-glass thermometer ...
* Relativistic heat conduction *
Uniform Mechanical Code The Uniform Mechanical Code (UMC) is a model code developed by the International Association of Plumbing and Mechanical Officials (IAPMO) to govern the installation, inspection and maintenance of HVAC (heating, ventilating and air-conditioning) ...
*
Uniform Solar Energy and Hydronics Code Designated as an American National Standard, the Uniform Solar, Hydronics and Geothermal Code (USHGC) is a model code developed by the International Association of Plumbing and Mechanical Officials (IAPMO) to govern the installation and inspectio ...
*
Waste heat Waste heat is heat that is produced by a machine, or other process that uses energy, as a byproduct of doing work. All such processes give off some waste heat as a fundamental result of the laws of thermodynamics. Waste heat has lower util ...

# References

## Bibliography of cited references

* Adkins, C.J. (1968/1983). ''Equilibrium Thermodynamics'', (1st edition 1968), third edition 1983, Cambridge University Press, Cambridge UK, . * Atkins, P., de Paula, J. (1978/2010). ''Physical Chemistry'', (first edition 1978), ninth edition 2010, Oxford University Press, Oxford UK, . * Bacon, F. (1620). ''Novum Organum Scientiarum'', translated by Devey, J., P.F. Collier & Son, New York, 1902. * * Bailyn, M. (1994). ''A Survey of Thermodynamics'', American Institute of Physics Press, New York, . * Born, M. (1949)
''Natural Philosophy of Cause and Chance''
Oxford University Press, London. * Bryan, G.H. (1907)
''Thermodynamics. An Introductory Treatise dealing mainly with First Principles and their Direct Applications''
B.G. Teubner, Leipzig. * Buchdahl, H.A. (1966). ''The Concepts of Classical Thermodynamics'', Cambridge University Press, Cambridge UK. * Callen, H.B. (1960/1985). ''Thermodynamics and an Introduction to Thermostatistics'', (1st edition 1960) 2nd edition 1985, Wiley, New York, . * A translation may be foun
here
A mostly reliable translation is to be found at Kestin, J. (1976). ''The Second Law of Thermodynamics'', Dowden, Hutchinson & Ross, Stroudsburg PA. * Chandrasekhar, S. (1961). ''Hydrodynamic and Hydromagnetic Stability'', Oxford University Press, Oxford UK. * * Clausius, R. (1854). ''
Annalen der Physik ''Annalen der Physik'' (English: ''Annals of Physics'') is one of the oldest scientific journals on physics; it has been published since 1799. The journal publishes original, peer-reviewed papers on experimental, theoretical, applied, and m ...
'' (''Poggendoff's Annalen''), Dec. 1854, vol. xciii. p. 481; translated in the ''Journal de Mathematiques'', vol. xx. Paris, 1855, and in the ''Philosophical Magazine'', August 1856, s. 4. vol. xii, p. 81. * Clausius, R. (1865/1867)
''The Mechanical Theory of Heat – with its Applications to the Steam Engine and to Physical Properties of Bodies''
London: John van Voorst. 1867. Also the second edition translated into English by W.R. Browne (1879
here
an
here
* De Groot, S.R., Mazur, P. (1962). ''Non-equilibrium Thermodynamics'', North-Holland, Amsterdam. Reprinted (1984), Dover Publications Inc., New York, . * Denbigh, K. (1955/1981). ''The Principles of Chemical Equilibrium'', Cambridge University Press, Cambridge . * Greven, A., Keller, G., Warnecke (editors) (2003). ''Entropy'', Princeton University Press, Princeton NJ, . * * * , Lecture on Matter, Living Force, and Heat. 5 and 12 May 1847. * Kittel, C. Kroemer, H. (1980). ''Thermal Physics'', second edition, W.H. Freeman, San Francisco, . * * Kondepudi, D., Prigogine, I. (1998). ''Modern Thermodynamics: From Heat Engines to Dissipative Structures'', John Wiley & Sons, Chichester, . * Landau, L., Lifshitz, E.M. (1958/1969)
''Statistical Physics''
volume 5 of ''Course of Theoretical Physics'', translated from the Russian by J.B. Sykes, M.J. Kearsley, Pergamon, Oxford. * Lebon, G., Jou, D., Casas-Vázquez, J. (2008). ''Understanding Non-equilibrium Thermodynamics: Foundations, Applications, Frontiers'', Springer-Verlag, Berlin, e-. * Lieb, E.H., Yngvason, J. (2003). The Entropy of Classical Thermodynamics, Chapter 8 of ''Entropy'', Greven, A., Keller, G., Warnecke (editors) (2003). * * * * Pippard, A.B. (1957/1966). ''Elements of Classical Thermodynamics for Advanced Students of Physics'', original publication 1957, reprint 1966, Cambridge University Press, Cambridge. * Planck, M., (1897/1903)
''Treatise on Thermodynamics''
translated by A. Ogg, first English edition, Longmans, Green and Co., London. * Planck. M. (1914)