TheInfoList

In
thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by ...

, heat is
energy In , energy is the that must be to a or to perform on the body, or to it. Energy is a ; the law of states that energy can be in form, but not created or destroyed. The unit of measurement in the (SI) of energy is the , which is the ...

in transfer to or from a thermodynamic system, by mechanisms other than
thermodynamic work In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, radiation, and physical properties of matter. The behavior of these quantities is govern ...
or transfer of matter. The various mechanisms of energy transfer that define heat are stated in the next section of this article. Like thermodynamic
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 * Work (physics), the product of ...
, heat transfer is a process involving more than one system, not a property of any one system. In thermodynamics, energy transferred as heat contributes to change in the system's
cardinal Cardinal or The Cardinal may refer to: Christianity * Cardinal (Catholic Church), a senior official of the Catholic Church * Cardinal (Church of England), two members of the College of Minor Canons of St. Paul's Cathedral Navigation * Cardina ...
energy variable of state, for example its
internal energy The internal energy of a thermodynamic system A thermodynamic system is a body of matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can ...
, or for example its
enthalpy Enthalpy , a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It is a state function used in many measurements in chemical, biological, and physical systems at a constant pr ...

. This is to be distinguished from the ordinary language conception of heat as a property of an isolated system. The quantity of energy transferred as heat in a process is the amount of transferred energy excluding any
thermodynamic work In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, radiation, and physical properties of matter. The behavior of these quantities is govern ...
that was done and any energy contained in matter transferred. For the precise definition of heat, it is necessary that it occur by a path that does not include transfer of matter. (1949), p. 44. Though not immediately by the definition, but in special kinds of process, quantity of energy transferred as heat can be measured by its effect on the states of interacting bodies. For example, respectively in special circumstances, heat transfer can be measured by the amount of ice melted, or by change in
temperature Temperature ( ) is a physical quantity that expresses hot and cold. It is the manifestation of thermal energy Thermal radiation in visible light can be seen on this hot metalwork. Thermal energy refers to several distinct physical concept ...

of a body in the surroundings of the system. Such methods are called
calorimetry upSnellen direct calorimetry chamber, University of Ottawa. 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 exam ...
. The conventional symbol used to represent the amount of heat transferred in a thermodynamic process is or '. As an amount of energy (being transferred), the
SI unit 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 The metric system is a system of measurement A syste ...
of heat is the
joule The joule ( ; symbol: J) is a derived unit of energy In physics, energy is the physical quantity, quantitative physical property, property that must be #Energy transfer, transferred to a physical body, body or physical system to perform W ...

(J).

# Mechanisms of transfer that define heat

The mechanisms of energy transfer that define heat include , through direct contact of immobile bodies, or through a wall or barrier that is impermeable to matter; or
radiation upThe international symbol for types and levels of ionizing radiation (radioactivity) that are unsafe for unshielded humans. Radiation, in general, exists throughout nature, such as in light and sound. In physics Physics (from grc ...
between separated bodies; or
friction Friction is the force In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related en ...

due to isochoric mechanical or electrical or magnetic or gravitational
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 * Work (physics), the product of ...
done by the surroundings on the system of interest, such as
Joule heating Joule heating, also known as resistive, resistance, or Ohmic heating, is the process by which the passage of an electric current An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical condu ...
due to an electric current driven through the system of interest by an external system, or through a
magnetic stirrer A magnetic stirrer or magnetic mixer is a laboratory device that employs a rotating magnetic field to cause a stir bar (or ''flea'') immersed in a liquid to spin very quickly, thus stirring it. The rotating field may be created either by a rotat ...

. When there is a suitable path between two systems with different
temperature Temperature ( ) is a physical quantity that expresses hot and cold. It is the manifestation of thermal energy Thermal radiation in visible light can be seen on this hot metalwork. Thermal energy refers to several distinct physical concept ...

s, heat transfer occurs necessarily, immediately, and spontaneously from the hotter to the colder system. Thermal conduction occurs by the
stochastic Stochastic () refers to the property of being well described by a random In common parlance, randomness is the apparent or actual lack of pattern or predictability in events. A random sequence of events, symbols or steps often has no :wi ...
(random) motion of microscopic particles (such as atoms or molecules). In contrast, thermodynamic work is defined by mechanisms that act macroscopically and directly on the system's whole-body state variables; for example, change of the system's volume through a piston's motion with externally measurable force; or change of the system's internal electric polarization through an externally measurable change in electric field. The definition of heat transfer does not require that the process be in any sense smooth. For example, a bolt of lightning may transfer heat to a body. Convective circulation allows one body to heat another, through an intermediate circulating fluid that carries energy from a boundary of one to a boundary of the other; the actual heat transfer is by conduction and radiation between the fluid and the respective bodies. Convective circulation, though
spontaneous Spontaneous may refer to: * Miscarriage, Spontaneous abortion * Spontaneous bacterial peritonitis * Spontaneous combustion * Excited utterance, Spontaneous declaration * Spontaneous emission * Spontaneous fission * Spontaneous generation * Spontane ...
, does not necessarily and immediately occur simply because of some slight temperature difference; for it to occur in a given arrangement of systems, there is a threshold that must be crossed. Although heat flows spontaneously from a hotter body to a cooler one, it is possible to construct a
heat pump A heat pump is a system used to heat or cool an enclosed space or domestic water by transferring thermal energy Thermal radiation in visible light can be seen on this hot metalwork. Thermal energy refers to several distinct physical concepts, ...

which expends work to transfer energy from a colder body to a hotter body. In contrast, a
heat engine In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these qu ...

reduces an existing temperature difference to supply work to another system. Another thermodynamic type of heat transfer device is an active
heat spreader A heat spreader transfers energy as heat In thermodynamics, heat is energy in transfer to or from a thermodynamic system, by mechanisms other than Work (thermodynamics), thermodynamic work or Mass transfer, transfer of matter. The various ...
, which expends work to speed up transfer of energy to colder surroundings from a hotter body, for example a computer component.

# Notation and units

As a form of energy, heat has the unit
joule The joule ( ; symbol: J) is a derived unit of energy In physics, energy is the physical quantity, quantitative physical property, property that must be #Energy transfer, transferred to a physical body, body or physical system to perform W ...

(J) in the
International System of Units International is an adjective (also used as a noun) meaning "between nations". International may also refer to: Music Albums * International (Kevin Michael album), ''International'' (Kevin Michael album), 2011 * International (New Order album), '' ...
(SI). However, in many applied fields in engineering the
British thermal unit The British thermal unit (BTU or Btu) is a unit of heat In thermodynamics, heat is energy in transfer to or from a thermodynamic system, by mechanisms other than Work (thermodynamics), thermodynamic work or Mass transfer, transfer of matter ...
(BTU) and the
calorie The calorie is a unit of energy Unit may refer to: Arts and entertainment * UNIT Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action, a di ...
are often used. The standard unit for the rate of heat transferred is the
watt The watt (symbol: W) is a unit of power Power typically refers to: * Power (physics) In physics, power is the amount of energy transferred or converted per unit time. In the International System of Units, the unit of power is the watt, equal ...

(W), defined as one joule per second. The symbol for the total amount of energy transferred as heat was used by
Rudolf Clausius Rudolf Julius Emanuel Clausius (; 2 January 1822 – 24 August 1888) was a German physicist A physicist is a scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branches of sci ...
in 1850: :"Let the amount of heat which must be imparted during the transition of the gas in a definite manner from any given state to another, in which its volume is ''v'' and its temperature ''t'', be called ''Q''" '' 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
.
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 $\dot$. This should not be confused with a time derivative of a
function of state In the Thermodynamics#Equilibrium_thermodynamics, thermodynamics of equilibrium, a state function, function of state, or point function is a function defined for a system relating several state variables or state quantities that depends only on the ...
(which can also be written with the dot notation) since heat is not a function of state.Baierlein, R. (1999), p. 21.
Heat flux Heat flux of \mathbf(\mathbf) with the unit normal vector \mathbf(\mathbf) ''(blue arrows)'' at the point \mathbf multiplied by the area dS. The sum of \mathbf\cdot\mathbf dS for each patch on the surface is the flux through the surface Flux ...
is defined as rate of heat transfer per unit cross-sectional area (units 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 A physicist is a scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branches of sci ...
, 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 establishes the concept of entropy Entropy is a scientific concept, as well as a measurable physical property that is most commonly associated with a state of disorder, randomness, or uncertainty. The term an ...
) 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 wov ...
(
thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by ...

): "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 * Work (physics), the product of ...
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 thermodynamics ...

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 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 An inexact differential or imperfect differential is a type of differential used in thermodynamics to express changes in path dependent quantities. In contrast, an integral of an exact differential (a differential of a function) is always path in ...
) is analyzed as a quantity , with (an
exact differential In multivariate calculus, a differential is said to be exact or perfect, as contrasted with an inexact differential, if it is of the form ''dQ'', for some differentiable function In calculus Calculus, originally called infinitesimal calculu ...
): :$T\,\mathrmS=\delta Q .$ 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 productionEntropy production (or generation) is the amount of entropy which is produced in any irreversible processes such as heat and mass transfer processes including motion of bodies, heat exchange, fluid flow, substances expanding or mixing, anelastic defo ...
, 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 establishes the concept of entropy Entropy is a scientific concept, as well as a measurable physical property that is most commonly associated with a state of disorder, randomness, or uncertainty. The term an ...
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 closed system is a physical system A physical system is a collection of physical objects. In physics, it is a portion of the physical universe chosen for analysis. Everything outside the system is known as the environment (systems), environme ...
(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 version of the law of conservation of energy, adapted for thermodynamic processes, distinguishing three kinds of transfer of energy, as heat, as thermodynamic work, and as energy associated with matter tran ...
states that the change in
internal energy The internal energy of a thermodynamic system A thermodynamic system is a body of matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can ...
of the system is equal to the amount of heat supplied to the system minus the amount of
thermodynamic work In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, radiation, and physical properties of matter. The behavior of these quantities is govern ...
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 Peter William Atkins (born 10 August 1940) is an English chemist A chemist (from Greek ''chēm(ía)'' alchemy; replacing ''chymist'' from Medieval Latin ''alchemist'') is a scientist A scientist is a person who conducts Scientific method ...

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 is a function defined for a system A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to form ...
. 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 In multivariate calculus, a differential is said to be exact or perfect, as contrasted with an inexact differential, if it is of the form ''dQ'', for some differentiable function In calculus Calculus, originally called infinitesimal calculu ...
. The symbol for
exact differential In multivariate calculus, a differential is said to be exact or perfect, as contrasted with an inexact differential, if it is of the form ''dQ'', for some differentiable function In calculus Calculus, originally called infinitesimal calculu ...
s 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 differential An inexact differential or imperfect differential is a type of differential used in thermodynamics to express changes in path dependent quantities. In contrast, an integral of an exact differential (a differential of a function) is always path in ...
s. 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 In multivariate calculus, a differential is said to be exact or perfect, as contrasted with an inexact differential, if it is of the form ''dQ'', for some differentiable function In calculus Calculus, originally called infinitesimal calculu ...
:$\mathrmS =\frac,$ 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 In thermodynamics, the fundamental thermodynamic relation are four fundamental equations which demonstrate how four important thermodynamic quantities depend on variables that can be controlled and measured experimentally. Thus, they are essentiall ...
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 (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 Thermal radiation in visible light can be seen on this hot metalwork. Thermal energy refers to several distinct physical concepts, such as the internal energy of a system; heat or sensible heat, which are defined as types of energy transfer (as is ...
or
temperature Temperature ( ) is a physical quantity that expresses hot and cold. It is the manifestation of thermal energy Thermal radiation in visible light can be seen on this hot metalwork. Thermal energy refers to several distinct physical concept ...

. Speculation on thermal energy or "heat" as a separate form of matter has a long history, see
caloric theoryThe caloric theory is an obsolete scientific theory that heat 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 en ...
,
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 Combustion, or burning, is a high-temperature ex ...
and
fire (classical element) Fire is one of the four classical element Classical elements typically refer to water Water is an Inorganic compound, inorganic, Transparency and translucency, transparent, tasteless, odorless, and Color of water, nearly colorless che ...
. The modern understanding of thermal energy originates with '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 In the history of science The history of science is the study of the development of science Science (from the Latin word ''scientia'', meaning "knowledge") is a systematic enterprise that Scientific method, builds and Taxonomy (general), ...
. A collaboration between
Nicolas Clément Nicolas Clément (12 January 1779 – 21 November 1841) was a French physicist A physicist is a scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branches of science, area of i ...
Reflections on the Motive Power of Fire ''Reflections on the Motive Power of Fire and on Machines Fitted to Develop that Power'' is a book published in 1824 by French people, French physicist Nicolas Léonard Sadi Carnot, Sadi Carnot.full text of 1897 ed. ( s:Reflections on the Motive P ...
'') 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 initial scientific fame arose in the 1850s from his study of diamagnetism Diamagnetic materials are repelled by a magnetic field A ...

'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 A physicist is a scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branches of sci ...
in 1850. Clausius described it with the German compound ''Wärmemenge'', translated as "amount of heat".
James Clerk Maxwell James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branches of science, area of interest. In classica ...

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 establishes the concept of entropy Entropy is a scientific concept, as well as a measurable physical property that is most commonly associated with a state of disorder, randomness, or uncertainty. The term an ...
. * 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 In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. ...
. * Heat is ''one of the forms of energy''. The
process function In thermodynamics, a quantity that is well defined so as to describe the path of a process through the equilibrium state space of a thermodynamic system A thermodynamic system is a body of matter and/or radiation, confined in space by walls, w ...
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 Enthalpy , a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It is a state function used in many measurements in chemical, biological, and physical systems at a constant pr ...

to refer to the "heat content at constant volume", and to
thermal energy Thermal radiation in visible light can be seen on this hot metalwork. Thermal energy refers to several distinct physical concepts, such as the internal energy of a system; heat or sensible heat, which are defined as types of energy transfer (as is ...
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 Leonard Benedict Loeb (September 16, 1891 – June 17, 1978) was a Swiss-born American physicist A physicist is a scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branches of sc ...
in his ''Kinetic Theory of Gases'' (1927) makes a point of using "quanitity 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 theoryThe caloric theory is an obsolete scientific theory that heat 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 en ...
,] 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.

## Carathéodory (1909)

A frequent definition of heat is based on the work of Carathéodory (1909), referring to processes in a closed system. The
internal energy The internal energy of a thermodynamic system A thermodynamic system is a body of matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can ...

# 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, 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 The internal energy of a thermodynamic system A thermodynamic system is a body of matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can ...
. 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 In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these qu ...

. 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 A heat pump is a system used to heat or cool an enclosed space or domestic water by transferring thermal energy Thermal radiation in visible light can be seen on this hot metalwork. Thermal energy refers to several distinct physical concepts, ...

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 operation A thermodynamic operation is an externally imposed manipulation that affects a thermodynamic system. The change can be either in the connection or wall between a thermodynamic system and its surroundings, or in the value of some variable in the sur ...
s 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 German(s) may refer to: Common uses * of or related to Germany * Germans, Germanic ethnic group, citizens of Germany or people of German ancestry * For cit ...

, 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 A physicist is a scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branches of science, area of intere ...

## Microscopic view

In the
kinetic theory of the ideal gas An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation o ...

, 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 for England and Wales, Attorney General and as Lord Chancellor of K ...

. Precise and detailed versions of it were developed in the nineteenth century. In
statistical mechanics In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular ...
, 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 work and on the
first law of thermodynamics The first law of thermodynamics is a version of the law of conservation of energy, adapted for thermodynamic processes, distinguishing three kinds of transfer of energy, as heat, as thermodynamic work, and as energy associated with matter tran ...
. 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 Mechanical engineering is an engineering Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineerin ...

and
chemical engineering Chemical engineering is a certain type of engineering Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline ...
, 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 Thermal conduction is the transfer of internal energy The internal energy of a thermodynamic system A thermodynamic system is a body of matter In classical physics and general chemistry, matter is any substance that has mass and takes u ...

,
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 of ...
,
thermal radiation Thermal radiation is electromagnetic radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space an ...
, but may include
mass transfer Mass transfer is the net movement of mass from one location, usually meaning stream, phase, fraction or component, to another. Mass transfer occurs in many processes, such as absorption Absorption may refer to: Chemistry and biology *Absorptio ...
and heat in processes of
phase changes In chemistry Chemistry is the scientific discipline involved with Chemical element, elements and chemical compound, compounds composed of atoms, molecules and ions: their composition, structure, properties, behavior and the changes they und ...

. 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 A physicist is a scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branches of science, ...

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 A thermodynamic system is a body of matter In classical physics and general chemistry, matter is any su ...
and
sensible heatSensible heat is heat In thermodynamics, heat is energy in transfer to or from a thermodynamic system, by mechanisms other than Work (thermodynamics), thermodynamic work or Mass transfer, transfer of matter. The various mechanisms of energy tr ...
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." (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 In , energy is the that must be to a or to perform on the body, or to it. Energy is a ; the law of states that energy can be in form, but not created or destroyed. The unit of measure ...

, and the sensible heat as an energy involving the motion of particles, i.e.
kinetic energy In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular ...
. Latent heat is the heat released or absorbed by a
chemical substance A chemical substance is a form of matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which ...
or a
thermodynamic system A thermodynamic system is a body of matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, whic ...
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), ''The State'' (newspaper), a daily newspaper in Columbia, South Carolina, Un ...
that occurs without a change in temperature. Such a process may be a
phase transition In chemistry Chemistry is the scientific Science () is a systematic enterprise that builds and organizes knowledge Knowledge is a familiarity or awareness, of someone or something, such as facts A fact is an occurrence in ...
, such as the melting of ice or the boiling of water.Perrot, P. (1998).

# Heat capacity

Heat capacity Heat capacity or thermal capacity is a physical property A physical property is any property Property is a system of rights that gives people legal control of valuable things, and also refers to the valuable things themselves. Depending on t ...
is a
measurable In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). ...

physical quantity A physical quantity is a physical property of a material or system that can be Quantification (science), quantified by measurement. A physical quantity can be expressed as a ''value'', which is the algebraic multiplication of a ''numerical value'' ...
equal to the ratio of the heat added to an object to the resulting
temperature Temperature ( ) is a physical quantity that expresses hot and cold. It is the manifestation of thermal energy Thermal radiation in visible light can be seen on this hot metalwork. Thermal energy refers to several distinct physical concept ...

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 Talpidae ...
) 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 Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. " ...
, solid, liquid, and gas. Some can also exist in a
plasma Plasma or plasm may refer to: Science * Plasma (physics), one of the four fundamental states of matter * Plasma (mineral) or heliotrope, a mineral aggregate * Quark–gluon plasma, a state of matter in quantum chromodynamics Biology * Blood plasma ...
. Many have further, more finely differentiated, states of matter, such as
glass Glass is a non- crystalline, often transparency and translucency, transparent amorphous solid, that has widespread practical, technological, and decorative use in, for example, window panes, tableware, and optics. Glass is most often formed by ...

and
liquid crystal Liquid crystals (LCs) are a state of matter In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time ...
. 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: Human activity * The exercise of political Politics (from , ) is the set of activities that are associated with Decision-making, making decisions in Social group, groups, or other forms of Power (social and po ...
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 , 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 Joseph Black (16 April 1728 – 6 December 1799) was a Scottish physicist and chemist, known for his discoveries of magnesium, latent heat, specific heat, and carbon dioxide. He was Professor of Anatomy and Chemistry at the University of Glasgo ...
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 Josiah Wedgwood (12 July 1730 – 3 January 1795) was an English potter, entrepreneur, and abolitionist. He founded the Wedgwood company. He developed improved pottery bodies by a long process of systematic experimentation, and was the lead ...

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. 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"

According to Denbigh (1981), 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 * Heat death of the Universe * Heat diffusion * Heat equation * Heat exchanger * Heat wave * 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 * Relativistic heat conduction * Uniform Mechanical Code * Uniform Solar Energy and Hydronics Code * Waste heat

# References

## Bibliography of cited references

* Adkins, C.J. (1968/1983). ''Equilibrium Thermodynamics'', (1st edition 1968), third edition 1983, Cambridge University Press, Cambridge UK, . * Peter Atkins, 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, . * (1949)
''Natural Philosophy of Cause and Chance''
Oxford University Press, London. * George H. Bryan, Bryan, G.H. (1907)
''Thermodynamics. An Introductory Treatise dealing mainly with First Principles and their Direct Applications''
B.G. Teubner, Leipzig. *Hans Adolf Buchdahl, Buchdahl, H.A. (1966). ''The Concepts of Classical Thermodynamics'', Cambridge University Press, Cambridge UK. * (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. * * Rudolf Clausius, Clausius, R. (1854). ''Annalen der Physik'' (''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. * Rudolf Clausius, 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., Peter Mazur, 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., Ilya Prigogine, Prigogine, I. (1998). ''Modern Thermodynamics: From Heat Engines to Dissipative Structures'', John Wiley & Sons, Chichester, . * Lev Landau, Landau, L., Evgeny Lifshitz, 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). * * * * Brian Pippard, Pippard, A.B. (1957/1966). ''Elements of Classical Thermodynamics for Advanced Students of Physics'', original publication 1957, reprint 1966, Cambridge University Press, Cambridge. * Max Planck, Planck, M., (1897/1903)
''Treatise on Thermodynamics''
translated by A. Ogg, first English edition, Longman, Longmans, Green and Co., London. * Max Planck, Planck. M. (1914)
a translation by Masius, M. of the second German edition, P. Blakiston's Son & Co., Philadelphia. * Max Planck, Planck, M., (1923/1927). ''Treatise on Thermodynamics'', translated by A. Ogg, third English edition, Longman, Longmans, Green and Co., London. * * Shavit, A., Gutfinger, C. (1995). ''Thermodynamics. From Concepts to Applications'', Prentice Hall, London, . * Clifford Truesdell, Truesdell, C. (1969). ''Rational Thermodynamics: a Course of Lectures on Selected Topics'', McGraw-Hill Book Company, New York. * Clifford Truesdell, Truesdell, C. (1980). ''The Tragicomical History of Thermodynamics 1822–1854'', Springer, New York, .

## Further bibliography

* * Gyftopoulos, E.P., & Beretta, G.P. (1991). ''Thermodynamics: foundations and applications.'' (Dover Publications) * Hatsopoulos, G.N., & Keenan, J.H. (1981). Principles of general thermodynamics. RE Krieger Publishing Company.

*
Plasma heat at 2 gigakelvins
– Article about extremely high temperature generated by scientists (Foxnews.com)
Correlations for Convective Heat Transfer
– ChE Online Resources {{Authority control Heat transfer Thermodynamics Physical quantities