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In physics and chemistry, heat is energy transferred from one body to another by thermal interactions. The transfer of energy can occur in a variety of ways, among them conduction, radiation, and convection. Heat is not a property of a system or body, but instead is always associated with a process of some kind, and is synonymous with heat flow and heat transfer.

Heat flow from hotter to colder systems occurs spontaneously, and is always accompanied by an increase in entropy. In a heat engine, internal energy of bodies is harnessed to provide useful work. The second law of thermodynamics prohibits heat flow directly from cold to hot systems, but with the aid of a heat pump external work can be used to transport internal energy indirectly from a cold to a hot body.

Transfers of energy as heat are macroscopic processes. The origin and properties of heat can be understood through the statistical mechanics of microscopic constituents such as molecules and photons. For instance, heat flow can occur when the rapidly vibrating molecules in a high temperature body transfer some of their energy (by direct contact, radiation exchange, or other mechanisms) to the more slowly vibrating molecules in a lower temperature body.

The SI unit of heat is the joule. Heat can be measured by calorimetry, or determined indirectly by calculations based on other quantities, relying for instance on the first law of thermodynamics. In calorimetry, the concepts of latent heat and of sensible heat are used. Latent heat produces changes of state without temperature change, while sensible heat produces temperature change.

Overview

Heat in physics is defined as energy transferred by thermal interactions. Heat flows spontaneously from hotter to colder systems. When two systems come into thermal contact, they exchange energy through the microscopic interactions of their particles. When the systems are at different temperatures, the result is a spontaneous net flow of energy that continues until the temperatures are equal. At that point the net flow of energy is zero, and the systems are said to be in thermal equilibrium. Spontaneous heat transfer is an irreversible process.

The first law of thermodynamics states that the internal energy of an isolated system is conserved. To change the internal energy of a system, energy must be transferred to or from the system. For a closed system, heat and work are the mechanisms by which energy can be transferred. For an open system, internal energy can be changed also by transfer of matter. Work performed by a body is, by definition, an energy transfer from the body that is due to a change to external or mechanical parameters of the body, such as the volume, magnetization, and location of center of mass in a gravitational field.

When energy is transferred to a body purely as heat, its internal energy increases. This additional energy is stored as kinetic and potential energy of the atoms and molecules in the body. Heat itself is not stored within a body. Like work, it exists only as energy in transit from one body to another or between a body and its surroundings.

Microscopic origin of heat

Heat characterizes macroscopic systems and processes, but like other thermodynamic quantities it has a fundamental origin in statistical mechanics — the physics of the underlying microscopic degrees of freedom.

For example, within a range of temperature set by quantum effects, the temperature of a gas is proportional (via Boltzmann's constant k_B) to the average kinetic energy of its molecules. Heat transfer between a low and high temperature gas brought into contact arises due to the exchange of kinetic and potential energy in molecular collisions. As more and more molecules undergo collisions, their kinetic energy equilibrates to a distribution that corresponds to an intermediate temperature somewhere between the low and high initial temperatures of the two gases. An early and vague expression of this was by Francis Bacon. Precise and detailed versions of it were developed in the nineteenth century.

For solids, conduction of heat occurs through collective motions of microscopic particles, such as phonons, or through the motion of mobile particles like conduction band electrons. As these excitations move around inside the solid and interact with it and each other, they transfer energy from higher to lower temperature regions, eventually leading to thermal equilibrium.

History

Scottish physicist James Clerk Maxwell, in his 1871 classic Theory of Heat, was one of many who began to build on the already established idea that heat has something to do with matter in motion. This was the same idea put forth by Sir Benjamin Thompson in 1798, who said he was only following up on the work of many others. One of Maxwell's recommended books was Heat as a Mode of Motion, by John Tyndall. Maxwell outlined 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.
• It is a measurable quantity, and thus treated mathematically.
• It cannot be treated as a substance, because it may be transformed into something that is not a substance, e.g., mechanical work.
• Heat is one of the forms of energy.

From empirically based ideas of heat, and from other empirical observations, the notions of internal energy and of entropy can be derived, so as to lead to the recognition of the first and second laws of thermodynamics. This was the way of the historical pioneers of thermodynamics.

Mechanisms of heat transfer

Transfers between one body and another

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 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."

Transfers involving more than two bodies

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.

Convective transfer of energy

Convective transfer of energy involves three or more systems, which may be closed or open. A process of convection takes some finite amount of time, because it involves three steps at least. The simplest kind of convection has a hot reservoir, a cold reservoir, and a carrier body. In this simplest kind of convection, the carrier body exchanges heat successively with the respective thermal reservoirs. The second law of thermodynamics requires the carrier body to be initially colder than the hot reservoir and finally warmer than the cold reservoir. For convection in general, the transfers of energy can be of more general kinds. For example, for convection between open systems, the transfers may be more conveniently described in terms of internal energy, or of enthalpy, or of some other quantity of energy. Here a convenient model is described by internal energy. First, the carrier body increases its internal energy by taking internal energy from the source reservoir. Then it moves through space and carries its internal energy from the location of the source reservoir to that of the destination reservoir; this step is characteristic of convection, and is sometimes called advection. Then it decreases its internal energy by giving energy to the destination reservoir. Convection can transfer internal energy as latent heat, and can be from a source at a lower temperature to a destination at a higher one, work being provided to drive the transfer.

Notation and units

As a form of energy heat has the unit joule (J) in the International System of Units (SI). However, in many applied fields in engineering the British Thermal Unit (BTU) and the calorie are often used. The standard unit for the rate of heat transferred is the watt (W), defined as joules per second.

The total amount of energy transferred as heat is conventionally written as Q for algebraic purposes. Heat released by a system into its surroundings is by convention a negative quantity (Q < 0); when a system absorbs heat from its surroundings, it is positive (Q > 0). Heat transfer rate, or heat flow per unit time, is denoted by ${\displaystyle {\dot {Q}}}$. This should not be confused with 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. Heat flux is defined as rate of heat transfer per unit cross-sectional area, resulting in the unit watts per square metre.

Estimation of quantity of heat

The quantity of heat transferred by some process can either be directly measured, or determined indirectly through calculations based on other quantities.

Direct measurement is by calorimetry and is the primary 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.

Indirect estimations of quantity of heat transferred rely on the law of conservation of energy, and, in particular cases, on the first law of thermodynamics. Indirect estimation is the primary approach of many theoretical studies of quantity of heat transferred.

Internal energy and enthalpy

For a closed system (a system from which no matter can enter or exit), the first law of thermodynamics states that the change in internal energy ΔU of the system is equal to the amount of heat Q supplied to the system minus the amount of work W done by system on its surroundings.

${\displaystyle \Delta U=Q-W\quad {\rm {(first\,\,law)}}.}$

This can also be interpreted as that Q makes contributions to the internal energy and to the work done by the system:

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

The work done by the system includes boundary work (when the system increases its volume against an external force, such as that exerted by a piston) and other work (e.g. shaft work performed by a compressor fan):

${\displaystyle Q=\Delta U+W_{\text{boundary}}+W_{\text{other}}.}$

In this Section we will neglect the "other-work" contribution.

The internal energy, U, is a state function. In cyclical processes, such as the operation of a heat engine, state functions return to their initial values after completing one cycle. Then the differential, or infinitesimal increment, for the internal energy in an infinitesimal process is an exact differential dU. The symbol for exact differentials is the lowercase letter d.

In contrast, neither of the infintestimal increments δQ nor δW in an infinitesimal process represents the state of the system. Thus, infinitesimal increments of heat and work are inexact differentials. The lowercase Greek letter delta, δ, is the symbol for inexact differentials. The integral of any inexact differential over the time it takes for a system to leave and return to the same thermodynamic state does not necessarily equal zero.

The second law of thermodynamics observes that if heat is supplied to a system in which no irreversible processes take place and which has a well-defined temperature T, the increment of heat δQ and the temperature T form the exact differential

${\displaystyle \mathrm {d} S={\frac {\delta Q}{T}},}$

and that S, the entropy of the working body, is a function of state. Likewise, with a well-defined pressure, P, behind the moving boundary, the work differential, δW, and the pressure, P, combine to form the exact differential

${\displaystyle \mathrm {d} V={\frac {\delta W}{P}},}$

with V the volume of the system, which is a state variable. In general, for homogeneous systems,

${\displaystyle \mathrm {d} U=T\mathrm {d} S-P\mathrm {d} V.}$

Associated with this differential equation is that the internal energy may be considered to be a function U (S,V) of its natural variables S and V. The internal energy representation of the fundamental thermodynamic relation is written

${\displaystyle U=U(S,V).}$

If V is constant

${\displaystyle T\mathrm {d} S=\mathrm {d} U\,\,\,\,\,\,\,\,\,\,\,\,(V\,\,{\text{constant)}}}$

and if P is constant

${\displaystyle T\mathrm {d} S=\mathrm {d} H\,\,\,\,\,\,\,\,\,\,\,\,(P\,\,{\text{constant)}}}$

with H the enthalpy defined by

${\displaystyle H=U+PV.}$

The enthalpy may be considered to be a function H (S,P) of its natural variables S and P. The enthalpy representation of the fundamental thermodynamic relation is written

${\displaystyle H=H(S,P).}$

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.

Examples of singularly simply specified and standard paths

One may consider a simple compressible system, such as a gas in a cylinder, subject to processes of change of the mechanical variables volume and pressure by movement of a piston. Two principal kinds of process, with singularly simply specified paths, respectively change the internal energy ΔU at constant volume and the enthalpy ΔH at constant pressure. These two processes are described by their respective principal heat capacity values, which are C_V and C_p.

For a process with a path that constrains the gas to have constant volume, of the mechanical variables, only the pressure changes, and then the heat, Q, required to change the gas temperature from an initial temperature, T₀, to a final temperature, T_f, is given by

${\displaystyle Q=\int _{T_{0}}^{T_{f}}C_{V}\mathrm {d} T=\Delta U.}$

For a process with a path that allows the system to expand or contract at constant pressure, of the mechanical variables, only the volume changes, and then the heat, Q, required to change the gas temperature from an initial temperature, T₀, to a final temperature, T_f, is given by

${\displaystyle Q=\int _{T_{0}}^{T_{f}}C_{p}\mathrm {d} T=\Delta U+\int _{V_{0}}^{V_{f}}p\mathrm {d} V=\Delta H.}$

Here we used the definition of the enthalpy and the fact that p is constant. When integrating an exact differential (e.g. dU), the lowercase letter d is substituted for Δ (e.g. ΔU). Note that the symbol Δ is convenient since it is compact, but it can lead to sign errors. So it may be better to write U_f - U₀ instead of ΔU.

When integrating an inexact differential (e.g. δQ), the lowercase Greek letter δ is removed with no replacement (e.g. Q).

Chemical reactions

For a closed system in which a chemical reaction is of interest, the extent of reaction, denoted by ξ, states the degree of advancement of the reaction and is included as a further natural variable for internal energy and for enthalpy. This is written

${\displaystyle U=U(S,V,\xi )\,\,\,\mathrm {and} \,\,\,H=H(S,p,\xi )\,.}$

In practice, chemists often use tables of a special but unnamed thermodynamic potential that is not the enthalpy expressed in its natural variables; instead they use the enthalpy expressed as a function of temperature instead of entropy. This special potential is related to the natural form of the enthalpy H (S,p,ξ) by another partial Legendre transform, that makes its natural variables T, p, and ξ. The special unnamed potential is still usually called the enthalpy. It can be written

${\displaystyle H=H(T,p,\xi )\,.}$

This enthalpy is used to report the enthalpy change of reaction, also called the heat of reaction.

Latent and sensible heat

In an 1847 lecture entitled On Matter, Living Force, and Heat, James Prescott Joule characterized the terms latent heat and sensible heat as components of heat each affecting distinct physical phenomena, namely the potential and kinetic energy of particles, respectively. 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, and the sensible heat as an energy involving the motion of particles or what was known as a living force. At the time of Joule kinetic energy either held 'invisibly' internally or held 'visibly' externally was known as a living force.

Latent heat is the heat released or absorbed by a chemical substance or a thermodynamic system during a change of state that occurs without a change in temperature. Such a process may be a phase transition, such as the melting of ice or the boiling of water. The term was introduced around 1750 by Joseph Black as derived from the Latin latere (to lie hidden), characterizing its effect as not being directly measurable with a thermometer.

Sensible heat, in contrast to latent heat, is the heat exchanged by a thermodynamic system that has as its sole effect a change of temperature. Sensible heat therefore only increases the thermal energy of a system.

Consequences of Black's distinction between sensible and latent heat are examined in the Misplaced Pages article on calorimetry.

Specific heat

Specific heat, also called specific heat capacity, is defined as the amount of energy that has to be transferred to or from one unit of mass (kilogram) or amount of substance (mole) to change the system temperature by one degree. Specific heat is a physical property, which means that it depends on the substance under consideration and its state as specified by its properties.

The specific heats of monatomic gases (e.g., helium) are nearly constant with temperature. Diatomic gases such as hydrogen display some temperature dependence, and triatomic gases (e.g., carbon dioxide) still more.

Rigorous mathematical definition of quantity of energy transferred as heat

It is sometimes convenient to have a very rigorous mathematically stated definition of quantity of energy transferred as heat. Such definition is customarily based on the work of Carathéodory (1909), referring to processes in a closed system, as follows.

The internal energy U_X of a body in an arbitrary state X can be determined by amounts of work adiabatically performed by the body on its surrounds when it starts from a reference state O, allowing that sometimes the amount of work is calculated by assuming that some adiabatic process is virtually though not actually reversible. Adiabatic work is defined in terms of adiabatic walls, which allow the frictionless performance of work but no other transfer, of energy or matter. In particular they do not allow the passage of energy as heat. According to Carathéodory (1909), passage of energy as heat is allowed, by walls which are "permeable only to heat".

For the definition of quantity of energy transferred as heat, it is customarily envisaged that an arbitrary state of interest Y is reached from state O by a process with two components, one adiabatic and the other not adiabatic. For convenience one may say that the adiabatic component was work done by the body through volume change through movement of the walls while the non-adiabatic partition was excluded, so that only adiabatic change occurs in this component. Then the non-adiabatic component is a process of energy transfer through the wall that passes only heat, newly made accessible for the purpose of this transfer, from the surroundings to the body. The change in internal energy to reach the state Y from the state O is the difference of the two amounts of energy transferred.

Although Carathéodory himself did not state such a definition, following his work it is customary in theoretical studies to define the quantity of energy transferred as heat, Q, to the body from its surroundings, in the combined process of change to state Y from the state O, as the change in internal energy, ΔU_Y, minus the amount of work, W, done by the body on its surrounds by the adiabatic process, so that Q = ΔU_Y − W.

In this definition, for the sake of mathematical rigour, the quantity of energy transferred as heat is not specified directly in terms of the non-adiabatic process. It is defined through knowledge of precisely two variables, the change of internal energy and the amount of adiabatic work done, for the combined process of change from the reference state O to the arbitrary state Y. It is important that this does not explicitly involve the amount of energy transferred in the non-adiabatic component of the combined process. It is assumed here that the amount of energy required to pass from state O to state Y, the change of internal energy, is known, independently of the combined process, by a determination through a purely adiabatic process, like that for the determination of the internal energy of state X above. The mathematical rigour that is prized in this definition is that there is one and only one kind of energy transfer admitted as fundamental: energy transferred as work. Energy transfer as heat is considered as a derived quantity. The uniqueness of work in this scheme is considered to provide purity of conception, which is considered as guaranteeing mathematical rigour. The conceptual purity of this definition, based on the concept of energy transferred as work as an ideal notion, relies on the idea that some frictionless and otherwise non-dissipative processes of energy transfer can be realized in physical actuality. The second law of thermodynamics, on the other hand, assures us that such processes are not found in nature.

In this customary definition, the mechanism of transfer of energy in the non-adiabatic component of the combined process is not explicitly specified.

Because this mathematical definition, based on the work of Carathéodory (1909), does not explicitly specify the mechanism of transfer of energy in the non-adiabatic component of the combined process from O to Y, this definition lacks physical definiteness. The physical set-up specified explicitly by Carathéodory involves walls "permeable only to heat". It also involves a "non-deformation variable" as a necessary element of the specification of every state of the body or closed system. This variable is not obtrusively noted by Carathéodory to be capable of interpretation as an empirical temperature, but such is nevertheless implicit in his account. The passage of energy as heat between one closed system and another requires difference of the equivalent values of the non-deformation variable, and a partition "permeable only to heat". It is evident enough that the quantity of energy transferred as heat so defined is transferred by the mechanisms that determine transfer of energy through a partition permeable only to heat. The only physical mechanisms known for that are thermal conduction and radiation. That Carathéodory refrains from mentioning this is an impressive feat of presentation, providing a pleasing mathematical rigour; the physics is still plain enough. Carathéodory defines absolute thermodynamic temperature after stating the second law of thermodynamics, but his whole presentation rests on the physical existence of empirical temperature, alias the "non-deformation variable", right from the start. An empirical temperature is a strictly monotonic function of the thermodynamic or absolute temperature.

Entropy

In 1856, German physicist Rudolf Clausius defined the second fundamental theorem (the second law of thermodynamics) in the mechanical theory of heat (thermodynamics): "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 at the temperature T, has the equivalence-value:"

${\displaystyle {}{\frac {Q}{T}}.}$

In 1865, he came to define the entropy 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

${\displaystyle \Delta S={\frac {Q}{T}}}$

and thus, for small changes, quantities of heat δQ (an inexact differential) are defined as quantities of TdS, with dS an exact differential:

${\displaystyle \delta Q=T\mathrm {d} S.}$

This equality is only valid for a closed system and if no irreversible processes take place inside the system while the heat δQ is applied. If, in contrast, irreversible processes are involved, e.g. some sort of friction, then there is entropy production and, instead of the above equation, one has

${\displaystyle \delta Q\leq T\mathrm {d} S\quad {\rm {(second\,\,law)}}\,.}$

This is the second law of thermodynamics for closed systems.

Heat transfer in engineering

The discipline of heat transfer, 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 includes the mechanisms of heat conduction, thermal radiation, and mass transfer.

In engineering, the term convective heat transfer is used to describe 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.

Although distinct physical laws may describe the behavior of each of these methods, real systems often exhibit a complicated combination which are often described by a variety of complex mathematical methods.

Practical applications

In accordance with the first law for closed systems, energy transferred as heat enters one body and leaves 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.

Heat engines operate by converting heat flow from a high temperature reservoir to a low temperature reservoir into work. One example are steam engines, where the high temperature reservoir is steam generated by boiling water. The flow of heat from the hot steam to water is converted into mechanical work via a turbine or piston. Heat engines achieve high efficiency when the difference between initial and final temperature is high.

Heat pumps, by contrast, use work to cause thermal energy to flow from low to high temperature, the opposite direction heat would flow spontaneously. An example is a refrigerator or air conditioner, where electric power is used to cool a low temperature system (the interior of the refrigerator) while heating a higher temperature environment (the exterior). High efficiency is achieved when the temperature difference is small.

Usage of words

The strictly defined physical term 'quantity of energy transferred as heat' has a resonance with the ordinary language noun 'heat' and the ordinary language verb 'heat'. This can lead to confusion if ordinary language is muddled with strictly defined physical language. In the strict terminology of physics, heat is defined as a word that refers to a process, not to a state of a system. In ordinary language one can speak of a process that increases the temperature of a body as 'heating' it, ignoring the nature of the process, which could be one of adiabatic transfer of energy as work. But in strict physical terms, a process is admitted as heating only when what is meant is transfer of energy as heat. Such a process does not necessarily increase the temperature of the heated body, which may instead change its phase, for example by melting. In the strict physical sense, heat cannot be 'produced', because the usage 'production of heat' misleadingly seems to refer to a state variable. Thus, it would be physically improper to speak of 'heat production by friction', or of 'heating by adiabatic compression on descent of an air parcel' or of 'heat production by chemical reaction'; instead, proper physical usage speaks of conversion of kinetic energy of bulk flow, or of potential energy of bulk matter, or of chemical potential energy, into internal energy, and of transfer of energy as heat. Occasionally a present-day author, especially when referring to history, writes of "adiabatic heating", though this is a contradiction in terms of present day physics. Historically, before the concept of internal energy became clear over the period 1850 to 1869, physicists spoke of "heat production" where nowadays one speaks of conversion of other forms of energy into internal energy.

See also

• Effect of sun angle on climate
• Heat death of the Universe
• Heat diffusion
• Heat equation
• Heat exchanger
• Heat flux sensor
• Heat transfer coefficient
• History of heat
• Sigma heat
• Shock heating
• Thermal management of electronic devices and systems
• Thermometer
• Relativistic heat conduction
• Waste heat

Notes

1. An alternate sign convention (followed by IUPAC) for the work is to consider the work performed on the system by its surroundings. 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.

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44. Published in 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
45. Clausius, R. (1865). The Mechanical Theory of Heat –with its Applications to the Steam Engine and to Physical Properties of Bodies. London: John van Voorst, 1 Paternoster Row. MDCCCLXVII.
46. Iribarne, J.V., Godson, W.L. (1973/1989). Atmospheric thermodynamics, second edition, reprinted 1989, Kluwer Academic Publishers, Dordrecht, ISBN 90-277-1296-4, p. 136.
47. Bailyn, M. (1994), Part D, pp. 50–56.
48. For example, Clausius, R. (1857). Über die Art der Bewegung, welche wir Wärme nennen, Annalen der Physik und Chemie, 100: 353–380. Translated as On the nature of the motion which we call heat, Phil. Mag. series 4, 14: 108–128.

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External links

• Heat on In Our Time at the BBC
• Plasma heat at 2 gigakelvins - Article about extremely high temperature generated by scientists (Foxnews.com)
• Correlations for Convective Heat Transfer - ChE Online Resources
• An Introduction to the Quantitative Definition and Analysis of Heat written for High School Students

• Heat transfer
• Thermodynamics
• Concepts in physics