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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 b ...
, heat is
energy Energy () is the physical quantity, quantitative physical property, property that is transferred to a physical body, body or to a physical system, recognizable in the performance of Work (thermodynamics), work and in the form of heat and l ...
in transfer between a
thermodynamic system A thermodynamic system is a body of matter and/or radiation separate from its surroundings that can be studied using the laws of thermodynamics. Thermodynamic systems can be passive and active according to internal processes. According to inter ...
and its surroundings by such mechanisms as
thermal conduction Thermal conduction is the diffusion of thermal energy (heat) within one material or between materials in contact. The higher temperature object has molecules with more kinetic energy; collisions between molecules distributes this kinetic energy ...
, electromagnetic radiation, and
friction Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. Types of friction include dry, fluid, lubricated, skin, and internal -- an incomplete list. The study of t ...
, which are microscopic in nature, involving sub-atomic, atomic, or molecular particles, or small surface irregularities, as distinct from the macroscopic modes of energy transfer, which are
thermodynamic work Thermodynamic work is one of the principal kinds of process by which a thermodynamic system can interact with and transfer energy to its surroundings. This results in externally measurable macroscopic forces on the system's surroundings, which c ...
and transfer of matter. For a
closed system A closed system is a natural physical system that does not allow transfer of matter in or out of the system, althoughin the contexts of physics, chemistry, engineering, etc.the transfer of energy (e.g. as work or heat) is allowed. Physics In cl ...
(transfer of matter excluded), the heat involved in a process is the difference in
internal energy The internal energy of a thermodynamic system is the energy of the system as a state function, measured as the quantity of energy necessary to bring the system from its standard internal state to its present internal state of interest, accoun ...
between the final and initial states of a system, after subtracting the work done in the process. For a closed system, this is the formulation of the
first law of thermodynamics The first law of thermodynamics is a formulation of the law of conservation of energy in the context of thermodynamic processes. For a thermodynamic process affecting a thermodynamic system without transfer of matter, the law distinguishes two ...
.
Calorimetry In chemistry and thermodynamics, calorimetry () is the science or act of measuring changes in '' state variables'' of a body for the purpose of deriving the heat transfer associated with changes of its state due, for example, to chemical reac ...
is measurement of quantity of energy transferred as heat by its effect on the states of interacting bodies, for example, by the amount of ice melted or by change in
temperature Temperature is a physical quantity that quantitatively expresses the attribute of hotness or coldness. Temperature is measurement, measured with a thermometer. It reflects the average kinetic energy of the vibrating and colliding atoms making ...
of a body. In the
International System of Units The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of measurement. It is the only system of measurement with official s ...
(SI), the unit of measurement for heat, as a form of energy, is the
joule The joule ( , or ; symbol: J) is the unit of energy in the International System of Units (SI). In terms of SI base units, one joule corresponds to one kilogram- metre squared per second squared One joule is equal to the amount of work d ...
(J). With various other meanings, the word 'heat' is also used in engineering, and it occurs also in ordinary language, but such are not the topic of the present article.


Notation and units

As a form of energy, heat has the unit
joule The joule ( , or ; symbol: J) is the unit of energy in the International System of Units (SI). In terms of SI base units, one joule corresponds to one kilogram- metre squared per second squared One joule is equal to the amount of work d ...
(J) in the
International System of Units The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of measurement. It is the only system of measurement with official s ...
(SI). In addition, many applied branches of engineering use other, traditional units, such as the
British thermal unit The British thermal unit (Btu) is a measure of heat, which is a form of energy. It was originally defined as the amount of heat required to raise the temperature of one pound of water by one degree Fahrenheit. It is also part of the United Stat ...
(BTU) and the
calorie The calorie is a unit of energy that originated from the caloric theory of heat. The large calorie, food calorie, dietary calorie, kilocalorie, or kilogram calorie is defined as the amount of heat needed to raise the temperature of one liter o ...
. The standard unit for the rate of heating is the
watt The watt (symbol: W) is the unit of Power (physics), power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m2⋅s−3. It is used to quantification (science), quantify the rate of Work ...
(W), defined as one joule per second. The symbol for heat was introduced by
Rudolf Clausius Rudolf Julius Emanuel Clausius (; 2 January 1822 – 24 August 1888) was a German physicist and mathematician and is considered one of the central founding fathers of the science of thermodynamics. By his restatement of Sadi Carnot's principle ...
and
Macquorn Rankine William John Macquorn Rankine (; 5 July 1820 – 24 December 1872) was a Scottish mathematician and physicist. He was a founding contributor, with Rudolf Clausius and William Thomson, 1st Baron Kelvin, William Thomson (Lord Kelvin), to the scien ...
in . Heat released by a system into its surroundings is by convention, as a contributor to internal energy, a negative quantity (); when a system absorbs heat from its surroundings, it is positive (). Heat transfer rate, or heat flow per unit time, is denoted by \dot, but it is not a time derivative of a
function of state In the thermodynamics of equilibrium, a state function, function of state, or point function for a thermodynamic system is a mathematical function relating several state variables or state quantities (that describe equilibrium states of a syste ...
(which can also be written with the dot notation) since heat is not a function of state.Baierlein, R. (1999), p. 21.
Heat flux In physics and engineering, heat flux or thermal flux, sometimes also referred to as heat flux density, heat-flow density or heat-flow rate intensity, is a flow of energy per unit area per unit time (physics), time. Its SI units are watts per sq ...
is defined as rate of heat transfer per unit cross-sectional area (watts per square metre).


History

In common language, English 'heat' or 'warmth', just as French ''chaleur'', German ''Hitze'' or ''Wärme'',
Latin Latin ( or ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken by the Latins (Italic tribe), Latins in Latium (now known as Lazio), the lower Tiber area aroun ...
''calor'',
Greek Greek may refer to: Anything of, from, or related to Greece, a country in Southern Europe: *Greeks, an ethnic group *Greek language, a branch of the Indo-European language family **Proto-Greek language, the assumed last common ancestor of all kno ...
θάλπος, etc. refers to either
thermal energy The term "thermal energy" is often used ambiguously in physics and engineering. It can denote several different physical concepts, including: * Internal energy: The energy contained within a body of matter or radiation, excluding the potential en ...
or
temperature Temperature is a physical quantity that quantitatively expresses the attribute of hotness or coldness. Temperature is measurement, measured with a thermometer. It reflects the average kinetic energy of the vibrating and colliding atoms making ...
, or the human perception of these. Later, ''chaleur'' (as used by Sadi Carnot), 'heat', and ''Wärme'' became equivalents also as specific scientific terms at an early stage of thermodynamics. Speculation on 'heat' as a separate form of matter has a long history, involving the
phlogiston The phlogiston theory, a superseded scientific theory, postulated the existence of a fire-like element dubbed phlogiston () contained within combustible bodies and released during combustion. The name comes from the Ancient Greek (''burnin ...
theory, the
caloric theory The caloric theory is an obsolete scientific theory that heat consists of a self-repellent fluid called caloric that flows from hotter bodies to colder bodies. Caloric was also thought of as a weightless gas that could pass in and out of pores ...
, and
fire Fire is the rapid oxidation of a fuel in the exothermic chemical process of combustion, releasing heat, light, and various reaction Product (chemistry), products. Flames, the most visible portion of the fire, are produced in the combustion re ...
. Many careful and accurate historical experiments practically exclude friction, mechanical and thermodynamic work and matter transfer, investigating transfer of energy only by thermal conduction and radiation. Such experiments give impressive rational support to the caloric theory of heat. To account also for changes of internal energy due to friction, and mechanical and thermodynamic work, the caloric theory was, around the end of the eighteenth century, replaced by the "mechanical" theory of heat, which is accepted today.


17th century–early 18th century


"Heat is motion"

As scientists of the early modern age began to adopt the view that matter consists of particles, a close relationship between heat and the motion of those particles was widely surmised, or even the equivalency of the concepts, boldly expressed by the English philosopher
Francis Bacon Francis Bacon, 1st Viscount St Alban (; 22 January 1561 – 9 April 1626) was an English philosopher and statesman who served as Attorney General and Lord Chancellor of England under King James I. Bacon argued for the importance of nat ...
in 1620. "It must not be thought that heat generates motion, or motion heat (though in some respects this be true), but that the very essence of heat ... is motion and nothing else." "not a ... motion of the whole, but of the small particles of the body." In ''
The Assayer ''The Assayer'' () is a book by Galileo Galilei, published in Rome in October 1623. It is generally considered to be one of the pioneering works of the scientific method, first broaching the idea that the book of nature is to be read with mathem ...
'' (published 1623)
Galileo Galilei Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642), commonly referred to as Galileo Galilei ( , , ) or mononymously as Galileo, was an Italian astronomer, physicist and engineer, sometimes described as a poly ...
, in turn, described heat as an artifact of our minds. Galileo wrote that heat and pressure are apparent properties only, caused by the movement of particles, which is a real phenomenon. In 1665, and again in 1681, English polymath
Robert Hooke Robert Hooke (; 18 July 16353 March 1703) was an English polymath who was active as a physicist ("natural philosopher"), astronomer, geologist, meteorologist, and architect. He is credited as one of the first scientists to investigate living ...
reiterated that heat is nothing but the motion of the constituent particles of objects, and in 1675, his colleague, Anglo-Irish scientist
Robert Boyle Robert Boyle (; 25 January 1627 – 31 December 1691) was an Anglo-Irish natural philosopher, chemist, physicist, Alchemy, alchemist and inventor. Boyle is largely regarded today as the first modern chemist, and therefore one of the foun ...
repeated that this motion is what heat consists of. Heat has been discussed in ordinary language by philosophers. An example is this 1720 quote from the English philosopher
John Locke John Locke (; 29 August 1632 (Old Style and New Style dates, O.S.) – 28 October 1704 (Old Style and New Style dates, O.S.)) was an English philosopher and physician, widely regarded as one of the most influential of the Enlightenment thi ...
: When Bacon, Galileo, Hooke, Boyle and Locke wrote “heat”, they might more have referred to what we would now call “temperature”. No clear distinction was made between heat and temperature until the mid-18th century, nor between the internal energy of a body and the transfer of energy as heat until the mid-19th century. Locke's description of heat was repeatedly quoted by English physicist
James Prescott Joule James Prescott Joule (; 24 December 1818 11 October 1889) was an English physicist. Joule studied the nature of heat and discovered its relationship to mechanical work. This led to the law of conservation of energy, which in turn led to the ...
. Also the transfer of heat was explained by the motion of particles. Scottish physicist and chemist
Joseph Black Joseph Black (16 April 1728 – 6 December 1799) was a British 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 Glasgow ...
wrote: "Many have supposed that heat is a tremulous ... motion of the particles of matter, which ... motion they imagined to be communicated from one body to another."
John Tyndall John Tyndall (; 2 August 1820 – 4 December 1893) was an Irish physicist. His scientific fame arose in the 1850s from his study of diamagnetism. Later he made discoveries in the realms of infrared radiation and the physical properties of air ...
'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.


18th century


Heat vs. temperature

Unstated distinctions between heat and “hotness” may be very old, heat seen as something dependent on the ''quantity'' of a hot substance, “heat”, vaguely perhaps distinct from the ''quality'' of "hotness". In 1723, the English mathematician
Brook Taylor Brook Taylor (18 August 1685 – 29 December 1731) was an English mathematician and barrister best known for several results in mathematical analysis. Taylor's most famous developments are Taylor's theorem and the Taylor series, essent ...
measured the temperature—the expansion of the liquid in a thermometer—of mixtures of various amounts of hot water in cold water. As expected, the increase in temperature was in proportion to the proportion of hot water in the mixture. The distinction between heat and temperature is implicitly expressed in the last sentence of his report.


Evaporative cooling

In 1748, an account was published in ''The Edinburgh Physical and Literary Essays'' of an experiment by the Scottish physician and chemist
William Cullen William Cullen (; 15 April 17105 February 1790) was a British physician, chemist and agriculturalist from Hamilton, Scotland, who also served as a professor at the Edinburgh Medical School. Cullen was a central figure in the Scottish Enli ...
. Cullen had used an
air pump An air pump is a pump for pushing air. Examples include a bicycle pump, pumps that are used to aerate an aquarium or a pond via an airstone; a gas compressor used to power a pneumatic tool, air horn or pipe organ; a bellows used to encoura ...
to lower the pressure in a container with
diethyl ether Diethyl ether, or simply ether, is an organic compound with the chemical formula , sometimes abbreviated as . It is a colourless, highly Volatility (chemistry), volatile, sweet-smelling ("ethereal odour"), extremely flammable liquid. It belongs ...
. The ether boiled, while no heat was withdrawn from it, and its temperature decreased. And in 1758 on a warm day in
Cambridge Cambridge ( ) is a List of cities in the United Kingdom, city and non-metropolitan district in the county of Cambridgeshire, England. It is the county town of Cambridgeshire and is located on the River Cam, north of London. As of the 2021 Unit ...
, England,
Benjamin Franklin Benjamin Franklin (April 17, 1790) was an American polymath: a writer, scientist, inventor, statesman, diplomat, printer, publisher and Political philosophy, political philosopher.#britannica, Encyclopædia Britannica, Wood, 2021 Among the m ...
and fellow scientist
John Hadley John Hadley (16 April 1682 – 14 February 1744) was an England, English mathematician, and laid claim to the invention of the octant (instrument), octant, two years after Thomas Godfrey (inventor), Thomas Godfrey claimed the same. Biograp ...
experimented by continually wetting the ball of a mercury
thermometer A thermometer is a device that measures temperature (the hotness or coldness of an object) or temperature gradient (the rates of change of temperature in space). A thermometer has two important elements: (1) a temperature sensor (e.g. the bulb ...
with ether and using
bellows A bellows or pair of bellows is a device constructed to furnish a strong blast of air. The simplest type consists of a flexible bag comprising a pair of rigid boards with handles joined by flexible leather sides enclosing an approximately airtig ...
to evaporate the ether. With each subsequent
evaporation Evaporation is a type of vaporization that occurs on the Interface (chemistry), surface of a liquid as it changes into the gas phase. A high concentration of the evaporating substance in the surrounding gas significantly slows down evapora ...
, the thermometer read a lower temperature, eventually reaching .


Discovery of specific heat

In 1756 or soon thereafter, Joseph Black, Cullen’s friend and former assistant, began an extensive study of heat. In 1760 Black realized that when two different substances of equal mass but different temperatures are mixed, the changes in number of degrees in the two substances differ, though the heat gained by the cooler substance and lost by the hotter is the same. Black related an experiment conducted by
Daniel Gabriel Fahrenheit Daniel Gabriel Fahrenheit FRS (; ; 24 May 1686 – 16 September 1736) was a physicist, inventor, and scientific instrument maker, born in Poland to a family of German extraction. Fahrenheit invented thermometers accurate and consistent enough t ...
on behalf of Dutch physician
Herman Boerhaave Herman Boerhaave (, 31 December 1668 – 23 September 1738Underwood, E. Ashworth. "Boerhaave After Three Hundred Years." ''The British Medical Journal'' 4, no. 5634 (1968): 820–25. .) was a Dutch chemist, botanist, Christian humanist, and ph ...
. For clarity, he then described a hypothetical but realistic variant of the experiment: If equal masses of 100 °F water and 150 °F mercury are mixed, the water temperature increases by 20 ° and the mercury temperature decreases by 30 ° (both arriving at 120 °F), even though the heat gained by the water and lost by the mercury is the same. This clarified the distinction between heat and temperature. It also introduced the concept of
specific heat capacity In thermodynamics, the specific heat capacity (symbol ) of a substance is the amount of heat that must be added to one unit of mass of the substance in order to cause an increase of one unit in temperature. It is also referred to as massic heat ...
, being different for different substances. Black wrote: "Quicksilver ercury... has less capacity for the matter of heat than water."


Degrees of heat

In his investigations of specific heat, Black used a unit of heat he called "degrees of heat"—as opposed to just "degrees" f temperature This unit was context-dependent and could only be used when circumstances were identical. It was based on change in temperature multiplied by the mass of the substance involved.


Discovery of latent heat

It was known that when the air temperature rises above freezing—air then becoming the obvious heat source—snow melts very slowly and the temperature of the melted snow is close to its freezing point. In 1757, Black started to investigate if heat, therefore, was required for the melting of a solid, independent of any rise in temperature. As far Black knew, the general view at that time was that melting was inevitably accompanied by a small increase in temperature, and that no additional heat was needed beyond what this increase in temperature would require in itself. Soon, however, Black was able to show that much more heat was required during melting than could be explained by any increase in temperature alone. He was also able to show that heat is ''released'' by a liquid during its freezing; again, much more than could be explained by the decrease of its temperature alone. In 1762, Black announced the following research and results to a society of professors at the University of Glasgow. Black had placed equal masses of ice at 32 °F (0 °C) and water at 33 °F (0.6 °C) respectively in two identical, well separated containers. The water and the ice were both evenly heated to 40 °F by the air in the room, which was at a constant 47 °F (8 °C). The water had therefore received 40 – 33 = 7 “degrees of heat”. The ice had been heated for 21 times longer and had therefore received 7 × 21 = 147 “degrees of heat”. The temperature of the ice had increased by 8 °F. The ice had thus absorbed 8 “degrees of heat”, which Black called ''sensible heat'', manifest as temperature change, which could be felt and measured. In addition to that, 147 – 8 = 139 “degrees of heat” were absorbed as ''latent heat'', manifest as phase change rather than as temperature change. Black next showed that a water temperature of 176 °F was needed to melt an equal mass of ice until it was all 32 °F. So now 176 – 32 = 144 “degrees of heat” seemed to be needed to melt the ice. The modern value for the heat of fusion of ice would be 143 “degrees of heat” on the same scale (79.5 “degrees of heat Celsius”). Finally, Black increased the temperature of a mass of water, then vaporized an equal mass of water by even heating. He showed that 830 “degrees of heat” was needed for the vaporization; again based on the time required. The modern value for the heat of vaporization of water would be 967 “degrees of heat” on the same scale.


First calorimeter

A calorimeter is a device used for measuring
heat capacity Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The SI unit of heat capacity is joule per kelvin (J/K). Heat capacity is a ...
, as well as the heat absorbed or released in
chemical reactions A chemical reaction is a process that leads to the chemical transformation of one set of chemical substances to another. When chemical reactions occur, the atoms are rearranged and the reaction is accompanied by an energy change as new products ...
or physical changes. In 1780, French chemist
Antoine Lavoisier Antoine-Laurent de Lavoisier ( ; ; 26 August 17438 May 1794), When reduced without charcoal, it gave off an air which supported respiration and combustion in an enhanced way. He concluded that this was just a pure form of common air and that i ...
used such an apparatus—which he named 'calorimeter'—to investigate the heat released by
respiration Respiration may refer to: Biology * Cellular respiration, the process in which nutrients are converted into useful energy in a cell ** Anaerobic respiration, cellular respiration without oxygen ** Maintenance respiration, the amount of cellul ...
, by observing how this heat melted snow surrounding his apparatus. A so called ''ice calorimeter'' was used 1782–83 by Lavoisier and his colleague
Pierre-Simon Laplace Pierre-Simon, Marquis de Laplace (; ; 23 March 1749 – 5 March 1827) was a French polymath, a scholar whose work has been instrumental in the fields of physics, astronomy, mathematics, engineering, statistics, and philosophy. He summariz ...
to measure the heat released in various chemical reactions. The heat so released melted a specific amount of ice, and the heat required for the melting of a certain amount of ice was known beforehand.


Classical thermodynamics

The modern understanding of heat is often partly attributed to Thompson's 1798
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. Due to the relevance of thermodynamics in much of science and technology, its history is finely wove ...
(" An Inquiry Concerning the Source of the Heat Which Is Excited by Friction"), postulating a
mechanical equivalent of heat In the history of science, the mechanical equivalent of heat states that motion and heat are mutually interchangeable and that in every case, a given amount of work would generate the same amount of heat, provided the work done is totally convert ...
. A collaboration between
Nicolas Clément Nicolas Clément (12 January 1779 – 21 November 1841) was a French physicist and chemist. He was a colleague of Charles Desormes, with whom he conducted the Clément-Desormes experiment. The two chemists are also credited with determining a ...
and Sadi Carnot (''
Reflections on the Motive Power of Fire ''Reflections on the Motive Power of Fire and on Machines Fitted to Develop that Power'' () is a scientific treatise written by the French military engineer Sadi Carnot.full text of 1897 ed. ( Full text of 1897 edition on Wikisource ) Publis ...
'') in the 1820s had some related thinking along similar lines. In 1842, Julius Robert Mayer frictionally generated heat in paper pulp and measured the temperature rise. 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", based on heat production by friction in the passage of electricity through a resistor and in the rotation of a paddle in a vat of water. The theory of classical thermodynamics matured in the 1850s to 1860s.


Clausius (1850)

In 1850, Clausius, responding to Joule's experimental demonstrations of heat production by friction, rejected the caloric doctrine of conservation of heat, writing: The process function was introduced by
Rudolf Clausius Rudolf Julius Emanuel Clausius (; 2 January 1822 – 24 August 1888) was a German physicist and mathematician and is considered one of the central founding fathers of the science of thermodynamics. By his restatement of Sadi Carnot's principle ...
in 1850. Clausius described it with the German compound ''Wärmemenge'', translated as "amount of heat".


James Clerk Maxwell (1871)

James Clerk Maxwell James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish physicist and mathematician who was responsible for the classical theory of electromagnetic radiation, which was the first theory to describe electricity, magnetism an ...
in his 1871 ''Theory of Heat'' outlines four stipulations for the definition of heat: * It is ''something which may be transferred from one body to another'', according to the
second law of thermodynamics The second law of thermodynamics is a physical law based on Universal (metaphysics), universal empirical observation concerning heat and Energy transformation, energy interconversions. A simple statement of the law is that heat always flows spont ...
. * 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 science, work is the energy transferred to or from an object via the application of force along a displacement. In its simplest form, for a constant force aligned with the direction of motion, the work equals the product of the force stre ...
. * Heat is ''one of the forms of energy''.


Bryan (1907)

In 1907, G.H. Bryan published an investigation of the foundations of thermodynamics, ''Thermodynamics: an Introductory Treatise dealing mainly with First Principles and their Direct Applications'', B.G. Teubner, Leipzig. Bryan was writing when thermodynamics had been established empirically, but people were still interested to specify its logical structure. The 1909 work of Carathéodory also belongs to this historical era. Bryan was a physicist while Carathéodory was a mathematician. Bryan started his treatise with an introductory chapter on the notions of heat and of temperature. He gives an example of where the notion of heating as raising a body's temperature contradicts the notion of heating as imparting a quantity of heat to that body. He defined an adiabatic transformation as one in which the body neither gains nor loses heat. This is not quite the same as defining an adiabatic transformation as one that occurs to a body enclosed by walls impermeable to radiation and conduction. He recognized calorimetry as a way of measuring quantity of heat. He recognized water as having a ''temperature of maximum density''. This makes water unsuitable as a thermometric substance around that temperature. He intended to remind readers of why thermodynamicists preferred an absolute scale of temperature, independent of the properties of a particular thermometric substance. His second chapter started with the recognition of friction as a source of heat, by
Benjamin Thompson Colonel (United Kingdom), Colonel Sir Benjamin Thompson, Count Rumford, Fellow of the Royal Society, FRS (26 March 175321 August 1814), was an American-born British military officer, scientist and inventor. Born in Woburn, Massachusetts, he sup ...
, by
Humphry Davy Sir Humphry Davy, 1st Baronet (17 December 177829 May 1829) was a British chemist and inventor who invented the Davy lamp and a very early form of arc lamp. He is also remembered for isolating, by using electricity, several Chemical element, e ...
, by Robert Mayer, and by
James Prescott Joule James Prescott Joule (; 24 December 1818 11 October 1889) was an English physicist. Joule studied the nature of heat and discovered its relationship to mechanical work. This led to the law of conservation of energy, which in turn led to the ...
. He stated the ''First Law of Thermodynamics'', or ''Mayer–Joule Principle'' as follows: He wrote: He explained how the caloric theory of Lavoisier and Laplace made sense in terms of pure calorimetry, though it failed to account for conversion of work into heat by such mechanisms as friction and conduction of electricity. Having rationally defined quantity of heat, he went on to consider the second law, including the Kelvin definition of absolute thermodynamic temperature. In section 41, he wrote: He then stated the principle of conservation of energy. He then wrote: On page 46, thinking of closed systems in thermal connection, he wrote: On page 47, still thinking of closed systems in thermal connection, he wrote: On page 48, he wrote:


Carathéodory (1909)

A celebrated and frequent definition of heat in thermodynamics is based on the work of Carathéodory (1909), referring to processes in a closed system. Carathéodory was responding to a suggestion by Max Born that he examine the logical structure of thermodynamics. The
internal energy The internal energy of a thermodynamic system is the energy of the system as a state function, measured as the quantity of energy necessary to bring the system from its standard internal state to its present internal state of interest, accoun ...
of a body in an arbitrary state can be determined by amounts of work adiabatically performed by the body on its surroundings when it starts from a reference state . Such work is assessed through quantities defined in the surroundings of the body. It is supposed that such work can be assessed accurately, without error due to friction in the surroundings; friction in the body is not excluded by this definition. The adiabatic performance of work is defined in terms of adiabatic walls, which allow transfer of energy as work, but no other transfer, of energy or matter. In particular they do not allow the passage of energy as heat. According to this definition, work performed adiabatically is in general accompanied by friction within the thermodynamic system or body. On the other hand, according to Carathéodory (1909), there also exist non-adiabatic, ''diathermal'' walls, which are postulated to be permeable only to heat. For the definition of quantity of energy transferred as heat, it is customarily envisaged that an arbitrary state of interest is reached from state by a process with two components, one adiabatic and the other not adiabatic. For convenience one may say that the adiabatic component was the sum of work done by the body through volume change through movement of the walls while the non-adiabatic wall was temporarily rendered adiabatic, and of isochoric adiabatic work. 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 from the state 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 heat, , to the body from its surroundings, in the combined process of change to state from the state , as the change in internal energy, , minus the amount of work, , done by the body on its surrounds by the adiabatic process, so that . In this definition, for the sake of conceptual 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 to the arbitrary state . 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 to state , 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 above. The 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 guarantee rigor and purity of conception. 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. Before the rigorous mathematical definition of heat based on Carathéodory's 1909 paper, historically, heat, temperature, and thermal equilibrium were presented in thermodynamics textbooks as jointly
primitive notion In mathematics, logic, philosophy, and formal systems, a primitive notion is a concept that is not defined in terms of previously-defined concepts. It is often motivated informally, usually by an appeal to Intuition (knowledge), intuition or taken ...
s. Carathéodory introduced his 1909 paper thus: "The proposition that the discipline of thermodynamics can be justified without recourse to any hypothesis that cannot be verified experimentally must be regarded as one of the most noteworthy results of the research in thermodynamics that was accomplished during the last century." Referring to the "point of view adopted by most authors who were active in the last fifty years", Carathéodory wrote: "There exists a physical quantity called heat that is not identical with the mechanical quantities (mass, force, pressure, etc.) and whose variations can be determined by calorimetric measurements."
James Serrin James Burton Serrin (1 November 1926, Chicago, Illinois – 23 August 2012, Minneapolis, Minnesota) was an American mathematician, and a professor at University of Minnesota. Life He graduated from Evanston Township High School in 1944. He then ...
introduces an account of the theory of thermodynamics thus: "In the following section, we shall use the classical notions of ''heat'', ''work'', and ''hotness'' as primitive elements, ... That heat is an appropriate and natural primitive for thermodynamics was already accepted by Carnot. Its continued validity as a primitive element of thermodynamical structure is due to the fact that it synthesizes an essential physical concept, as well as to its successful use in recent work to unify different constitutive theories." This traditional kind of presentation of the basis of thermodynamics includes ideas that may be summarized by the statement that heat transfer is purely due to spatial non-uniformity of temperature, and is by conduction and radiation, from hotter to colder bodies. It is sometimes proposed that this traditional kind of presentation necessarily rests on "
circular reasoning Circular reasoning (, "circle in proving"; also known as circular logic) is a fallacy, logical fallacy in which the reasoner begins with what they are trying to end with. Circular reasoning is not a formal logical fallacy, but a pragmatic defect ...
". This alternative approach to the definition of quantity of energy transferred as heat differs in logical structure from that of Carathéodory, recounted just above. This alternative approach admits calorimetry as a primary or direct way to measure quantity of energy transferred as heat. It relies on temperature as one of its primitive concepts, and used in calorimetry. It is presupposed that enough processes exist physically to allow measurement of differences in internal energies. Such processes are not restricted to adiabatic transfers of energy as work. They include calorimetry, which is the commonest practical way of finding internal energy differences. The needed temperature can be either empirical or absolute thermodynamic. In contrast, the Carathéodory way recounted just above does not use calorimetry or temperature in its primary definition of quantity of energy transferred as heat. The Carathéodory way regards calorimetry only as a secondary or indirect way of measuring quantity of energy transferred as heat. As recounted in more detail just above, the Carathéodory way regards quantity of energy transferred as heat in a process as primarily or directly defined as a residual quantity. It is calculated from the difference of the internal energies of the initial and final states of the system, and from the actual work done by the system during the process. That internal energy difference is supposed to have been measured in advance through processes of purely adiabatic transfer of energy as work, processes that take the system between the initial and final states. By the Carathéodory way it is presupposed as known from experiment that there actually physically exist enough such adiabatic processes, so that there need be no recourse to calorimetry for measurement of quantity of energy transferred as heat. This presupposition is essential but is explicitly labeled neither as a law of thermodynamics nor as an axiom of the Carathéodory way. In fact, the actual physical existence of such adiabatic processes is indeed mostly supposition, and those supposed processes have in most cases not been actually verified empirically to exist.


Planck (1926)

Over the years, for example in his 1879 thesis, but particularly in 1926, Planck advocated regarding the generation of heat by rubbing as the most specific way to define heat. Planck criticised Carathéodory for not attending to this. Carathéodory was a mathematician who liked to think in terms of adiabatic processes, and perhaps found friction too tricky to think about, while Planck was a physicist.


Heat transfer


Heat transfer between two bodies

Referring to conduction,
Partington Partington is a town and civil parish in the Metropolitan Borough of Trafford, Greater Manchester, England. It is sited south-west of Manchester city centre. Within the boundaries of the Historic counties of England, historic county of Ches ...
writes: "If a hot body is brought in conducting contact with a cold body, the temperature of the hot body falls and that of the cold body rises, and it is said that a ''quantity of heat'' has passed from the hot body to the cold body." Referring to radiation,
Maxwell Maxwell may refer to: People * Maxwell (surname), including a list of people and fictional characters with the name ** James Clerk Maxwell, mathematician and physicist * Justice Maxwell (disambiguation) * Maxwell baronets, in the Baronetage of N ...
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 is the energy of the system as a state function, measured as the quantity of energy necessary to bring the system from its standard internal state to its present internal state of interest, accoun ...
. 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 A heat engine is a system that transfers thermal energy to do mechanical or electrical work. While originally conceived in the context of mechanical energy, the concept of the heat engine has been applied to various other kinds of energy, pa ...
. 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 device that uses electricity to transfer heat from a colder place to a warmer place. Specifically, the heat pump transfers thermal energy using a heat pump and refrigeration cycle, cooling the cool space and warming the warm s ...
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 theoretical physicist whose discovery of energy quanta won him the Nobel Prize in Physics in 1918. Planck made many substantial contributions to theoretical p ...
, there are three main conceptual approaches to heat. One is the microscopic or kinetic theory approach. The other two are macroscopic approaches. One of the macroscopic approaches is 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-British theoretical physicist who was instrumental in the development of quantum mechanics. He also made contributions to solid-state physics and optics, and supervised the work of a ...
. It regards quantity of heat transferred as heat as a derived concept, defined for closed systems as quantity of heat transferred by mechanisms other than work transfer, the latter being regarded as primitive for thermodynamics, defined by macroscopic mechanics. According to Born, the transfer of internal energy between open systems that accompanies transfer of matter "cannot be reduced to mechanics". Born, M. (1949), p. 44. It follows that there is no well-founded definition of quantities of energy transferred as heat or as work associated with transfer of matter. Nevertheless, for the thermodynamical description of non-equilibrium processes, it is desired to consider the effect of a temperature gradient established by the surroundings across the system of interest when there is no physical barrier or wall between system and surroundings, that is to say, when they are open with respect to one another. The impossibility of a mechanical definition in terms of work for this circumstance does not alter the physical fact that a temperature gradient causes a diffusive flux of internal energy, a process that, in the thermodynamic view, might be proposed as a candidate concept for transfer of energy as heat. In this circumstance, it may be expected that there may also be active other drivers of diffusive flux of internal energy, such as gradient of chemical potential which drives transfer of matter, and gradient of electric potential which drives electric current and iontophoresis; such effects usually interact with diffusive flux of internal energy driven by temperature gradient, and such interactions are known as cross-effects. If cross-effects that result in diffusive transfer of internal energy were also labeled as heat transfers, they would sometimes violate the rule that pure heat transfer occurs only down a temperature gradient, never up one. They would also contradict the principle that all heat transfer is of one and the same kind, a principle founded on the idea of heat conduction between closed systems. One might to try to think narrowly of heat flux driven purely by temperature gradient as a conceptual component of diffusive internal energy flux, in the thermodynamic view, the concept resting specifically on careful calculations based on detailed knowledge of the processes and being indirectly assessed. In these circumstances, if perchance it happens that no transfer of matter is actualized, and there are no cross-effects, then the thermodynamic concept and the mechanical concept coincide, as if one were dealing with closed systems. But when there is transfer of matter, the exact laws by which temperature gradient drives diffusive flux of internal energy, rather than being exactly knowable, mostly need to be assumed, and in many cases are practically unverifiable. Consequently, when there is transfer of matter, the calculation of the pure 'heat flux' component of the diffusive flux of internal energy rests on practically unverifiable assumptions.Denbigh states in a footnote that he is indebted to correspondence with Professor E.A. Guggenheim and with Professor N.K. Adam. From this, Denbigh concludes "It seems, however, that when a system is able to exchange both heat and matter with its environment, it is impossible to make an unambiguous distinction between energy transported as heat and by the migration of matter, without already assuming the existence of the 'heat of transport'." Denbigh K.G. (1951), p. 56. This is a reason to think of heat as a specialized concept that relates primarily and precisely to closed systems, and applicable only in a very restricted way to open systems. In many writings in this context, the term "heat flux" is used when what is meant is therefore more accurately called diffusive flux of internal energy; such usage of the term "heat flux" is a residue of older and now obsolete language usage that allowed that a body may have a "heat content".


Microscopic view

In the kinetic theory, 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) was an English philosopher and statesman who served as Attorney General and Lord Chancellor of England under King James I. Bacon argued for the importance of nat ...
. Precise and detailed versions of it were developed in the nineteenth century. In
statistical mechanics In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applicati ...
, for a closed system (no transfer of matter), heat is the energy transfer associated with a disordered, microscopic action on the system, associated with jumps in occupation numbers of the energy levels of the system, without change in the values of the energy levels themselves. It is possible for macroscopic thermodynamic work to alter the occupation numbers without change in the values of the system energy levels themselves, but what distinguishes transfer as heat is that the transfer is entirely due to disordered, microscopic action, including radiative transfer. A mathematical definition can be formulated for small increments of quasi-static adiabatic work in terms of the statistical distribution of an ensemble of microstates.


Calorimetry

Quantity of heat transferred can be measured by calorimetry, or determined through calculations based on other quantities. Calorimetry is the empirical basis of the idea of quantity of heat transferred in a process. The transferred heat is measured by changes in a body of known properties, for example, temperature rise, change in volume or length, or phase change, such as melting of ice. A calculation of quantity of heat transferred can rely on a hypothetical quantity of energy transferred as adiabatic work and on the
first law of thermodynamics The first law of thermodynamics is a formulation of the law of conservation of energy in the context of thermodynamic processes. For a thermodynamic process affecting a thermodynamic system without transfer of matter, the law distinguishes two ...
. 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 the study of physical machines and mechanism (engineering), mechanisms that may involve force and movement. It is an engineering branch that combines engineering physics and engineering mathematics, mathematics principl ...
and
chemical engineering Chemical engineering is an engineering field which deals with the study of the operation and design of chemical plants as well as methods of improving production. Chemical engineers develop economical commercial processes to convert raw materials ...
, 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 diffusion of thermal energy (heat) within one material or between materials in contact. The higher temperature object has molecules with more kinetic energy; collisions between molecules distributes this kinetic energy 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 emitted by the thermal motion of particles in matter. All matter with a temperature greater than absolute zero emits thermal radiation. The emission of energy arises from a combination of electro ...
, 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, evaporation, drying, precipitation, membrane filtra ...
and heat in processes of
phase changes In physics, chemistry, and other related fields like biology, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic s ...
. 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. Joule studied the nature of heat and discovered its relationship to mechanical work. This led to the law of conservation of energy, which in turn led to the ...
characterized the terms
latent heat Latent heat (also known as latent energy or heat of transformation) is energy released or absorbed, by a body or a thermodynamic system, during a constant-temperature process—usually a first-order phase transition, like melting or condensation. ...
and
sensible heat Sensible heat is heat exchanged by a body or thermodynamic system in which the exchange of heat changes the temperature of the body or system, and some macroscopic variables of the body or system, but leaves unchanged certain other macroscopic vari ...
as components of heat each affecting distinct physical phenomena, namely the potential and kinetic energy of particles, respectively."Heat must therefore consist of either living force or of attraction through space. In the former case we can conceive the constituent particles of heated bodies to be, either in whole or in part, in a state of motion. In the latter we may suppose the particles to be removed by the process of heating, so as to exert attraction through greater space. I am inclined to believe that both of these hypotheses will be found to hold good,—that in some instances, particularly in the case of sensible heat, or such as is indicated by the thermometer, heat will be found to consist in the living force of the particles of the bodies in which it is induced; whilst in others, particularly in the case of latent heat, the phenomena are produced by the separation of particle from particle, so as to cause them to attract one another through a greater space." Joule, J.P. (1884). He described latent energy as the energy possessed via a distancing of particles where attraction was over a greater distance, i.e. a form of
potential energy In physics, potential energy is the energy of an object or system due to the body's position relative to other objects, or the configuration of its particles. The energy is equal to the work done against any restoring forces, such as gravity ...
, and the sensible heat as an energy involving the motion of particles, i.e.
kinetic energy In physics, the kinetic energy of an object is the form of energy that it possesses due to its motion. In classical mechanics, the kinetic energy of a non-rotating object of mass ''m'' traveling at a speed ''v'' is \fracmv^2.Resnick, Rober ...
. Latent heat is the heat released or absorbed by a
chemical substance A chemical substance is a unique form of matter with constant chemical composition and characteristic properties. Chemical substances may take the form of a single element or chemical compounds. If two or more chemical substances can be com ...
or a
thermodynamic system A thermodynamic system is a body of matter and/or radiation separate from its surroundings that can be studied using the laws of thermodynamics. Thermodynamic systems can be passive and active according to internal processes. According to inter ...
during a change of
state State most commonly refers to: * State (polity), a centralized political organization that regulates law and society within a territory **Sovereign state, a sovereign polity in international law, commonly referred to as a country **Nation state, a ...
that occurs without a change in temperature. Such a process may be a
phase transition In physics, chemistry, and other related fields like biology, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic Sta ...
, 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 of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The SI unit of heat capacity is joule per kelvin (J/K). Heat capacity is a ...
is a
measurable In mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notions, such as magnitude, mass, and probability of events. These seemingly distinct concepts hav ...
physical quantity A physical quantity (or simply quantity) is a 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 ''nu ...
equal to the ratio of the heat added to an object to the resulting
temperature Temperature is a physical quantity that quantitatively expresses the attribute of hotness or coldness. Temperature is measurement, measured with a thermometer. It reflects the average kinetic energy of the vibrating and colliding atoms making ...
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" * Golden mole, southern African mammals * Marsupial mole Marsupial moles, the Notoryctidae family, are two species of highly specialized marsupial mammals that are found i ...
) of a pure substance, and the ''specific heat capacity'', often called simply ''specific heat'', is the heat capacity per unit mass of a material. Heat capacity is a physical property of a substance, which means that it depends on the state and properties of the substance under consideration. The specific heats of monatomic gases, such as helium, are nearly constant with temperature. Diatomic gases such as hydrogen display some temperature dependence, and triatomic gases (e.g., carbon dioxide) still more. Before the development of the laws of thermodynamics, heat was measured by changes in the states of the participating bodies. Some general rules, with important exceptions, can be stated as follows. In general, most bodies expand on heating. In this circumstance, heating a body at a constant volume increases the pressure it exerts on its constraining walls, while heating at a constant pressure increases its volume. Beyond this, most substances have three ordinarily recognized
states of matter In physics, a state of matter is one of the distinct forms in which matter can exist. Four states of matter are observable in everyday life: solid, liquid, gas, and plasma. Different states are distinguished by the ways the component parti ...
, solid, liquid, and gas. Some can also exist in a plasma. Many have further, more finely differentiated, states of matter, such as
glass Glass is an amorphous (non-crystalline solid, non-crystalline) solid. Because it is often transparency and translucency, transparent and chemically inert, glass has found widespread practical, technological, and decorative use in window pane ...
and
liquid crystal Liquid crystal (LC) is a state of matter whose properties are between those of conventional liquids and those of solid crystals. For example, a liquid crystal can flow like a liquid, but its molecules may be oriented in a common direction as i ...
. 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 Phase or phases may refer to: Science *State of matter, or phase, one of the distinct forms in which matter can exist *Phase (matter), a region of space throughout which all physical properties are essentially uniform *Phase space, a mathematica ...
within the 'body'. Definite
rules Rule or ruling may refer to: Human activity * The exercise of political or personal control by someone with authority or power * Business rule, a rule pertaining to the structure or behavior internal to a business * School rule, a rule tha ...
are known, telling how distinct phases may coexist in a 'body'. Mostly, at a fixed pressure, there is a definite temperature at which heating causes a solid to melt or evaporate, and a definite temperature at which heating causes a liquid to evaporate. In such cases, cooling has the reverse effects. All of these, the commonest cases, fit with a rule that heating can be measured by changes of state of a body. Such cases supply what are called ''thermometric bodies'', that allow the definition of empirical temperatures. Before 1848, all temperatures were defined in this way. There was thus a tight link, apparently logically determined, between heat and temperature, though they were recognized as conceptually thoroughly distinct, especially by
Joseph Black Joseph Black (16 April 1728 – 6 December 1799) was a British 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 Glasgow ...
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. Founding the Wedgwood company in 1759, he developed improved pottery bodies by systematic experimentation, and was the leader in the indu ...
in his
pyrometer A pyrometer, or radiation thermometer, 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 de ...
. The temperature reached in a process was estimated by the shrinkage of a sample of clay. The higher the temperature, the more the shrinkage. This was the only available more or less reliable method of measurement of temperatures above 1000 °C (1,832 °F). But such shrinkage is irreversible. The clay does not expand again on cooling. That is why it could be used for the measurement. But only once. It is not a thermometric material in the usual sense of the word. Nevertheless, the thermodynamic definition of absolute temperature does make essential use of the concept of heat, with proper circumspection.


"Hotness"

The property of hotness is a concern of thermodynamics that should be defined without reference to the concept of heat. Consideration of hotness leads to the concept of empirical temperature. All physical systems are capable of heating or cooling others. With reference to hotness, the comparative terms hotter and colder are defined by the rule that heat flows from the hotter body to the colder. If a physical system is inhomogeneous or very rapidly or irregularly changing, for example by turbulence, it may be impossible to characterize it by a temperature, but still there can be transfer of energy as heat between it and another system. If a system has a physical state that is regular enough, and persists long enough to allow it to reach thermal equilibrium with a specified thermometer, then it has a temperature according to that thermometer. An empirical thermometer registers degree of hotness for such a system. Such a temperature is called empirical. For example, Truesdell writes about classical thermodynamics: "At each time, the body is assigned a real number called the ''temperature''. This number is a measure of how hot the body is." Physical systems that are too turbulent to have temperatures may still differ in hotness. A physical system that passes heat to another physical system is said to be the hotter of the two. More is required for the system to have a thermodynamic temperature. Its behavior must be so regular that its empirical temperature is the same for all suitably calibrated and scaled thermometers, and then its hotness is said to lie on the one-dimensional hotness manifold. This is part of the reason why heat is defined following Carathéodory and Born, solely as occurring other than by work or transfer of matter; temperature is advisedly and deliberately not mentioned in this now widely accepted definition. This is also the reason that the
zeroth law of thermodynamics The zeroth law of thermodynamics is one of the four principal laws of thermodynamics. It provides an independent definition of temperature without reference to entropy, which is defined in the second law. The law was established by Ralph H. Fowl ...
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 The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Sola ...
' 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.


Classical thermodynamics


Heat and enthalpy

For a
closed system A closed system is a natural physical system that does not allow transfer of matter in or out of the system, althoughin the contexts of physics, chemistry, engineering, etc.the transfer of energy (e.g. as work or heat) is allowed. Physics In cl ...
(a system from which no matter can enter or exit), one version of the
first law of thermodynamics The first law of thermodynamics is a formulation of the law of conservation of energy in the context of thermodynamic processes. For a thermodynamic process affecting a thermodynamic system without transfer of matter, the law distinguishes two ...
states that the change in
internal energy The internal energy of a thermodynamic system is the energy of the system as a state function, measured as the quantity of energy necessary to bring the system from its standard internal state to its present internal state of interest, accoun ...
of the system is equal to the amount of heat supplied to the system minus the amount of
thermodynamic work Thermodynamic work is one of the principal kinds of process by which a thermodynamic system can interact with and transfer energy to its surroundings. This results in externally measurable macroscopic forces on the system's surroundings, which c ...
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 and a Fellow of Lincoln College at the University of Oxford. He retired in 2007. He is a prolific writer of popular chemistry textbooks, including ''Physical Chemistry'', ''Ino ...
and Ira Levine, but many textbooks on physics define work as work done by the system. \Delta U = Q - W \, . This formula can be re-written so as to express a definition of quantity of energy transferred as heat, based purely on the concept of adiabatic work, if it is supposed that is defined and measured solely by processes of adiabatic work: Q = \Delta U + W. The thermodynamic work done by the system is through mechanisms defined by its thermodynamic state variables, for example, its volume , not through variables that necessarily involve mechanisms in the surroundings. The latter are such as shaft work, and include isochoric work. The internal energy, , is a
state function In the thermodynamics of equilibrium, a state function, function of state, or point function for a thermodynamic system is a mathematical function relating several state variables or state quantities (that describe equilibrium states of a syste ...
. 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 (infinitesimal), differential or differential form is said to be exact or perfect (''exact differential''), as contrasted with an inexact differential, if it is equal to the general differential dQ for som ...
. The symbol for
exact differential In multivariate calculus, a differential (infinitesimal), differential or differential form is said to be exact or perfect (''exact differential''), as contrasted with an inexact differential, if it is equal to the general differential dQ for som ...
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 differential whose integral is path dependent. It is most often used in thermodynamics to express changes in path dependent quantities such as heat and work, but is defined more generally wit ...
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 (infinitesimal), differential or differential form is said to be exact or perfect (''exact differential''), as contrasted with an inexact differential, if it is equal to the general differential dQ for som ...
\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 essential ...
is written asAdkins, C.J. (1983), p. 101. U=U(S,V). If is constant T\mathrmS=\mathrmU\,\,\,\,\,\,\,\,\,\,\,\,(V\,\, \text and if is constant T\mathrmS=\mathrmH\,\,\,\,\,\,\,\,\,\,\,\,(P\,\, \text with the enthalpy defined by H=U+PV. The enthalpy may be considered to be a function of its natural variables and . The enthalpy representation of the fundamental thermodynamic relation is written Callen, H.B. (1985), p. 147. H=H(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. 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(PV)\,. 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 (PV) = 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(\frac\right)_P \mathrm dS +\int_^ \left(\frac\right)_S \mathrm dP \\ &=\int_^ \left(\frac\right)_P \mathrm dS\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \text \end It is known that the temperature is identically stated by \left(\frac\right)_P \equiv T(S,P)\,. Consequently, \Delta H=\int_^ T(S,P) \mathrm dS\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \text In this case, the integral specifies a quantity of heat transferred at constant pressure.


Heat and entropy

In 1856,
Rudolf Clausius Rudolf Julius Emanuel Clausius (; 2 January 1822 – 24 August 1888) was a German physicist and mathematician and is considered one of the central founding fathers of the science of thermodynamics. By his restatement of Sadi Carnot's principle ...
, referring to closed systems, in which transfers of matter do not occur, defined the ''second fundamental theorem'' (the
second law of thermodynamics The second law of thermodynamics is a physical law based on Universal (metaphysics), universal empirical observation concerning heat and Energy transformation, energy interconversions. A simple statement of the law is that heat always flows spont ...
) 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. Due to the relevance of thermodynamics in much of science and technology, its history is finely wove ...
(
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 b ...
): "if two transformations which, without necessitating any other permanent change, can mutually replace one another, be called equivalent, then the generations of the quantity of heat ''Q'' from
work Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical work done by humans ** House work, housework, or homemaking ** Working animal, an ani ...
at the temperature ''T'', has the ''equivalence-value'':" \frac . In 1865, he came to define the
entropy Entropy is a scientific concept, most commonly associated with states of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the micros ...
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' +\Delta S'' . This may also be written \Delta S_ = \Delta S_+\Delta S_\,\,\,\,\text\,\,\,\,\Delta S_=-\Delta S_. The total change of entropy in the system and surroundings is thus \Delta S_ = \Delta S^\prime+\Delta S^-\Delta S^\prime=\Delta S^ . This may also be written \Delta S_ = \Delta S_+\Delta S_+\Delta S_=\Delta S_ . It is then said that an amount of entropy has been transferred from the surroundings to the system. Because entropy is not a conserved quantity, this is an exception to the general way of speaking, in which an amount transferred is of a conserved quantity. From the second law of thermodynamics it follows that in a spontaneous transfer of heat, in which the temperature of the system is different from that of the surroundings: \Delta S_ > 0 . For purposes of mathematical analysis of transfers, one thinks of fictive processes that are called ''reversible'', with the temperature of the system being hardly less than that of the surroundings, and the transfer taking place at an imperceptibly slow rate. Following the definition above in formula (), for such a fictive reversible process, a quantity of transferred heat (an
inexact differential An inexact differential or imperfect differential is a differential whose integral is path dependent. It is most often used in thermodynamics to express changes in path dependent quantities such as heat and work, but is defined more generally wit ...
) is analyzed as a quantity , with (an
exact differential In multivariate calculus, a differential (infinitesimal), differential or differential form is said to be exact or perfect (''exact differential''), as contrasted with an inexact differential, if it is equal to the general differential dQ for som ...
): T\,\mathrmS=\delta Q . This equality is only valid for a fictive transfer in which there is no production of entropy, that is to say, in which there is no uncompensated entropy. If, in contrast, the process is natural, and can really occur, with irreversibility, then there is
entropy production Entropy production (or generation) is the amount of entropy which is produced during heat process to evaluate the efficiency of the process. Short history Entropy is produced in irreversible processes. The importance of avoiding irreversible p ...
, with . The quantity was termed by Clausius the "uncompensated heat", though that does not accord with present-day terminology. Then one has T_\,\mathrmS=\delta Q+T\,\mathrmS_ > \delta Q . This leads to the statement T_\,\mathrmS \geq \delta Q \quad \text\,. which is the
second law of thermodynamics The second law of thermodynamics is a physical law based on Universal (metaphysics), universal empirical observation concerning heat and Energy transformation, energy interconversions. A simple statement of the law is that heat always flows spont ...
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 thatLebon, g., Jou, D., Casas-Vásquez, J. (2008), p. 41. \mathrm d S_ > 0 .


See also

*
Effect of sun angle on climate The amount of heat energy received at any location on the globe is a direct effect of Sun angle on climate, as the angle of incidence (optics), angle at which sunlight strikes Earth varies by location, time of day, and season due to Earth's orbit a ...
*
Heat death of the Universe The heat death of the universe (also known as the Big Chill or Big Freeze) is a scientific hypothesis regarding the ultimate fate of the universe which posits the universe will evolve to a state of no thermodynamic free energy and, having ...
*
Heat diffusion In mathematics and physics (more specifically thermodynamics), the heat equation is a parabolic partial differential equation. The theory of the heat equation was first developed by Joseph Fourier in 1822 for the purpose of modeling how a quanti ...
*
Heat equation In mathematics and physics (more specifically thermodynamics), the heat equation is a parabolic partial differential equation. The theory of the heat equation was first developed by Joseph Fourier in 1822 for the purpose of modeling how a quanti ...
*
Heat exchanger A heat exchanger is a system used to transfer heat between a source and a working fluid. Heat exchangers are used in both cooling and heating processes. The fluids may be separated by a solid wall to prevent mixing or they may be in direct contac ...
*
Heat flux sensor ] A heat flux sensor is a transducer that generates an electrical signal proportional to the total heat transfer, heat rate applied to the surface of the sensor. The measured heat rate is divided by the surface area of the sensor to determine th ...
*
Heat recovery steam generator A heat recovery steam generator (HRSG) is a heat exchanger that recovers heat from a hot gas stream, such as a combustion turbine or other waste gas stream. It produces steam that can be used in a process (cogeneration) or used to drive a steam ...
*
Heat recovery ventilation Heat recovery ventilation (HRV), also known as mechanical ventilation heat recovery (MVHR) is a ventilation system that recovers energy by operating between two air sources at different temperatures. It is used to reduce the heating and cooling ...
*
Heat transfer coefficient In thermodynamics, the heat transfer coefficient or film coefficient, or film effectiveness, is the Proportional (mathematics), proportionality constant between the heat flux and the thermodynamic driving force for the Heat transfer, flow of heat ...
*
Heat wave A heat wave or heatwave, sometimes described as extreme heat, is a period of abnormally hot weather generally considered to be at least ''five consecutive days''. A heat wave is usually measured relative to the usual climate in the area and ...
*
History 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. Due to the relevance of thermodynamics in much of science and technology, its history is finely wove ...
*
Orders of magnitude (temperature) List of orders of magnitude for temperature Detailed list for 100 K to 1000 K Most ordinary human activity takes place at temperatures of this order of magnitude. Circumstances where water naturally occurs in liquid form are shown in light g ...
*
Relativistic heat conduction Relativistic heat conduction refers to the modelling of heat conduction (and similar diffusion processes) in a way compatible with special relativity. In special (and general) relativity, the usual heat equation for non-relativistic heat conductio ...
* Renewable heat *
Sigma heat Sigma heat, denoted S , is a measure of the specific energy of humid air. It is used in the field of mining engineering for calculations relating to the temperature regulation of mine air. Sigma heat is sometimes called ''total heat'', although t ...
*
Thermal energy storage Thermal energy storage (TES) is the storage of thermal energy for later reuse. Employing widely different technologies, it allows surplus thermal energy to be stored for hours, days, or months. Scale both of storage and use vary from small t ...
*
Thermal management of electronic devices and systems All electronic devices and circuitry generate excess heat and thus require thermal management to improve reliability and prevent premature failure. The amount of heat output is equal to the power input, if there are no other energy in ...
*
Thermometer A thermometer is a device that measures temperature (the hotness or coldness of an object) or temperature gradient (the rates of change of temperature in space). A thermometer has two important elements: (1) a temperature sensor (e.g. the bulb ...
*
Waste heat Waste heat is heat that is produced by a machine, or other process that uses energy, as a byproduct of doing work. All such processes give off some waste heat as a fundamental result of the laws of thermodynamics. Waste heat has lower utility ...
*
Waste heat recovery unit A waste heat recovery unit (WHRU) is an energy recovery heat exchanger that transfers heat from process outputs at high temperature to another part of the process for some purpose, usually increased efficiency. The WHRU is a tool involved in cog ...
* Water heat recycling


Notes


References


Quotations


Bibliography of cited references

* Adkins, C.J. (1968/1983). ''Equilibrium Thermodynamics'', (1st edition 1968), third edition 1983, Cambridge University Press, Cambridge UK, . * * Atkins, P., de Paula, J. (1978/2010). ''Physical Chemistry'', (first edition 1978), ninth edition 2010, Oxford University Press, Oxford UK, . * * * Bailyn, M. (1994). ''A Survey of Thermodynamics'', American Institute of Physics Press, New York, . * * * Born, M. (1949)
''Natural Philosophy of Cause and Chance''
Oxford University Press, London. * Bryan, G.H. (1907)
''Thermodynamics. An Introductory Treatise dealing mainly with First Principles and their Direct Applications''
B.G. Teubner, Leipzig. * Buchdahl, H.A. (1966). ''The Concepts of Classical Thermodynamics'', Cambridge University Press, Cambridge UK. * * Callen, H.B. (1960/1985). ''Thermodynamics and an Introduction to Thermostatistics'', (1st edition 1960) 2nd edition 1985, Wiley, New York, . * A translation may be foun
here
A mostly reliable translation is to be found at Kestin, J. (1976). ''The Second Law of Thermodynamics'', Dowden, Hutchinson & Ross, Stroudsburg PA. * Chandrasekhar, S. (1961). ''Hydrodynamic and Hydromagnetic Stability'', Oxford University Press, Oxford UK. * * Clausius, R. (1854). ''
Annalen der Physik ''Annalen der Physik'' (English: ''Annals of Physics'') is one of the oldest scientific journals on physics; it has been published since 1799. The journal publishes original, peer-reviewed papers on experimental, theoretical, applied, and mathem ...
'' (''Poggendoff's Annalen''), Dec. 1854, vol. xciii. p. 481; translated in the ''Journal de Mathematiques'', vol. xx. Paris, 1855, and in the ''Philosophical Magazine'', August 1856, s. 4. vol. xii, p. 81. * Clausius, R. (1865/1867)
''The Mechanical Theory of Heat – with its Applications to the Steam Engine and to Physical Properties of Bodies''
London: John van Voorst. 1867. Also the second edition translated into English by W.R. Browne (1879
here
an
here
* De Groot, S.R., Mazur, P. (1962). ''Non-equilibrium Thermodynamics'', North-Holland, Amsterdam. Reprinted (1984), Dover Publications Inc., New York, . * Denbigh, K. (1955/1981). ''The Principles of Chemical Equilibrium'', Cambridge University Press, Cambridge . * * Greven, A., Keller, G., Warnecke (editors) (2003). ''Entropy'', Princeton University Press, Princeton NJ, . * * * * * , Lecture on Matter, Living Force, and Heat. 5 and 12 May 1847. * Kittel, C. Kroemer, H. (1980). ''Thermal Physics'', second edition, W.H. Freeman, San Francisco, . * * Kondepudi, D., Prigogine, I. (1998). ''Modern Thermodynamics: From Heat Engines to Dissipative Structures'', John Wiley & Sons, Chichester, . * Landau, L., Lifshitz, E.M. (1958/1969)
''Statistical Physics''
volume 5 of ''Course of Theoretical Physics'', translated from the Russian by J.B. Sykes, M.J. Kearsley, Pergamon, Oxford. * * Lebon, G., Jou, D., Casas-Vázquez, J. (2008). ''Understanding Non-equilibrium Thermodynamics: Foundations, Applications, Frontiers'', Springer-Verlag, Berlin, e-. * Lieb, E.H., Yngvason, J. (2003). The Entropy of Classical Thermodynamics, Chapter 8 of ''Entropy'', Greven, A., Keller, G., Warnecke (editors) (2003). * * * * * Pippard, A.B. (1957/1966). ''Elements of Classical Thermodynamics for Advanced Students of Physics'', original publication 1957, reprint 1966, Cambridge University Press, Cambridge. * Planck, M., (1897/1903)
''Treatise on Thermodynamics''
translated by A. Ogg, first English edition, Longmans, Green and Co., London. * Planck. M. (1914)
''The Theory of Heat Radiation''
a translation by Masius, M. of the second German edition, P. Blakiston's Son & Co., Philadelphia. * Planck, M., (1923/1927). ''Treatise on Thermodynamics'', translated by A. Ogg, third English edition, Longmans, Green and Co., London. * * * Shavit, A., Gutfinger, C. (1995). ''Thermodynamics. From Concepts to Applications'', Prentice Hall, London, . * * Truesdell, C. (1969). ''Rational Thermodynamics: a Course of Lectures on Selected Topics'', McGraw-Hill Book Company, New York. * 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.


External links

*
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