In common language, English 'heat' or 'warmth', just as French chaleur, German Hitze or Wärme, Latin calor, Greek θάλπος, etc.

Black related an experiment conducted by Daniel Gabriel Fahrenheit on behalf of Dutch physician Herman Boerhaave.

[29][b] A so called ice calorimeter was used 1782–83 by Lavoisier and his colleague Pierre-Simon Laplace to measure the heat released in various chemical reactions.

A collaboration between Nicolas Clément and Sadi Carnot (Reflections on the Motive Power of Fire) in the 1820s had some related thinking along similar lines.

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, by Humphry Davy, by Robert Mayer, and by James Prescott Joule.

[36]He wrote: If heat be measured in dynamical units the mechanical equivalent becomes equal to unity, and the equations of thermodynamics assume a simpler and more symmetrical form.

[36]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.

][36]A celebrated and frequent definition of heat in thermodynamics is based on the work of Carathéodory (1909), referring to processes in a closed system.

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

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.

"[44][45] 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.

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.

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.

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.

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.

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.

The other macroscopic approach is the thermodynamic one, which admits heat as a primitive concept, which contributes, by scientific induction[56] to knowledge of the law of conservation of energy.

[63] In the kinetic theory, heat is explained in terms of the microscopic motions and interactions of constituent particles, such as electrons, atoms, and molecules.

In microscopic terms, heat is a transfer quantity, and is described by a transport theory, not as steadily localized kinetic energy of particles.

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.

There was thus a tight link, apparently logically determined, between heat and temperature, though they were recognized as conceptually thoroughly distinct, especially by Joseph Black in the later eighteenth century.

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'.

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.

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.

If this is constrained to happen at constant pressure, i.e. with ΔP = 0, the expansion work W done by the body is given by W = P ΔV; recalling the first law of thermodynamics, one has

Since many processes do take place at constant atmospheric pressure, the enthalpy is sometimes given the misleading name of 'heat content'[92] or heat function,[93] while it actually depends strongly on the energies of covalent bonds and intermolecular forces.

In 1856, Rudolf Clausius, referring to closed systems, in which transfers of matter do not occur, defined the second fundamental theorem (the second law of thermodynamics) in the mechanical theory of heat (thermodynamics): "if two transformations which, without necessitating any other permanent change, can mutually replace one another, be called equivalent, then the generations of the quantity of heat Q from work at the temperature T, has the equivalence-value:"[94][95]