In thermodynamics, heat is defined as energy in transfer between a body and its surroundings, other than through thermodynamic work or through transfer of matter.
Rather than by mechanical or other effects in the surroundings, thermodynamic work is defined through changes in the system's macroscopic state variables, in conjugate pairs such as pressure and volume, or magnetisation and magnetic field strength. The thermodynamic definition of heat is by exclusion of other defined modes of transfer in order to ensure a strict logical distinction.
In the process of transfer, heat is not necessarily conserved, but can be generated (though not destroyed) by friction. In thermodynamics, temperature is defined in macroscopic terms, through the concepts of heat and work. Heat is not a state variable or state function; it is a process quantity. A thermodynamic system does not contain heat.
Heat can enter or leave a body of matter by thermal conduction, by electromagnetic radiation, or through friction, due to macroscopic mechanical rubbing, drilling, grinding or stirring, or due to electrical resistance to the passage of electrical current through the body, known as Joule heating, or due to repeated magnetization and demagnetization. When heat is generated by friction, it may end up partly in each of the two engaged bodies. When energy enters or leaves a body through transfer of matter, it cannot be resolved uniquely into work and heat.
By assuming conservation of heat in a transfer, calorimetry measures it by its effect on the states of interacting bodies, for example, by the amount of ice melted or by change in temperature of a body.Maxwell, J.C. (1871), Chapter III.
In the International System of Units (SI), the unit of measurement for heat is the joule (J).
Notation and units As a form of energy, heat has the unit joule (J) in the International System of Units (SI). In addition, many applied branches of engineering use other, traditional units, such as the British thermal unit (BTU) and the calorie. The standard unit for the rate of heating is the watt (W), defined as one joule per second.
The symbol for heat was introduced by Rudolf Clausius and Macquorn Rankine in .Caneva, K.L. (2021). Helmholtz and the Conservation of Energy: Contexts of Creation and Reception. p. 562. (Macquorn Rankine in the same year used the same symbol. The two physicists were in correspondence at the time, so that it is difficult to say which of the two first introduced the symbol.)
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 , but it is not a time derivative of a function of state (which can also be written with the dot notation) since heat is not a function of state.Baierlein, R. (1999), p. 21. Heat flux is defined as rate of heat transfer per unit cross-sectional area (watts per square metre).
History
In ordinary language, English 'heat' or 'warmth', just as French chaleur, German Hitze or Wärme, Latin calor, Greek θάλπος, etc. refers to either thermal energy or temperature, 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 theory, the caloric theory, and fire. 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 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 (published 1623) Galileo Galilei, 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,: (Facsimile, with pagination): (Machine-readable, no pagination) and again in 1681, English polymath Robert Hooke reiterated that heat is nothing but the motion of the constituent particles of objects, and in 1675, his colleague, Anglo-Irish scientist Robert Boyle 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:
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. Also the transfer of heat was explained by the motion of particles. Scottish physicist and chemist Joseph Black 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'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 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. Cullen had used an air pump to lower the pressure in a container with diethyl ether. The ether boiled, while no heat was withdrawn from it, and its temperature decreased. And in 1758 on a warm day in Cambridge, England, Benjamin Franklin and fellow scientist John Hadley experimented by continually wetting the ball of a mercury thermometer with ether and using bellows to evaporate the ether. With each subsequent evaporation, 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 on behalf of Dutch physician Herman Boerhaave. 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, being different for different substances. Black wrote: "Quicksilver [mercury] ... 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" [of 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