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A form of energy associated with the motion (translational, rotational, or vibrational) of atoms and molecules. Heat is transferred as a result of a temperature difference, and is conducted through solid and fluid media by conduction, through fluid media by convection, and through empty space by radiation.

The heat contained by a body is the product of its mass, temperature, and specific heat, and is measured in calories or joules. (An older unit, the British thermal unit, or BTU, is still sometimes used in engineering applications, especially in the US.)

The chief observable physical effects of a change in the heat content of a body may include rise in temperature; change of state from solid to liquid (melting), solid to gas (sublimation), and liquid to gas (evaporation); expansion; and electrical effects such as the Peltier effect and Seebeck effect.

Development of ideas about heat

The scientific concept of heat is derived from our sense-perception, and the thermometer enables us to define a scale with which to measure its "intensity." Galileo invented the first thermometer and Amontons first used mercury. Different scales were introduced by Fahrenheit, Réamur, and Celsius. The idea of heat as a quantity was suggested by observation in distilleries, but it was Joseph Black who cleared up the still existing confusion between heat and temperature, calling them quantity and intensity of heat. He studied the change of state from ice to water and water to steam, finding that, in each case, much heat was absorbed with no rise in temperature; heat, as he said, was rendered latent (see latent heat). He explained the different amounts of heat needed by different substances to produce the same rise in temperature by assigning to each substance a "specific heat," and showed how to measure quantities of heat in a calorimeter – a vessel containing a known mass of weight with a thermometer immersed in it.

Towards a new theory of heat

It is evident that these experiments needed a theory of heat laying stress on the idea of a quantity which remained constant as the heat passed from one body to another. Although Henry Cavendish, Robert Boyle, and Isaac Newton had regarded heat as a vibratory motion of the particles of substances, that view did not lend itself, before the days of the theory of energy, to the idea of a quantity remaining constant. It was better to take the alternative hypothesis that heat was a subtle, invisible, weightless fluid, passing freely between the particles of bodies, and this caloric theory served well until the middle of the 19th century.

The calorists explained the heat developed by friction by supposing that the filings or abrasions, or the main body after friction, had a lower specific heat, so that heat was, as it were, squeezed out. Though the American Benjamin Thompson, who in Bavaria became famous as Count Rumford, had shown in 1798 by experiments on the boring of cannon that the heat developed was proportional to the work done, and had no relation to the amount of shavings, his work was forgotten or ignored, and the caloric theory flourished.

But by 1840 it had become apparent that some of the powers of nature were mutually convertible. Assuming that when air is compressed all the work appears as heat, J. R. Mayer calculated the mechanical equivalent of a unit of heat. W. R. Grove wrote on the "Correlation of Physical Forces," and Hermann von Helmholtz, published Ueber die Erhaltung der Kraft. The idea of correlation was in the air.

Mechanical equivalent of heat

From 1840 to 1850 James Joule was engaged in measuring experimentally the heat liberated by mechanical and electrical work. He found that, however the work was done, the expenditure of the same amount of work produced the same quantity of heat. To warm one pound of water through one degree Fahrenheit needed about 772 foot pounds of work – a figure afterwards corrected to 778. This became known as the mechanical equivalent of heat.

Heat as a form of energy

A troublesome double meaning in the word "force," which had been pointed out by Thomas Young, was cleared up when Rankine and William Thomson (Lord Kelvin) used the word "energy" in a specialized sense to denote the power of doing work, and measured, if the transformation is complete, by the work done. Joule's experiments showed that the total amount of energy in an isolated system is constant, the quantity lost in work reappearing as heat. Thus, the somewhat vague "correlation of forces" became the quite definite "conservation of energy." And the law of conservation of energy, in turn, became the first law of thermodynamics.

Birth of statistical mechanics

If heat is a form of energy, it must consist in motion of molecules. This kinetic theory, given in early forms by Bernoulli, Waterston, and Joule, was first properly expounded by Rudolf Clausius in 1857. The chances of molecular collision will produce molecules moving in all directions with all velocities, the average value of which was calculated by Joule; for hydrogen it is 1,844 meters (more than a mile) per second, and for oxygen 461 m/s. But James Clerk Maxwell and Ludwig Boltzmann applied to the velocities a law of error derived by Laplace and by Gauss from Pascal's theory of probability. Maxwell and Boltzann also showed that, on the kinetic theory, the total energy of a molecule shoud be divided equally among its degrees of freedom, that is the number of coordinates needed to specify its position and condition. From this it follows that the ration of the specific heats of a gas at constant pressure and at constant volume is 1.67 for three degrees of freedom and 1.4 for five – figures confirmed experimentally for gases with monatomic and diatomic molecules respectively.

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