Microscopic Origin of Heat
Heat characterizes macroscopic systems and processes, but like other thermodynamic quantities it has a fundamental origin in statistical mechanics — the physics of the underlying microscopic degrees of freedom.
For example, within a range of temperature set by quantum effects, the temperature of a gas is proportional (via Boltzmann's constant kB) to the average kinetic energy of its molecules. Heat transfer between a low and high temperature gas brought into contact arises due to the exchange of kinetic and potential energy in molecular collisions. As more and more molecules undergo collisions, their kinetic energy equilibrates to a distribution that corresponds to an intermediate temperature somewhere between the low and high initial temperatures of the two gases. An early and vague expression of this was by Francis Bacon. Precise and detailed versions of it were developed in the nineteenth century.
For solids, conduction of heat occurs through collective motions of microscopic particles, such as phonons, or through the motion of mobile particles like conduction band electrons. As these excitations move around inside the solid and interact with it and each other, they transfer energy from higher to lower temperature regions, eventually leading to thermal equilibrium.
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