The Diatomic Gas and Other Separable Quantum Systems

Abstract

An early major success of classical statistical mechanics was the prediction $C_v = \frac{2}{3}NAK_B \equiv \frac{3}{2}R$ for the molar specific heat of a monoatomic gas, N _A being Avogadro’s number and R being the gas constant. In testing this equation, R is a known parameter, since it also appears in the ideal gas law PV = nRT, (10.2) n being the number of moles of gas present. When (10.1) was first developed, the sole known monoatomic gas was mercury; the specific heat of mercury vapor is in accord with theory. The noble gases, discovered near the end of the nineteenth century, show behavior consistent with the above. The same approach, based on the first generalized equipartition theorem, predicts the Law of Dulong and Petit, namely that the molar specific heat of a crystalline elemental solid is in good agreement with late nineteenth century experiment.