The Quantum Theory of the Equation of State

Abstract

It is shown that the quantum theory analogue to the quantity $e^{-\frac{\epsilon \mathrm{pot}}{\mathrm{kT}}}$ giving the distribution in coordinates of systems at temperature $T$ can be easily set up. Similarly in quantum theory the computation of the free energy can be reduced to the integration of such a function over the coordinates, as in classical theory. The result is applied to a qualitative discussion of the equation of state of an imperfect gas, showing that He and ${\mathrm{H}}_2$ may be expected to show quantum effects in their equations of state, but hardly any other gases.