Joule-Thomson effect and quantum statistics

Abstract

In view of the numerous physical and astro-physical applications of the new quantum statistics it may be worth while to investigate the Joule-Thomson effect for a gas obeying Fermi-Dirac or Bose-Einstein statistics. The calculation is simple and runs on the usual lines. The results obtained are quite interesting. It is found that for a degenerate gas, degenerate in the sense of Fermi-Dirac statistics, Joule-Thomson expansion produces a heating effect, the rise in temperature for a given fall in pressure being greater, the greater the degree of degeneracy of the gas. In fact where n denotes the number of particles (each of mass m) per unit volume, p the pressure, T the temperature, g the weight factor (for electrons g = 2), k the Boltzmann constant and h is Plank's constant. A₀ is called the "degeneracy discriminant" and its value gives a measure of the degree of degeneracy (or of non-degeneracy in the case of non-degenerate gas). For degeneracy A₀ ≫1 and in non-degeneracy A0 ≪ 1.