Statistical Mechanics · Problem 8.19

Statistical Mechanics of Interacting Systems: The Method of Cluster Expansions — R. K. Pathria

Physics — Statistical Mechanics · relativistic-fermi-gas-specific-heat

Problem

Show that the low-temperature specific heat of the relativistic Fermi gas, studied in Sec. 8.4, is given by

\frac{C_V}{Nk} = \pi^2 \frac{(x^2+1)^{1/2}}{x^2}\frac{kT}{mc^2} \quad \left(x = \frac{p_F}{mc}\right).

Check that this formula gives correct results for the nonrelativistic case as well as for the extreme relativistic case.