Statistical Mechanics · Problem 8.6

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

Physics — Statistical Mechanics · fermi-gas-speed-of-sound

Problem

Show that the velocity of sound

w

in an ideal Fermi gas is given by

w^2 = \frac{5kT}{3m}\frac{f_{5/2}(z)}{f_{3/2}(z)} = \frac{5}{9}\langle u^2 \rangle,

where

\langle u^2 \rangle

is the mean square speed of the particles in the gas. Evaluate

w

in the limit

z \to \infty

and compare it with the Fermi velocity

u_F