Statistical Mechanics · Problem 6.6

Ideal Bose Systems — R. K. Pathria

Physics — Statistical Mechanics · molecular-speed-distribution-inequality

Problem

Show that, for any law of distribution of molecular speeds,

\left\{\langle u\rangle\left\langle \frac{1}{u}\right\rangle\right\} \geq 1.

Check that the value of this quantity for the Maxwellian distribution is

4/\pi