Consider a collection of identical, classical (i.e., with 1) particles with a distribution function N

Consider a collection of identical, classical (i.e., with η ≪ 1) particles with a distribution function N that is thermalized at a temperature T such that k_BT ≪ mc² (nonrelativistic temperature).(a) Show that the distribution function, expressed in terms of the particles’ momenta or velocities in their mean rest frame, is

with v being the speed of a particle.

(b) Show that the number density of particles in the mean rest frame is given by Eq. (3.39a).

(c) Show that this gas satisfies the equations of state (3.39b).

Transcribed Image Text:

N = 8se/(KBT) e-p²/(2mk BT), where p where p = [p] = mv, h3 (3.56)