Statistical Mechanics · Problem 3.25

The Grand Canonical Ensemble — R. K. Pathria

Physics — Statistical Mechanics · kinetic-argument-pressure

Problem

Develop a kinetic argument to show that in a non-interacting system the average value of the quantity

\sum_i p_i \dot{q}_i

is precisely equal to

3PV

. Hence show that, regardless of relativistic considerations,

PV = NkT