Statistical Mechanics · Problem 5.5

The Theory of Simple Gases — R. K. Pathria

Physics — Statistical Mechanics · partition-function-statistical-potential

Problem

Show that in the first approximation the partition function of a system of

N

non-interacting, indistinguishable particles is given by

Q_N(V,T) = \frac{1}{N!\lambda^{3N}} Z_N(V,T),

where

Z_N(V,T) = \int \exp\left\{-\beta\sum_{i<j} v_s(r_{ij})\right\} d^{3N}r,

v_s(r)

being the statistical potential (5.5.28). Hence evaluate the first-order correction to the equation of state of this system.