Blundell Thermal Physics · Problem 22.5

The chemical potential

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

Problem

If the partition function

Z_N

of a gas of

N

indistinguishable particles is given by

Z_N = Z_1^N/N!

, where

Z_1

is the single-particle partition function, show that the chemical potential is given by

\mu = -k_\mathrm{B}T \ln \frac{Z_1}{N}. \tag{22.103}