Free Bosons: Bose—Einstein Condensation; Photon Gas

Abstract

The thermodynamic properties of an ideal gas of bosons can be obtained from the grand partition function

$$ln\Xi (T,V,\mu ) = - \sum\limits_j {\ln } \left\{ {1 - \exp [ - \beta (\varepsilon j - \mu )]} \right\},$$

(10.1)

where the sum is over all single-particle states. In the thermodynamic limit, the pressure as a function of temperature and chemical potential is given by

$$p(T,\mu ) = - {k_B}T\mathop {\lim }\limits_{V \to \infty } \frac{1}{V}\ln \Xi (T,V,\mu ).$$

(10.2)