Thermodynamics, Statistical Physics, and Quantum Mechanics

THERMODYNAMICS AND STATISTICAL PHYSICS 193

Let us calculate the Helmholtz free energy F. For a Bose gas with
the grand thermodynamic potential is given by

The free energy F would coincide with Again
replacing the sum by an integral in (S.4.78.4) and substituting
yield

Integrating by parts gives

where

although we really do not need this, and so

with a positive constant. The pressure P of the photon gas is