Thermodynamics, Statistical Physics, and Quantum Mechanics

186 SOLUTIONS

where is the energydensity. So,

c) Using the equation of state for a photon gas

and

we have

The entropySis then

d) The energyEof the system of particles +photons is

The entropy of the system is the sum of the entropy of an ideal gas and

radiation. Thefreeenergy of a single-particleideal gaswith (see

Problem 4.38) of created particles and the radiation is then

Minimizing the freeenergy with respect to thenumber ofparticles, we have

From (S.4.74.12)we obtain