Thermodynamics, Statistical Physics, and Quantum Mechanics

THERMODYNAMICS AND STATISTICAL PHYSICS 179

Using theequation ofstate for aFermi gas (seeProblem 4.66),

we have

Now,using(S.4.69.11), we cancalculate

Alternatively, we can use the expression obtained in (a) and the fact that,
at the chemicalpotential From(S.4.69.8),

and we againrecover (S.4.69.12) in

c) We can explicitly calculate the total energy of the Bose gas, which will be

defined by the particles that are outside the condensate (since the condensed

particles are in the ground state with At a temperature below the

Bose–Einstein condensation the particles outside the condensate

(with aredistributed according to a regular Bose distribution with

(seeProblem 4.70):

The total number ofparticles outside the condensate istherefore