Thermodynamics, Statistical Physics, and Quantum Mechanics

180 SOLUTIONS

The energy of the Bose gas at is

The free energy Fis

since and So thepressure

So we see that thepressure does not depend on the volume and

at We could havedetermined the result without the above calcu-

lations since at the particles which areinside the condensate

(with = 0) have no momentum and do notcontribute topressure.

4.70 Bose Condensation Critical Parameters (MIT)

a) The number of particles dNin an element of phase space is given by

where With theusualdispersion law for anideal gas
and integratingover wefind the particledistributionoverenergy:

Integrating (S.4.70.2), we obtaina formula for the total numberNof par-
ticles in the gas: