Thermodynamics, Statistical Physics, and Quantum Mechanics

THERMODYNAMICS AND STATISTICAL PHYSICS 177

where

b) The condition for validity of this approximation is that the first correc-

tion should be muchless thanunity:

Thisgives thecondition on the density for which(S.4.68.15) isvalid:

It is interesting todetermine the de Brogliewavelength at this tem-

perature Wefindthat

We see that thisapproximation is valid when the separationbetween par-

ticles is much largerthan the deBrogliewavelength. (S.4.68.16)expresses

the samecondition as for the applicability of Boltzmann statistics(which

implies Since thechemicalpotential may bewritten(see

Problem4.39)

we see that

4.69 Speed of Sound in Quantum Gases (MIT)

a) The GibbsfreeenergyGis a function of which do notdepend on

the number ofparticles; i.e.,

where is somefunction of On theotherhand,