Understanding the Degeneracy Discriminant in Classical and Quantum Regimes

[hokhani]

The degeneracy discriminant, that specifies the requirement for applicability of classical Maxwell-Blotzman statistics, is z<<1 where z is fugacity and [itex]z=exp^(\mu/kT)[/itex]. However when [itex]
T\to \infty [/itex] we would have [itex]
z\to 1 [/itex] which means we are in quantum regime while it is obvious that we are in classical regime at high temperatures. And there is also such a discrepancy when [itex]
T\to 0 [/itex]. Could anyone please guide me?

 

[DrClaude]

I'm not sure where you got the condition ##z \ll 1## from. See http://en.wikipedia.org/wiki/Maxwell–Boltzmann_statistics#Limits_of_applicability