Partition Function, Grand Potential

unscientific · Mar 8, 2014

It seems like they have missed out a factor of ##(2S+1)## in the final expression for grand potential? I'm thinking it should be ##(2S+1)^2## instead.

Typeset derivation of the grand potential for an ideal gas of bosons or fermions with spin S, showing Phi_G = -kT ln Z, the sum and integral forms with g(E), the density of states g(E)dE, and the final expression Phi_G = -+kT (2S+1)V/(2pi)^2 (2m/h^2)^(3/2) integral of ln(1+-e^(-beta(E-mu))) E^(1/2) dE.

Bill_K · Mar 8, 2014

I don't know, didn't they write the (2S+1) factor twice? There are 2S+1 states for each value of k, so in Eq.(30.3) you can put this factor in front of the integral, or include it in g(E), but you should not do both!

unscientific · Mar 8, 2014

Bill_K said:

I don't know, didn't they write the (2S+1) factor twice? There are 2S+1 states for each value of k, so in Eq.(30.3) you can put this factor in front of the integral, or include it in g(E), but you should not do both!

Good point. Thanks a lot

Partition Function, Grand Potential

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