The canonical partition function for the ideal gas is much
easier to evaluate than the microcanonical partition function.
Recall the expression for the canonical partition function *Q*(*N*,*V*,*T*):

Note that this can be expressed as

since the Hamiltonian is completely separable. Evaluating the Gaussian integral gives us the final result immediately:

The expressions for the energy

and pressure

gives rise to the results *E*=3*NkT*/2 and *PV*=*NkT* just as
for the microcanonical ensemble. Note also that
the entropy *S*(*N*,*V*,*T*) given by

becomes

which reduces to the microcanonical expression exactly if we use the fact that :

Thus, the canonical and microcanonical ensembles gives rise to exactly the same thermodynamics!! Let us now look more carefully at the expression for the entropy.

Thu Feb 20 00:47:55 EST 2003