In lecture we derived the canonical partition function QN(V,N) for the idea gas using a factorization method. One can also directly compute it by taking the Laplace transform of the microcanonical partition function Q(E,V,N). Using our result from lecture, Q(E,V,N) = [3 (2TME)3/2 ]N [(3N/2) - 1]! N! (Δ/Ε) compute directly the Laplace transform, QN(T,V) = | dE A Q(E,V,N)e-BE and show that you get the same result for QN(T,V) as found in lecture using the factorization method.

In lecture we derived the canonical partition function QN(V,N) for the idea gas using a factorization method. One can also directly compute it by taking the Laplace transform of the microcanonical partition function Q(E,V,N). Using our result from lecture, Q(E,V,N) = [3 (2TME)3/2 ]N [(3N/2) - 1]! N! (Δ/Ε) compute directly the Laplace transform, QN(T,V) = | dE A Q(E,V,N)e-BE and show that you get the same result for QN(T,V) as found in lecture using the factorization method.