# Canonical ensemble, entropy of a classical gas

## Homework Statement

I have the equation
Z=1/N!h3N∫∫d3qid3pie-βH(q,p)

How can I get the entropy from this equation assuming a classical gas of N identical, noninteracting atoms inside a volume V in equilibrium at T where it has an internal degree of freedom with energies 0 and ε
What about the specific heat at constant volume Cv?
Can anyone explain the equation?

## Homework Equations

Z=1/N!h3N∫∫d3qid3pie-βH(q,p)

## The Attempt at a Solution

Well I integrated the momentum and the volume separately. At the end I did get PV=NRT where I'm supposed to show that from this equation I can derive to the ideal gas law equation
∫d3q=VN=Vn/N!
∫d3p=0

However by using Z equation I can derive the entropy for this problem, how?

$$Z_1 = \int d^3p d^3q \sum_{\epsilon} \exp(-\beta H_1(p,q,\epsilon))$$
$$Z_N = \frac{1}{N!} Z_1^N$$