Partition function for position-independent hamiltonian

[Einj]

Hi everyone. Suppose I have an Hamiltonian which doesn't depend on the position (think for example to the free-particle one $H=p^2/2m$). I know that the classical partition function for the canonical ensemble is given by:
$$
Z(\beta)=\int{dpdq e^{-\beta H(p,q)}}.
$$

What does it happen to the integration over $dq$ if there is no q-dependence in the Hamiltonian? Is it just the volume of the system?

Thank you

 

[andrien]

yes,what you will get by this free particle hamiltonian is the single particle partition function for the classical ideal gas.You can evaluate things per unit volume.