[QUE/SM-04018] SM-PROBLEM

Consider N particles having volume V with the energy per particle be given by the relativistic expression $\sqrt{c^2\,p^2\,+\,m^2\, c^4}$. It is in equilibrium with a reservoir at temperature T. Assuming $\frac{p}{mc}$ is small, find the leading correction to the (a) Canonical partition function and (b) Entropy in terms of V,N and T up to an overall constant.