[QUE/SM-04003] SM-PROBLEM

The canonical partition function of a system of $N$ hypothetical particles each of mass $m$, confined to a volume $V$ at temperature $T$ is given by, $$Q(T,V,N) = V^N\left(\frac{2\pi k_B T}{m}\right)^{5N/2}.$$ Determine the equation of state of the hypothetical system. Also find $C_V$ - heat capacity at constant volume. Identify the hypothetical system. How many degrees of freedom does each particle of the hypothetical system have ?

KPN