[QUE/SM-04020] SM-PROBLEM

A circular cylinder of height $H$, ($0\,\leq \,z\,H$) cross sectional area A, is filled with $N$ non-interacting particles of mass m. They are at temperature $T$. Further they are acted upon by a gravitational field, giving a potential energy $mgz$. Find the specific heat at constant volume. Find the value in the two limiting cases (a) $T\,\rightarrow\,0$ and $T\,\rightarrow\,\infty$.