An ideal classical gas composed of \(N\) particles, each of mass \(m\), is enclosed in a vertical cylinder of height \(L\) placed in a uniform gravitational field (of acceleration \(g\) ) and is in thermal equilibrium; ultimately, both \(N\) and \(L ightarrow \infty\). Evaluate the partition function of the gas and derive expressions for its major thermodynamic properties. Explain why the specific heat of this system is larger than that of a corresponding system in free space.