(a) Derive the Clausius-Clapeyron equation in the study of the vaporization process of a pure substance.

(b) In a frictionless piston-cylinder assembly, an ideal gas undergoes a compression process from an initial state of 1 bar at \(300 \mathrm{~K}\) to 10 bar at \(300 \mathrm{~K}\). The entire process comprises the following two mechanically reversible processes:

(a) Cooling at constant pressure followed by heating at constant volume;

(b) Heating at constant volume followed by cooling at constant pressure.
Calculate \(Q, \Delta U\) and \(\Delta H\) for the two processes, given that \(C_{P}=29.10 \mathrm{~kJ} / \mathrm{kmol}-\mathrm{K}\), \(C_{V}=20.78 \mathrm{~kJ} / \mathrm{kmol}-\mathrm{K}\) and Volume of the gas at initial state- \(24.942 \mathrm{~m}^{3} / \mathrm{kmol}\).