An engine working on the constant volume (Otto) cycle has a compression ratio of 6.5 to 1 , and the compression follows the law \(p V^{1.3}=\mathrm{C}\), the initial pressure and temperature being 1 bar and \(40^{\circ} \mathrm{C}\). The specific heats at constant pressure and constant volume throughout compression and combustion are \(0.96+0.00002 T \mathrm{~kJ} / \mathrm{kg} \mathrm{K}\) and \(0.67+0.00002 T \mathrm{~kJ} / \mathrm{kg} \mathrm{K}\) respectively, where \(T\) is in \(\mathrm{K}\).

Find:

(a) the change in entropy during compression;

(b) the heat rejected per unit mass during compression;

(c) the heat rejected per unit mass during combustion if the maximum pressure is 43 bar and the energy liberated by the combustion is \(2150 \mathrm{~kJ} / \mathrm{kg}\) of air.

[(a) \(-0.1621 \mathrm{~kJ} / \mathrm{kg} \mathrm{K}\); (b) \(-67.8 \mathrm{~kJ} / \mathrm{kg}\); (c) \(-1090.6 \mathrm{~kJ} / \mathrm{kg}\) ]