The following data refer to an analysis of a dual combustion cycle with a gas having specific heats varying linearly with temperature:

The pressure and temperature of the gas at the end of compression are 31 bar and \(227^{\circ} \mathrm{C}\) respectively; the maximum pressure achieved during the cycle is \(62 \mathrm{bar}\), while the maximum temperature achieved is \(1700^{\circ} \mathrm{C}\). The temperature at the end of the expansion stroke is \(1240{ }^{\circ} \mathrm{C}\). The increases in entropy during constant volume and constant pressure combustion are 0.882 and \(1.450 \mathrm{~kJ} / \mathrm{kg} \mathrm{K}\) respectively. Assuming that the fluid behaves as an ideal gas of molecular weight, \(m_{w}=30.5\) calculate the equations for the specific heats, and also the expansion ratio if that process is isentropic.

\([0.6747+0.000829 T ; 0.94735+0.000829 T ; 7.814]\)