The Stirling engine operates on the following cycle beginning at $P_0,V_0,$ and

$T_0$:

I. Isothermal expansion to $4V_0$;

II$.$ Constant volume heating to $\frac{P_0}{2}$;

III. Isothermal compression to $V_0$;

IV$.$ Constant volume cooling back to $T_0.$

Sketch the cycle on a $P-V$ diagram. Calculate the change in $T$ for each leg in terms

of $T_0,$ the net work done by the cycle, the heat absorbed by the cycle, and

determine the efficiency of the engine. Compare this efficiency to the Carnot

efficiency operating between the highest and lowest temperatures of this cycle.

Treat the gas as $1$ mole of ideal gas, with a value of $C_v=3R.$