I am trying to prove that the efficiency of the above cycle is equal to:
$e = 1 - \gamma \frac{V_2 - V_1}{P_1 - P_2}$ for 1 mole of an ideal gas.
I assume I should use the equation $e \equiv \frac{\Delta W_{cycle}}{Q_H} = 1 - \frac{T_C}{T_H}$.
For the adiabatic process, the work is: $\frac{PV^\gamma (V_2^{1-\gamma} - V_1^{1-\gamma})}{(1-\gamma)}=C_V(T_2-T_1)$ and for the isobaric process, the work is $P_2(V_2 - V_1)$. The isochoric has no work done because there is no change in volume.
I guess that I would find the change in work of the cycle as the work done from the isobaric process minus the work done from the adiabatic process.
I am a little unsure of how to proceed. I don't know where I can get the $P_1$ and $P_2$ values from. What should I be looking for and how should I determine $Q_H$?
Any help would be greatly appreciated, Thanks!