Another (or the same) Cyclic Heat Engine

A certain heat engine uses an ideal gas as a medium and follows the cycle a-b: isothermal expansion at $T_1$ = 600$^\circ$ K; b-c: constant volume cooling to a new temperature $T_2$ = 300$^\circ$ k; c-d: isothermal compression to the original volume; d-a: constant volume heating back to $T_1$. This cycle is shown on the $PV$-diagram above. $V_a = V_d = 1$ liter, $V_b = V_c = 2$ liters and $P_a = 2$ atm.

a) Evaluate $Nk$ for this engine, and find $N$.

b) How much work is done per cycle of this engine?

c) For extra credit, determine how much heat is absorbed (d-a and a-b) and rejected (b-c and c-d) by the engine and evaluate its efficiency. You will need to use the first law extensively. Note that even if you can't do all of this part, showing what you can do might get you some extra credit.