1.An ideal gas undergoes a polytropic process $P V^n = \text{Constant}$. Find the molar heat capacity $C$ of the gas in terms of $C_v$, $R$, and $n$.
2.One mole of monoatomic gas goes through a cyclic process $A \to B \to C \to A$ on a $P-V$ diagram consisting of constant volume heating $A(P_0,V_0) \to B(2P_0,V_0)$, isobaric expansion $B \to C(2P_0,2V_0)$, and linear process $C \to A$. Find net work done and efficiency of cycle.
