An engine (consisting of one mole of an ideal gas in a cylinder with a piston) follows the cycle shown in the figure. Find the heat exchanged by the engine with the surroundings in each part of the cycle. Given $C_V = \frac{3}{2}R$.
$(a)$ $A$ to $B$: Constant volume
$(b)$ $B$ to $C$: Constant pressure
$(c)$ $C$ to $D$: Adiabatic expansion
$(d)$ $D$ to $A$: Constant pressure

(N/A) For a process,the heat exchanged is given by $Q = nC\Delta T$.
$(a)$ $A$ to $B$ (Isochoric): $W = 0$,so $Q_{AB} = \Delta U = nC_V(T_B - T_A) = \frac{3}{2}nR(T_B - T_A)$. Since $P_B > P_A$ and $V$ is constant,$T_B > T_A$,so heat is absorbed.
$(b)$ $B$ to $C$ (Isobaric): $Q_{BC} = nC_P(T_C - T_B) = n(\frac{5}{2}R)(T_C - T_B)$. Since $V_C > V_B$,$T_C > T_B$,so heat is absorbed.
$(c)$ $C$ to $D$ (Adiabatic): By definition,$Q_{CD} = 0$.
$(d)$ $D$ to $A$ (Isobaric): $Q_{DA} = nC_P(T_A - T_D) = n(\frac{5}{2}R)(T_A - T_D)$. Since $V_A < V_D$,$T_A < T_D$,so heat is released.