An ideal gas exists in a state with pressure $P_0$ and volume $V_0$. It is isothermally expanded to 4 times its initial volume, then isobarically compressed to its original volume. Finally the system is heated isochorically to bring it to its initial state. The amount of heat exchanged in this process is:
Answer: (A) $P_0V_0(2\ln2 - 0.75)$
The gas returns to its initial state, so $\Delta U = 0$ and the net heat equals the net work done by the gas.
1. Isothermal expansion $V_0 \to 4V_0$: $W_1 = P_0V_0\ln4 = 2P_0V_0\ln2$. The pressure falls to $P_0/4$.
2. Isobaric compression at $P_0/4$ from $4V_0$ to $V_0$: $W_2 = \dfrac{P_0}{4}(V_0 - 4V_0) = -\tfrac34P_0V_0$.
3. Isochoric heating: $W_3 = 0$.
$$Q = W = P_0V_0(2\ln2 - 0.75)$$
Solution by Sreeraj P, M.Sc Physics