Monatomic Ideal Gas Thermodynamic Cycle in TV Diagram

To determine the correct statements for the given thermodynamic cycle of an ideal gas in the $T$-$V$ plane:

1. Process I: The volume $V$ changes as temperature $T$ varies, meaning the process cannot be isochoric. Therefore, statement (A) is incorrect.

2. Processes I and III: For an isobaric process, Charles's law requires $T \propto V$, which represents a straight line passing through the origin with a positive slope. Since neither Process I nor Process III follows this relation, neither process is isobaric. Therefore, statement (D) is correct.

3. Process II: This is an isothermal expansion at constant temperature ($T = \text{constant}$) with increasing volume ($dV > 0$). Since $\Delta U = nC_v \Delta T = 0$ and work done $W = \int P\,dV > 0$, the first law of thermodynamics gives $Q = \Delta U + W > 0$. Thus, heat is absorbed by the gas, making statement (B) correct.

4. Process IV: This is an isothermal compression at constant temperature ($T = \text{constant}$) with decreasing volume ($dV < 0$). With $\Delta U = 0$ and work done $W < 0$, the first law yields $Q = W < 0$. Thus, heat is released by the gas, making statement (C) correct.

Hence, the correct statements are (B), (C), and (D).