Question

Which of the following statement(s) is/are correct for a thermodynamic closed system?

• A. The entropy change is positive for a reversible adiabatic process.
• B. The entropy change is positive for a reversible cycle.
• C. The entropy change is positive for a reversible isothermal heat addition process.
• D. The entropy change is negative for a reversible isothermal heat rejection process.

Hint:

1. In a reversible process, entropy change is directly proportional to the heat transferred and inversely proportional to the temperature (\( \Delta S = \frac{Q_{\text{rev}}}{T} \)).
2. Adiabatic processes do not involve heat transfer, so \( \Delta S = 0 \).
3. For cyclic processes, \( \Delta S_{\text{cycle}} = 0 \).

Answer 1

The Correct Option is C

Step 1: Understanding entropy changes. Entropy (\(S\)) is a measure of disorder in a system. For a thermodynamic closed system: 1. In a reversible adiabatic process, there is no heat transfer (\(Q = 0\)), so entropy remains constant (\( \Delta S = 0 \)). 2. In a reversible cycle, the system returns to its initial state, so the total entropy change is zero (\( \Delta S = 0 \)). 3. For a reversible isothermal heat addition process, entropy increases as heat is added to the system (\( \Delta S > 0 \)). 4. For a reversible isothermal heat rejection process, entropy decreases as heat is removed from the system (\( \Delta S < 0 \)). Step 2: Analysis of options.
(A) The entropy change is positive for a reversible adiabatic process: Incorrect. In a reversible adiabatic process, \( \Delta S = 0 \). (B) The entropy change is positive for a reversible cycle: Incorrect. For a complete cycle, \( \Delta S = 0 \). (C) The entropy change is positive for a reversible isothermal heat addition process: Correct. Heat addition increases entropy. (D) The entropy change is negative for a reversible isothermal heat rejection process: Correct. Heat rejection decreases entropy. Conclusion: The correct statements for a thermodynamic closed system are \( \mathbf{(C)} \) and \( \mathbf{(D)} \).