Question

Second law of thermodynamics can be stated as:

• A. Work done by the system is zero
• B. \( \Delta H = 0 \)
• C. \( \Delta U_{\text{cycle}} = 0 \)
• D. \( dS = \frac{\delta q_{\text{rev}}}{T} \)

Hint:

The second law of thermodynamics introduces entropy. For reversible processes, remember the formula: \( dS = \frac{\delta q_{\text{rev}}}{T} \).

Answer 1

The Correct Option is D

Step 1: Understanding the Second Law of Thermodynamics
The Second Law introduces the concept of entropy and states that in a reversible process, the change in entropy \( dS \) is equal to the heat exchanged reversibly (\( \delta q_{\text{rev}} \)) divided by the absolute temperature \( T \): \begin{equation} dS = \frac{\delta q_{\text{rev}}}{T} \end{equation} Step 2: Implications of the Law
This equation expresses that entropy change depends on the reversible transfer of heat. It signifies that for any spontaneous (irreversible) process, the entropy of the universe increases, while for a reversible process, entropy remains constant. Step 3: Evaluation of Options
- (A) "Work done by the system is zero" is unrelated to the second law; this may refer to isolated systems, not thermodynamic laws.
- (B) \( \Delta H = 0 \) is not a general statement of the second law; it may apply to specific processes.
- (C) \( \Delta U_{\text{cycle}} = 0 \) is from the First Law — in cyclic processes, internal energy change is zero.
- (D) Correct: This is the mathematical statement of the second law for reversible processes. Conclusion: The correct thermodynamic expression of the second law is: \[ dS = \frac{\delta q_{\text{rev}}}{T} \]