Question

In a reversible cycle, the sum of change in \( \frac{q}{T} \) is
(where \( q \) is heat absorbed and \( T \) is absolute temperature):

• A. Zero
• B. One
• C. Two
• D. Three

Hint:

In reversible cycles, always remember: \( \oint \frac{\delta q_{\text{rev}}}{T} = 0 \). This reflects the fact that entropy is a state function and there’s no net change over a closed loop.

Answer 1

The Correct Option is A

Step 1: Apply Clausius' Theorem
According to Clausius’ theorem, the entropy change in a reversible cycle is given by: \[ \oint \frac{\delta q_{\text{rev}}}{T} = 0 \] This implies that over the course of a full reversible cycle, the net entropy change is zero. Step 2: Entropy as a State Function
Entropy is a state function, meaning its total change in a cyclic process (returning to the same state) is zero, just like internal energy. This is why the sum of \( \frac{q}{T} \) over a reversible cycle is also zero. Step 3: Misleading Alternatives
- Option B: Would imply non-zero entropy generation, which occurs in irreversible processes.
- Options C and D: Have no basis in thermodynamic theory. Conclusion: In a reversible cycle, \( \sum \frac{q}{T} = 0 \), in accordance with Clausius' formulation of the second law.