Question

For a thermodynamic cycle to be reversible, it is necessary that

• A. $\oint \frac{dQ}{T} = 0$
• B. $\oint \frac{dQ}{T} \lt 0$
• C. $\oint \frac{dQ}{T} \gt 0$
• D. $\oint \frac{dQ}{T} = \infty$

Hint:

Think of "=" as "Perfect" (Reversible) and "<" as "Real" (Irreversible). Since a reversible cycle is a perfect theoretical concept, it must balance out exactly to Zero.

Answer 1

The Correct Option is A

1. The Clausius Inequality: The theorem states that for any thermodynamic cycle, the cyclic integral of $\frac{dQ}{T}$ must satisfy: $$\oint \frac{dQ}{T} \leq 0$$

2. Interpreting the Integral: The value of this cyclic integral tells us about the nature of the cycle:

• Case 1 (Reversible Cycle): If the cycle is perfectly reversible (no friction, no rapid expansions, and heat transfer only across infinitesimal temperature differences), then: $$\oint \frac{dQ}{T} = 0$$

• Case 2 (Irreversible Cycle): If there are any internal or external irreversibilities (which occur in all real-world processes), then: $$\oint \frac{dQ}{T} \lt 0$$

• Case 3 (Impossible Cycle): If the integral is greater than zero, the cycle violates the Second Law of Thermodynamics.