Question

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : A gas is confined by a piston at pressure '$P$' and the external pressure is $P_{ex}$. If the $P_{ex}$ is measurably greater than internal pressure, then decreasing $P_{ex}$ infinitesimally will not decrease it below the pressure of the gas and will not change the direction of the process.
Reason (R) : The system is in mechanical equilibrium with its surrounding and the compression is thermodynamically reversible.
In the light of the above statements, choose the most appropriate answer from the options given below :

• A. Both (A) and (R) are correct and (R) is the correct explanation of (A)
• B. Both (A) and (R) are correct but (R) is not the correct explanation of (A)
• C. (A) is correct but (R) is not correct
• D. (A) is not correct but (R) is correct

Hint:

Reversibility in thermodynamics implies that a process can be perfectly reversed by an infinitesimally small change in external conditions. If there's a macroscopic, measurable difference in forces or pressures, the process is spontaneous and irreversible.

Answer 1

The Correct Option is C

Step 1: Concept:
This problem addresses the thermodynamic concepts of reversible versus irreversible processes, mechanical equilibrium, and the driving forces behind gas compression.

Step 2: Key Formula or Approach:
- A process is reversible if the system is in mechanical equilibrium with its surroundings at every step, meaning the driving force (pressure difference) is infinitesimally small: $P_{ex} \approx P_{int} \pm dP$.
- A process is irreversible if there is a finite, measurable driving force: e.g., $P_{ex} \gg P_{int}$.

Step 3: Step-by-step Explanation:

• Evaluating Assertion (A): The assertion specifies that $P_{ex}$ is measurably greater than the internal pressure $P$. This large pressure gradient drives an irreversible compression. Because the difference $P_{ex} - P$ is finite (not infinitesimal), a tiny infinitesimal decrease in $P_{ex}$ will still leave the external pressure substantially greater than the internal pressure ($P_{ex} - dP_{ex} > P$). Consequently, the gas will continue to be compressed; the direction of the process will not change. Therefore, Assertion (A) is physically sound and correct.

• Evaluating Reason (R): The reason claims the system is in mechanical equilibrium and the process is thermodynamically reversible. By definition, mechanical equilibrium requires that the pressures are balanced ($P_{ex} = P$). Since Assertion (A) explicitly established that $P_{ex}$ is measurably greater than $P$, the system is fundamentally not in equilibrium. A process driven by a large, finite pressure difference is inherently irreversible, not reversible. Therefore, Reason (R) is false.

Step 4: Final Answer:
Assertion (A) is true, but Reason (R) is false. This corresponds to option (C).