A: Work done in an irreversible isothermal process at constant volume is zero.
R: Work is assigned negative sign during expansion and is assigned positive sign during compression.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion , then mark (1)
B. If both Assertion & Reason are true and the reason is not the correct explanation of the assertion, then mark (2)
C. If Assertion is true statement but Reason is false, then mark (3)
D. If both Assertion is true statement but Reason is false, then mark (3)

Answer

To solve the question, we need to analyze the assertion (A) and the reason (R) provided.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that "Work done in an irreversible isothermal process at constant volume is zero."
- In an isothermal process, the temperature remains constant. For an ideal gas, the work done (W) during a process can be calculated using the formula:
\[ W = nRT \ln \left( \frac{V_f}{V_i} \right) \]
- Here, \(V_f\) is the final volume and \(V_i\) is the initial volume. If the volume is constant, then \(V_f = V_i\), which means:
\[ W = nRT \ln(1) = 0 \]
- Therefore, the assertion is **true**.

2. **Understanding the Reason (R)**:
- The reason states that "Work is assigned a negative sign during expansion and is assigned a positive sign during compression."
- In thermodynamics, during expansion, the system does work on the surroundings, which is considered negative work (W < 0). Conversely, during compression, work is done on the system, which is considered positive work (W > 0).
- This statement is also **true**.

3. **Analyzing the Relationship**:
- Although both the assertion and reason are true, we need to determine if the reason correctly explains the assertion.
- The assertion is about the work done in an irreversible isothermal process at constant volume being zero. The reason discusses the sign of work during expansion and compression but does not directly relate to the condition of constant volume in the assertion.
- Therefore, while both statements are true, the reason does not adequately explain the assertion.

### Conclusion:
- Both the assertion (A) and the reason (R) are true, but the reason is not the correct explanation of the assertion. Thus, the answer to the question is that both statements are correct, but the reason does not explain the assertion.

### Final Answer:
- Both A and R are true, but R is not the correct explanation of A.

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