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

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states: "Work done in an irreversible isothermal process at constant volume is zero."
- In an isothermal process, the temperature remains constant. For a gas, the work done (W) is given by the equation:
\[ W = -P_{\text{ext}} \Delta V \]
- Here, \(P_{\text{ext}}\) is the external pressure and \(\Delta V\) is the change in volume.
- If the process occurs at constant volume, then \(\Delta V = 0\).
- Therefore, substituting \(\Delta V = 0\) into the equation gives:
\[ W = -P_{\text{ext}} \times 0 = 0 \]
- Thus, the assertion is **true**.

2. **Understanding the Reason (R)**:
- The reason states: "Work is assigned a negative sign during expansion and is assigned a positive sign during compression."
- In thermodynamics, the sign convention for work is as follows:
- When a system expands (volume increases), it does work on the surroundings, and this work is considered negative.
- Conversely, when a system is compressed (volume decreases), work is done on the system, and this work is considered positive.
- This statement about the sign convention is also **true**.

3. **Evaluating the Relationship Between A and R**:
- The assertion is true because work done at constant volume in an irreversible isothermal process is indeed zero.
- The reason is also true, but it does not directly explain why the work done in the assertion is zero. The reason discusses the sign convention of work during expansion and compression, which is not directly related to the assertion about work done at constant volume.
- Therefore, while both statements are true, the reason does not correctly explain the assertion.

4. **Conclusion**:
- Since both the assertion and the reason are true, but the reason does not explain the assertion, the correct answer is that both A and R are true, but R is not the correct explanation of A.

### Final Answer:
**Both assertion and reason are true, but the reason is not the correct explanation of the assertion.**