Assertion: In a thermodynamic process, initial volume of gas is equal to final volume of gas. Work done by gas in this process should be zero
Reason: Work done by gas in isochoric process is zero.

Options

A. (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. (b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
C. (c) If Assertion is true, but the Reason is false.
D. (d) If Assertion is false but the Reason is true.

Explanation

To solve the given question, we need to analyze the assertion and the reason provided:

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that in a thermodynamic process, if the initial volume of the gas is equal to the final volume, then the work done by the gas in this process should be zero.
- This implies that there is no change in volume, which is a key point in thermodynamics.

2. **Understanding the Reason**:
- The reason states that the work done by the gas in an isochoric process (where volume remains constant) is zero.
- This is a fundamental principle in thermodynamics: if there is no change in volume, there can be no work done since work is defined as the product of pressure and change in volume (W = PΔV).

3. **Analyzing the Assertion**:
- While it is true that in an isochoric process (constant volume), the work done is zero, the assertion claims that any process where initial and final volumes are equal must also have zero work done.
- This is not necessarily true. For example, in a cyclic process, the gas can return to the same volume but may have done work during the cycle.

4. **Conclusion on Assertion and Reason**:
- The assertion is incorrect because it generalizes that any process with equal initial and final volumes results in zero work done, which is not true for all processes (e.g., cyclic processes).
- The reason is correct because it accurately describes the work done in an isochoric process.

5. **Final Answer**:
- Therefore, we conclude that the assertion is false, but the reason is true. The correct answer is that the assertion is incorrect while the reason is correct.