Assertion : Work done during free expansion of an ideal gas whether reversible or irreversible is positive.
Reason : During free expansion, external pressure is always less than the pressure of the system.

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanation of assertion
C. If assertion is true but reason is false.
D. If both assertion and reason are false.

Explanation

To solve the question, we need to analyze both the assertion and the reason provided in the context of thermodynamics, particularly focusing on the concept of work done during the free expansion of an ideal gas.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that "Work done during free expansion of an ideal gas whether reversible or irreversible is positive."
- In thermodynamics, work done by a gas is calculated using the formula \( W = P_{\text{ext}} \Delta V \), where \( P_{\text{ext}} \) is the external pressure and \( \Delta V \) is the change in volume.

2. **Analyzing Free Expansion**:
- During free expansion, the gas expands into a vacuum (or an area with no opposing pressure).
- Since there is no external pressure acting on the gas, we can conclude that \( P_{\text{ext}} = 0 \).

3. **Calculating Work Done**:
- Substituting \( P_{\text{ext}} = 0 \) into the work done formula:
\[ W = P_{\text{ext}} \Delta V = 0 \times \Delta V = 0 \]
- Therefore, the work done during free expansion is actually zero, not positive.

4. **Conclusion on the Assertion**:
- Since the assertion claims that the work done is positive, and we have determined that it is zero, the assertion is **false**.

5. **Understanding the Reason**:
- The reason states that "During free expansion, external pressure is always less than the pressure of the system."
- In free expansion, there is no external pressure acting on the gas, which means the concept of external pressure being less than the system pressure does not apply.

6. **Conclusion on the Reason**:
- Since there is no external pressure during free expansion, the reason is also **false**.

7. **Final Answer**:
- Both the assertion and the reason are false. Therefore, the correct option is that both the assertion and reason are false.