Two moles of an ideal gas expand spontaneouly into vacuum. The work done is :-

Options

A. Zero
B. 2J
C. 4J
D. 8J

Answer

To solve the question regarding the work done when two moles of an ideal gas expand spontaneously into a vacuum, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Scenario**:
- We have two moles of an ideal gas that is expanding into a vacuum. This means there is no external pressure acting on the gas.

2. **Identifying External Pressure**:
- In a vacuum, the external pressure (P_external) is equal to zero. This is a crucial point because the work done by or on the gas depends on this pressure.

3. **Work Done Formula**:
- The work done (W) by the gas during expansion can be calculated using the formula:
\[ W = - P_{\text{external}} \Delta V \]
- Here, \(\Delta V\) is the change in volume, which is the final volume minus the initial volume.

4. **Substituting Values**:
- Since \(P_{\text{external}} = 0\) (because it is a vacuum), we can substitute this value into the work done formula:
\[ W = - 0 \cdot \Delta V \]

5. **Calculating Work Done**:
- This simplifies to:
\[ W = 0 \]
- Therefore, the work done by the gas during its expansion into a vacuum is zero.

6. **Conclusion**:
- The correct answer is that the work done is **zero**.

### Final Answer:
The work done when two moles of an ideal gas expand spontaneously into a vacuum is **0 Joules**.

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