One mole of an ideal gas expand spontaneously into a vacccum. The work done is

Options

A. 2J
B. 4 J
C. zero
D. infinity

Answer

To solve the problem of finding the work done when one mole of an ideal gas expands spontaneously into a vacuum, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Scenario**:
- We have one mole of an ideal gas that is expanding into a vacuum. In this case, there is no opposing pressure acting on the gas.

2. **Work Done Formula**:
- The work done (W) by a gas during expansion or compression is given by the formula:
\[ W = - P_{\text{external}} \Delta V \]
where \( P_{\text{external}} \) is the external pressure and \( \Delta V \) is the change in volume.

3. **Identifying External Pressure**:
- Since the gas is expanding into a vacuum, the external pressure (\( P_{\text{external}} \)) is 0 atm (or 0 Pa).

4. **Calculating Work Done**:
- Substituting the values into the work done formula:
\[ W = - (0) \Delta V = 0 \]
- Therefore, the work done by the gas during this expansion is 0.

5. **Conclusion**:
- The work done when one mole of an ideal gas expands spontaneously into a vacuum is:
\[ W = 0 \]

### Final Answer:
The work done is **0**.