Three moles of an ideal gas expanded spontaneously into vacuum. The work done will be

Options

A. (a) 3 Joules
B. (b) 9 Joules
C. (c) Zero
D. (d) Infinite

Answer

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

### Step-by-Step Solution:

1. **Understand the Scenario**: The problem states that three moles of an ideal gas are expanding into a vacuum. This type of expansion is known as free expansion.

2. **Identify Key Concepts**: In free expansion, the gas expands without any external pressure acting on it. Therefore, the external pressure (P_external) is equal to zero.

3. **Recall the Formula for Work Done**: The work done (W) by a gas during expansion can be calculated using the formula:
\[ W = - P_{\text{external}} \times \Delta V \]
where \(\Delta V\) is the change in volume.

4. **Substitute the Values**: Since the external pressure (P_external) is zero during free expansion:
\[ W = - 0 \times \Delta V = 0 \]

5. **Conclusion**: The work done by the gas when it expands spontaneously into a vacuum is zero. Therefore, the answer is:
\[ \text{Option C: } 0 \]