What happens to the random motion when an ideal gas undergoes free expansion (i.e., expansion into a vacuum) ?

Explanation

### Step-by-Step Solution:

1. **Understanding Free Expansion**: Free expansion refers to the process where an ideal gas expands into a vacuum. In this scenario, there is no external pressure opposing the expansion.

2. **Work Done by the Gas**: During free expansion, the gas does not perform any work on the surroundings because there is no opposing force (since it is expanding into a vacuum). Mathematically, work done (W) is defined as:
\[ W = P \Delta V \]
...