About 0.014 kg nitrogen is enclosed in a vessel at temperature of `27^(@)C` How much heat has to be transferred to the gas to double the rms speed of its molecules ? `(R = 2 cal//mol K)`

Explanation

To solve the problem of how much heat needs to be transferred to the nitrogen gas to double the root mean square (RMS) speed of its molecules, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between RMS speed and temperature**:
The RMS speed \( v_{rms} \) of gas molecules is given by the formula:
\[
v_{rms} = \sqrt{\frac{3RT}{M}}
...