The root mean square velocity of an ideal gas in a closed container of fixed volume is increased from `5xx10^(4)cms^(-1)` to `10xx10^(4)cm s^(-1)`. Which of the following statements correctly explains how the change is accomplished?

Options

A. By heating the gas, the temperature is doubled.
B. By heating the gas, the pressure is quadrupled.
C. By heating the gas, the temperature is quadrupled.
D. By heating the gas, the pressure is doubled.

Explanation

To solve the problem, we need to understand how the root mean square (RMS) velocity of an ideal gas changes with respect to its temperature and pressure. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Formula for RMS Velocity
The root mean square velocity (Vrms) of an ideal gas is given by the formula:
\[ V_{rms} = \sqrt{\frac{3RT}{M}} \quad \text{or} \quad V_{rms} = \sqrt{\frac{3PV}{M}} \]
Where:
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