According to the kinetic theory of gases, the root mean velocity of gas molecules is directly proportional to

Options

A. T
B. `sqrt(T)`
C. `T^(2)`
D. `T^(3//2)`

Explanation

To solve the question regarding the root mean square (RMS) velocity of gas molecules according to the kinetic theory of gases, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Concept**: The root mean square velocity (Vrms) of gas molecules is a measure of the average velocity of the molecules in a gas. According to the kinetic theory of gases, this velocity is influenced by temperature and molecular mass.

2. **Relevant Formula**: The formula for the root mean square velocity is given by:
\[ V_{rms} = \sqrt{\frac{3RT}{M}} \]
where:
- \( R \) is the universal gas constant,
- \( T \) is the absolute temperature of the gas,
- \( M \) is the molar mass of the gas.

3. **Analyzing the Formula**: From the formula, we can observe that:
- \( R \) is a constant for any specific gas,
- \( M \) is also a constant for a specific gas.

4. **Identifying Proportionality**: Since \( R \) and \( M \) are constants, the root mean square velocity \( V_{rms} \) is directly proportional to the square root of the temperature \( T \):
\[ V_{rms} \propto \sqrt{T} \]

5. **Conclusion**: Therefore, we conclude that the root mean square velocity of gas molecules is directly proportional to the square root of the absolute temperature.

### Final Answer:
The root mean square velocity of gas molecules is directly proportional to \( \sqrt{T} \).

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