The root mean square velocity of molecules of gas is

Options

A. Inversely proportional to square root of temperature(`sqrt(1/T)`)
B. Proportional to square root of temperature (`sqrtT`)
C. Proportional to square of temperature (`T^2`)
D. Proportional to temperature (T)

Answer

To find the root mean square (RMS) velocity of the molecules of a gas, we can use the formula:

\[ v_{rms} = \sqrt{\frac{3RT}{M}} \]

where:
- \( v_{rms} \) is the root mean square velocity,
- \( R \) is the universal gas constant,
- \( T \) is the absolute temperature in Kelvin,
- \( M \) is the molar mass of the gas.

### Step-by-Step Solution:

1. **Identify the Formula for RMS Velocity**:
The formula for the root mean square velocity of gas molecules is given by:
\[ v_{rms} = \sqrt{\frac{3RT}{M}} \]

2. **Understand the Dependencies**:
From the formula, we can see that:
- \( v_{rms} \) is directly proportional to the square root of the temperature \( T \) (since \( R \) and \( M \) are constants for a given gas).
- This means that if the temperature increases, the RMS velocity increases.

3. **Analyze the Options**:
- Since \( v_{rms} \) is proportional to \( \sqrt{T} \), we can conclude that it is not proportional to \( T \) or \( T^2 \) directly.
- Therefore, we can rule out options that suggest direct proportionality to \( T \) or \( T^2 \).

4. **Conclusion**:
Based on our analysis, we conclude that the correct relationship is:
\[ v_{rms} \propto \sqrt{T} \]
Hence, the correct answer is that the root mean square velocity is proportional to the square root of the temperature.

### Final Answer:
The root mean square velocity of molecules of gas is proportional to the square root of the temperature \( T \).