Question

The root mean square velocity of a gas is doubled when the temperature is ________.

• A. increased four times
• B. increased two times
• C. reduced to half
• D. reduced to one fourth

Hint:

The root mean square velocity of a gas is doubled when the temperature is ____.

Answer 1

The Correct Option is A

Step 1: Formula
The rms velocity is given by $v_{rms} = \sqrt{\frac{3RT}{M}}$.
Step 2: Evaluation
This shows that $v_{rms} \propto \sqrt{T}$.
Step 3: Calculation
To double the velocity ($2v_{rms}$), the temperature must be increased to $4T$ because $\sqrt{4T} = 2\sqrt{T}$.
Step 4: Conclusion
Thus, the velocity is doubled when the temperature is increased four times.
Hence, the Answer is: (A)