Question:
The root mean square velocity of a gas is doubled when the temperature is ________.
The root mean square velocity of a gas is doubled when the temperature is ________.
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The root mean square velocity of a gas is doubled when the temperature is ____.
Updated On: Apr 15, 2026
- increased four times
- increased two times
- reduced to half
- reduced to one fourth
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The Correct Option is A
Solution and Explanation
Step 1: Formula
The rms velocity is given by $v_{rms} = \sqrt{\frac{3RT}{M}}$.
Step 2: Analysis
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.
Final Answer: (A)
The rms velocity is given by $v_{rms} = \sqrt{\frac{3RT}{M}}$.
Step 2: Analysis
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.
Final Answer: (A)
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