A) increased four times
B) increased two times
C) reduced to half
D) reduced to one fourth
Correct Answer: B
Solution :
\[{{v}_{rms}}=\sqrt{\frac{3RT}{M}}\] \[\therefore \] \[{{v}_{rms}}\propto \sqrt{T}\] \[\therefore \]At two different temperatures, \[\frac{{{v}_{rms}}}{{{v}_{rms}}}=\sqrt{\frac{T}{T}}\] Given, \[{{v}_{rms}}=2{{v}_{rms}}\] \[\frac{1}{2}=\sqrt{\frac{T}{T}}\] or \[\frac{1}{4}=\frac{T}{T}\] \[\therefore \] \[T=4T\] \[\therefore \,\,{{v}_{rms}}\]gets doubled, when the temperature is increased four times.
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