The RMS velocity of ${CO}_{2}$ at a temperature "T" is x cm/ sec . At what temperature, the RMS velocity of ${CO}_{2}$ would be 2x

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16T

32T

answer is C.

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Detailed Solution

$\frac{C_{1}}{C_{2}} = \sqrt{\frac{T_{1}}{T_{2}}} \Rightarrow \frac{x}{2 x} = \sqrt{\frac{T}{T_{2}}} \frac{1}{4} = \frac{T}{T_{2}} \Rightarrow T_{2} = 4 T$

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