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  4. At what temperature, rms (root mean square) speed of air molecules is double of that at STP?

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Q. At what temperature, rms (root mean square) speed of air molecules is double of that at STP?

NTA AbhyasNTA Abhyas 2022

Solution:

$v_{rms} \propto \sqrt{T}$
$\Rightarrow \frac{v_{1}^{2}}{v_{2}^{2}}=\frac{T_{1}}{T_{2}}$
$\Rightarrow \, \frac{v^{2}}{4 v^{2}}=\frac{273}{T_{2}}$
$\Rightarrow \, T_{2}=1092K=819^\circ C$