The root mean square speed of molecules of a | vedclass

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(C) The root mean square speed $(v_{rms})$ of gas molecules is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$.Since $R$ and $M$ are constants f

Vedclass · Accepted Answer

$400$

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(C) The root mean square speed $(v_{rms})$ of gas molecules is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$.Since $R$ and $M$ are constants for a given gas,$v_{rms} \propto \sqrt{T}$.Note that $v_{rms}$ is independent of pressure.Given $T_1 = 27^{\circ} C = 300\, K$ and $(v_{rms})_1 = 200\, ms^{-1}$.Given $T_2 = 127^{\circ} C = 400\, K$.Using the ratio: $\frac{(v_{rms})_2}{(v_{rms})_1} = \sqrt{\frac{T_2}{T_1}} = \sqrt{\frac{400}{300}} = \sqrt{\frac{4}{3}} = \frac{2}{\sqrt{3}}$.Therefore,$(v_{rms})_2 = \frac{2}{\sqrt{3}} 	imes (v_{rms})_1 = \frac{2}{\sqrt{3}} 	imes 200 = \frac{400}{\sqrt{3}}\, ms^{-1}$.Comparing this with $\frac{x}{\sqrt{3}}$,we get $x = 400$.

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