For a gas,the r.m.s. speed at 800 , K is | vedclass

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

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Twice the value at $200 \, K$

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(C) The root mean square $(r.m.s.)$ speed of a gas molecule is given by the formula: $v_{rms} = \sqrt{\frac{3RT}{M}}$.Since $R$ and $M$ are constants for a given gas,the $r.m.s.$ speed is directly proportional to the square root of the absolute temperature: $v_{rms} \propto \sqrt{T}$.Let $v_1$ be the $r.m.s.$ speed at $T_1 = 200 \, K$ and $v_2$ be the $r.m.s.$ speed at $T_2 = 800 \, K$.Then,$\frac{v_2}{v_1} = \sqrt{\frac{T_2}{T_1}} = \sqrt{\frac{800}{200}} = \sqrt{4} = 2$.Therefore,$v_2 = 2v_1$,which means the $r.m.s.$ speed at $800 \, K$ is twice the value at $200 \, K$.

For a gas,the $r.m.s.$ speed at $800 \, K$ is

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