(D) The root mean square (r.m.s.) speed of an ideal gas is given by the formula: $V_{rms} = \sqrt{\frac{3RT}{M}}$.From this relation,we can see that $

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(D) The root mean square (r.m.s.) speed of an ideal gas is given by the formula: $V_{rms} = \sqrt{\frac{3RT}{M}}$.From this relation,we can see that $V_{rms} \propto \sqrt{T}$.Let $T_1 = 200 \ K$ and $T_2 = 800 \ K$.Given $V_{rms,1} = v_0$.We have the ratio: $\frac{V_{rms,2}}{V_{rms,1}} = \sqrt{\frac{T_2}{T_1}}$.Substituting the values: $\frac{V_{rms,2}}{v_0} = \sqrt{\frac{800}{200}} = \sqrt{4} = 2$.Therefore,$V_{rms,2} = 2 v_0$.

Class 11 Physics Kinetic Theory Speed (velocity) of Gas (rms, mean and Most probable speed)

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The temperature of an ideal gas is increased from $200 \ K$ to $800 \ K$. If the r.m.s. speed of the gas at $200 \ K$ is $v_0$,then the r.m.s. speed of the gas at $800 \ K$ will be:

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A
$v_0$
B
$4 v_0$
C
$\frac{v_0}{4}$
D
$2 v_0$

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The temperature of an ideal gas is increased from $200 \ K$ to $800 \ K$. If the r.m.s. speed of the gas at $200 \ K$ is $v_0$,then the r.m.s. speed of the gas at $800 \ K$ will be:

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The $rms$ speed of gas molecules in a container is $400 \, ms^{-1}$. If half of the gas is removed at a constant temperature,the new $rms$ speed will be .... $ms^{-1}$.

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