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(D) The root mean square (r.m.s.) velocity $v_{rms}$ of gas molecules is given by the formula: $v_{rms} = \sqrt{\frac{3RT}{M}}$.From this relation,it

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$\sqrt{5}$ times

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(D) The root mean square (r.m.s.) velocity $v_{rms}$ of gas molecules is given by the formula: $v_{rms} = \sqrt{\frac{3RT}{M}}$.From this relation,it is clear that $v_{rms} \propto \sqrt{T}$.Let the initial temperature be $T_1 = T$ and the final temperature be $T_2 = 5T$.Let the initial r.m.s. velocity be $v_1$ and the final r.m.s. velocity be $v_2$.Then,$\frac{v_2}{v_1} = \sqrt{\frac{T_2}{T_1}} = \sqrt{\frac{5T}{T}} = \sqrt{5}$.Therefore,$v_2 = \sqrt{5} v_1$.Thus,the r.m.s. velocity becomes $\sqrt{5}$ times the initial velocity.

If the absolute temperature of a gas is increased $5$ times,the r.m.s. velocity of the gas molecules will be

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