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  4. The absolute temperature of a gas is increased to 16 times of the original temperature. The rms speed of its molecules will become

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Q. The absolute temperature of a gas is increased to $ 16 $ times of the original temperature. The rms speed of its molecules will become

J & K CETJ & K CET 2017Kinetic Theory

Solution:

Let initial absolute temperature of gas be $T$
$\therefore $ New absolute temperature of gas, $T'=16\,T$
Root mean square speed of molecules of gas is given by
$v_{rms}=\sqrt{\frac{3RT}{M}}$
$\therefore $ At new absolute temperature, $v_{rms}$ become $4$ times