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  4. The root mean square velocity of a gas is doubled when the temperature is

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Q. The root mean square velocity of a gas is doubled when the temperature is

ManipalManipal 2010States of Matter

Solution:

$ v_{rms}=\sqrt{\frac{3 R T}{M}}$
$\therefore v_{rms} \propto \sqrt{T}$
$\therefore $ At two different temperatures,
$\frac{v_{rms}}{v'_{rms}}=\sqrt{\frac{T}{T'}}$
Given $v'_{rms}=2 v_{r m s}$
$\frac{1}{2}=\sqrt{\frac{T}{T'}}$
or $\frac{1}{4}=\frac{T}{T'}$
$\therefore T'=4 T$
$\therefore v_{rms}$ gets doubled, when the temperature is increased four times.