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  4. The temperature of an ideal gas is increased from 100 K to 400 K. If the rms speed of the gas molecule is v at 100 K, then at 400 K it becomes

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Q. The temperature of an ideal gas is increased from $100\, K$ to $400\, K$. If the rms speed of the gas molecule is $v$ at $100\, K$, then at $400\, K$ it becomes

KEAMKEAM 2018Kinetic Theory

Solution:

$\because$ rms speed of molecule $V_{\text {rms }} \propto \sqrt{T}$
for $T=100\, K$
$\left(V_{ rms }\right)_{1} \propto \sqrt{100}$
for $T=400\, K$
$\left(V_{ rms }\right)_{2}=\sqrt{400}$
therefore, $\frac{\left(V_{ rms }\right)_{1}}{\left(V_{ rms }\right)_{2}}=\frac{\sqrt{100}}{\sqrt{400}}$
or $\frac{v}{\left(V_{ rms }\right)_{2}}=\frac{1}{2}$
or $\left(V_{ rms }\right)_{2}=2 v$