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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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The correct answer is:
$\sqrt{5}$ times
The mean kinetic energy $\frac{1}{2} \mathrm{~m}<\mathrm{v}>^2$ of the gas molecule is proportional to the temperature $\mathrm{T}$ :
$<\mathrm{v}>2 \propto \mathrm{T}$
$\frac{\left\langle\mathrm{v}_2\right\rangle}{\left\langle\mathrm{v}_1\right\rangle}=\sqrt{\frac{\mathrm{T}_2}{\mathrm{~T}_1}}$
$\therefore\left\langle\mathrm{v}_2\right\rangle=\sqrt{5}\left\langle\mathrm{v}_1\right\rangle$
$<\mathrm{v}>2 \propto \mathrm{T}$
$\frac{\left\langle\mathrm{v}_2\right\rangle}{\left\langle\mathrm{v}_1\right\rangle}=\sqrt{\frac{\mathrm{T}_2}{\mathrm{~T}_1}}$
$\therefore\left\langle\mathrm{v}_2\right\rangle=\sqrt{5}\left\langle\mathrm{v}_1\right\rangle$
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