The absolute temperature of a gas is increased 3 times. What will be the increase in rms velocity of the gas molecule ?

The r.m.s velocity of gas molecule is given by
$\begin{array}{l}{\mathrm{V}}_{\text{rms }}=\sqrt{\frac{3\mathrm{KT}}{\mathrm{M}}}\\ \mathrm{V}\propto \sqrt{\mathrm{T}}\frac{{\mathrm{V}}_1}{{\mathrm{V}}_2}=\sqrt{\frac{{\mathrm{T}}_1}{{\mathrm{T}}_2}}=\sqrt{\frac{\mathrm{T}}{3\mathrm{T}}}\\ {\mathrm{V}}_2=\sqrt{3}{\mathrm{V}}_1\end{array}$
The r.m.s velocity of gas molecule is increase by $\sqrt{3}$times of its original velocity.
Increases in RMS velocity = V₂ – V₁$=\sqrt{3}{V}_1-V_1=0.732V_1$