The r.m.s. velocity of hydrogen at S.T.P. is ' u ' \(\mathrm{m} / \mathrm{s}\). If the gas is heated at constant pressure till its volume becomes three times, then the final temperature of the gas and the r.m.s. speed are respectively

As the process is adiabatic,
\(\frac{V_2}{V_1} =\frac{T_2}{T_1} \Rightarrow \frac{3 V_1}{V_1}=\frac{T_2}{T_1} \)
\( \therefore 3 T_1 =T_2 \)
\( \therefore T_2 =3 \times 273=819 \mathrm{~K}\)
Also,
\(\begin{aligned}
& \mathrm{V}_{\mathrm{rms}}=\sqrt{\frac{3 \mathrm{RT}}{\mathrm{M}_0}} \\
& \Rightarrow \mathrm{~V}_{\mathrm{rms}} \propto \sqrt{\mathrm{~T}} \\
& \frac{\mathrm{~V}_{\mathrm{rms}}^{\prime}}{\mathrm{V}_{\mathrm{rms}}}=\sqrt{\frac{\mathrm{T}_2}{\mathrm{~T}_1}}
\end{aligned}\)
\(\therefore \quad \mathrm{V}_{\mathrm{rms}}^{\prime}=\mathrm{V}_{\mathrm{rms}} \sqrt{\frac{819}{273}}=\sqrt{3} \mathrm{um} / \mathrm{s} \ldots\left(\text { given } \mathrm{V}_{\mathrm{rms}}=\mathrm{u}\right)\)