For one mole of an ideal gas, increasing the temperature from \(10^{\circ} \mathrm{C}\) to \(20^{\circ} \mathrm{C}\)

Given, \(\mathrm{T}_{1}=273+10=283 \mathrm{~K}\)
\[
\mathrm{T}_{2}=273+20=293 \mathrm{~K}
\]
Average \(\mathrm{KE}=\frac{3}{2} \mathrm{KT}\)
\[
\frac{\left(\mathrm{KE}_{1}\right)}{\left(\mathrm{KE}_{2}\right)}=\frac{283}{293}=0.96
\]
Root mean square (rms) velocity,
\[
\mathrm{v}_{\mathrm{rms}}=\sqrt{\frac{3 \mathrm{RT}}{\mathrm{M}}}
\]
\[
\begin{aligned}
\frac{\mathrm{v}_{(\mathrm{rms})_{1}}}{\mathrm{v}_{(\mathrm{rms})_{2}}} &=\sqrt{\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}} \\
&=\sqrt{\frac{283}{293}}=0.98
\end{aligned}
\]
Thus, both average kinetic energy and root mean square velocity increase but not significantly when temperature is increased from \(10^{\circ} \mathrm{C}\) to \(20^{\circ} \mathrm{C}\).