For a gas sample with   number of molecules, function N(V) is given by : $\text{N}\left(\text{V}\right)=\frac{\text{dN}}{\text{dV}}=\left(\frac{3{\text{N}}_0}{{\text{V}}_0^3}\right){\mathrm{V}}^2$ for $0\le \text{V}\le {\text{V}}_0$ and $\text{N}\left(\text{V}\right)=0$$\mathrm{for} V>{\text{V}}_0\text{.}$ Where dN is number of molecules in speed range  . The rms speed of the molecules is :