What is the expression between pressure and kinetic energy of gas molecules ?

By kinetic theory, pressure
$\left(\mathrm{P}\right)=\frac{1}{3}\mathrm{mn}{\overline{\mathrm{V}}}^2$.......................(1)
Kinetic energy(k) $=\frac{1}{2}\mathrm{mn}{\overline{\mathrm{V}}}^2$............(2)
Dividins (1) & (2)
$\begin{array}{l}\therefore \text{ Pressure }\left(\mathrm{P}\right)=\frac{1}{3}\mathrm{mn}{\overline{\mathrm{V}}}^2=\frac{2}{3}\left[\frac{\mathrm{mn}{\overline{\mathrm{V}}}^2}{2}\right]=\frac{2}{3}\left(\mathrm{KE}\right)\\ \Rightarrow \mathrm{P}=\frac{2}{3}\mathrm{k}\end{array}$
Where m is mass of the molecule n is number of molecules per unit volume
$\overline{\mathrm{V}}$is the mean–square–speed.