According to kinetic theory of gases, the P exerted by a gas density ρ and r.m.s. velocity v is given by
P = \(\frac{1}{3}\)ρv2
Mass per unit volume of gas = Density (ρ)
Average K.E. of translation per unit of volume of the gas.
\(E=\frac{1}{2}\)ρv2
\(\frac{P}{E}=\frac{\frac{1}{3}ρv^2}{\frac{1}{2}ρv^2}=\frac{2}{3}\)
P= \(\frac{2}{3}E\)
= \(\frac{2}{3}\)× Average K.E. per unit volume.