If `P` is the pressure of gas, then the kinetic energy per unit volume of the gas is .

Explanation

According to the kinetic theory of an ideal gas, the pressure p exerted by the gas is given by
`p=(1)/(3)rhoc^(2)_(rms)=(1)/(3)(m)/(V)c^(2)_(rms)`
where `c_(rms)` is the rms speed (root-maen-square speed) of the gas molecules,m, V and `rho` are the mass, volume and density of the gas, respectively.
`:. pV=(1)/(3)mc^(2)_(rms)=(2)/(3)((1)/(2)mc^(2)_(rms))`
Here,`(1)/(2)mc^(2)_(rms)` is the total kinetic energy (KE) of all molecules of the gas.
`:. pV=(2)/(3)(KE)" " :. KE=(3)/(2)pV" " :. (KE)/(V)=(3)/(2)p`
Thus, the kinetic energy per unit volume of a gas is `(3)/(2)`p.