From the relation `p=1/3 mnc_(rms)^2` show that the mean kinetic energy of a molecule is the same for all types of gases.

Explanation

Given `p=1/2mnc_(rms)^2=1/3(mN)/Vc_(rms)^2`
[N=number of moles,V=volume]
or, `1/3mc_(rms)^2=(pV)/N=((N/N_A)RT)/N` [`N_A` Avogadro.s number]
or, `1/3mc_(rms)^2=(3RT)/(2N_A)`
`therefore` mean kinetic energy of a molecule `1/3mc_(rms)^2=(3RT)/(2N_A)` is same for all types of gases at a particular temperature.