From kinetic theory of gases prove that the pressure of a gas p=`2E//3V`, where V=1 molar volume E=kinetic energy.

Explanation

Molar mass of the gas =M, Number of molecules=Avogadro number =N.
Molar volume =`V=M/P` pressure `p=1/3pc^2` here p=density of gas , c= rms speed
Kinetic energy of gas molecule E
`=1/2mc_1^2+1/2mc_2^2+....+1/2mc_N^2`
`=1/2mN(c_1^2+c_2^2+......c_N^2)/N=1/2Mc^2=1/2M.(3p)/c=3/2pV`
Therefore `p=(2E)/(3V)`