From kinetic theory prove that 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 of the gas=`v=M/P`
We know pressure `,p=1/3 pc^2`
Hence p= density of the gas
c=rms speed of gas molecules
Now kinetc energy of gas molecules
`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)/p=3/2pv`
Hence `p=(2E)/(3v)`