What is the relation between the average kinetic energy and pressure?

Explanation

The internal energy of the gas `U=3/2NkT`
The above equation can also be written as `U=3/2PV`
since PV=NkT
`P=2/3 U/V=2/3u`.
Write From the equation (1). we can state that the perssure of the gas is equal to two thrids of internal energy per unit volume or internal energy density `(u=U/V)`
writing perssure in temer of mean kinetic energy density
`P=P=1/3nm barv^(2)=1/3 rho barv^(2)`
Where p=nm= mass density (Note n is number density )
Multipiy and divide R.H.S of eqution (2) by 2 , we get
`P=2/3 (pi/2 bar(v^(2)))`
From the equation (3), presure is equal to `2/3` of mean kinetic energy per unit volume.