Explain in detail the kinetic interpretation of temperature .

Explanation

We know that ,
`P=1/3N/V mbar(v^2)`

`PV=1/3Nmbar(v^2)`
Comparing the equation (1) with ideal gas equation PV = NkT,
`NkT=1/3Nmbar(v^2)`
`kT =1/3mbar(v^2)" "...(2)`
Multiply the above equation by 3/2 on both sides,
`3/2kT = 1/2 mbar(v^2)" "....(3)`
R.H.S of the equation (3) is called average kinetic energy of a single molecule `bar(KE)` .
The average kinetic energy per molecule
`bar(KE)= in =3/2kT " "...(4)`
It is implied from equation (3) that the temperature of a gas is a measure of the average translational kinetic energy per molecule of the gas.