Prove that kinetic energy of gas is proportional to absolute temperature.

Explanation

Relation between kinetic energy and temperature
This relation can be drawn on the basis of kinetic theory of gases.
K. E. of one molecule `=(1)/(2)m u^(2)`
K. E. of n molecules `=(1)/(2)m u^(2) xx n =(3)/(2) xx (1)/(3) m n u^(2)=(3)/(2)pV " " ( :.pV=(1)/(3)m n u^(2))`
But pV=RT for one mole of an ideal gas
So, K.E. of gas `=(3)/(2)Rt" " `(Here R is gas constant)
or K.E. of gas `prop` T.
This means that kinetic energy of a gas is directly proportional to absolute temperature.