Relation between Average Kinetic Energy and Temperature

From equation (i)   PV = (2/3) Kinetic energy [As PV = RT for 1 mole]

Then R.T = (2/3) Kinetic energy

Or Kinetic energy = (3/2) RT for 1 mole of gas

Kinetic energy = (3/2) nRT (for n moles of gas)

(Average Kinetic energy) Kinetic energy = (3/2) (R/No) x RT (Kinetic energy for 1 molecule)

Or Kinetic energy = (3/2) k T (k → Boltzman’s constant

So Kinetic energy ∝ T (as (3/2) k → constant)

So at T = OK, u = 0 i.e. Kinetic energy is zero to motion of gas molecules due to temperature is called thermal motion.