Question

Derive the Charle's law on the basis of kinetic theory.

Answer 1

Charle's law:-

It states that for a given mass of a gas, the volume of the gas is directly proportional to the absolute temperature of the gas, provided pressure is constant.

According to kinetic theory

p = 1/3 M/V C²

or, pV = 1/3 MC²

or, pV = 1/3 m NC²

N is Avogadro's number

But mean kinetic energy of a molecule is

1/2 mC² = 3/2 k_BT or mC² = 3k_BT

Therefore, pV = 1/2 N x 3k_BT = Nk_BT

or, V = Nk_B/P T

If is constant, V ∝ T or V/T = constant

Graph between V and T is shown in figure. If volume and temperature of a given mass of a gas at constant pressure changes from V₁.T₁ to V₂,T₂ then

V₁/T₁ = V₂/T₂ = constant