A gas at 2 atm and 300 K occupies 20 litres. If the pressure is increased to 4 atm at constant temperature, what is the
**Mean free path variation** λ ∝1/n ∝1/P at constant T, λ ∝ T/P, temperature increase increases λ because n decreases at constant P, but also v increases, overall λ ∝ T/P, for gas at 2 atm λ=4×10⁻⁷ m, at 4 atm λ=2×10⁻⁷ m halves when pressure doubles, as n doubles. Boyle’s law: P₁ V₁ = P₂ V₂.P₁ = 2 atm, V₁ = 20 litres, P₂ = 4 atm.V₂ = (P₁ V₁)/(P₂) = (2 × 20)/(4) = 10 litres. Substituting values gives 10 litres, which matches expected kinetic theory result, confirming mean free path λ = 1/(√2 n π d²), ideal gas law P V =
Ref: NCERT > Physics Book > Behaviour of Perfect Gas and Kinetic Theory > Collision Frequency and Mean Free Path Variation