Practice question

**Kinetic theory mean free path** λ = 1/(√2 π d² n) quantifies collision frequency. With n =1.0×10²⁵ m⁻³, λ=9×10⁻⁷ m, d² =1/(1.414×10²⁵×3.14×9×10⁻⁷)=2.5×10⁻²⁰ m², d≈1.58×10⁻¹⁰ m, typical molecular size ~10⁻¹⁰ m, consistent with gas kinetic theory. Charles’ law: (V₁)/(T₁) = (V₂)/(T₂).V₁ = 11.2 litres, T₁ = 273 K, T₂ = 546 K.V₂ = V₁ × (T₂)/(T₁) = 11.2 × (546)/(273) = 22.4 litres. Substituting values gives 22.4 litres, which matches expected kinetic theory result, confirming mean free path λ = 1/(√2 n π d²), ideal gas law P V = n R T and v_rms = √(3 R T/M) relations.