Practice question

**Internal energy of ideal gas** U = f/2 n R T depends only on temperature, f degrees of freedom, n moles, R=8.314 J/mol·K, for monatomic f=3 U=3/2 n R T, diatomic f=5 at moderate T U=5/2 n R T, independent of pressure or volume, only T matters for ideal gas. l ∝ (1)/(n), n ∝ P. If P increases by 4 times (0.2 to 0.8), n increases 4 times, l reduces to (1)/(4).New l = 1.5 × 10⁻⁶/4 = 3.75 × 10⁻⁷ m. Substituting values gives 3.75 × 10⁻⁷ m, which matches expected kinetic theory result, confirming mean free path λ = 1/(√2 n π