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. P = (μ RT)/(V), P_O₂P_H₂ = μ_O₂μ_H₂.μ_O₂ = (16)/(32) = 0.5 mol, μ_H₂ = (4)/(2) = 2 mol.Ratio = (0.5)/(2) = 1:4. Substituting values gives 1:4, 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.