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. v_rms ∝ (1)/(√(m)), v_Nev_N₂ = √(m_N)₂m_Ne.v_Nev_N₂ = √((28)/(20.2)) ≈ √(1.386) ≈ 1.18. Substituting values gives 1.18:1, 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.