Practice question

**Ideal gas internal energy** proportional to temperature, U = (f/2) R T per mole, monatomic 3/2 R T, diatomic 5/2 R T, change ΔU = f/2 n R ΔT, for temperature increase internal energy rises, explaining why heating gas at constant volume raises U entirely as heat. v_rms ∝ (1)/(√(m)), v_Hev_Ar = √(m_Ar)m_He = √((39.9)/(4)) ≈ √(10) ≈ 3.16. Substituting values gives 3.16:1, 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.