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 = √((3k_B T)/(m)), m = 39.9 × 10⁻³⁶.02 × 10²³ = 6.63 × 10⁻²⁶ kg.860² = 3 × 1.38 × 10⁻²/³ × T6.63 × 10⁻²⁶, T = 7.396 × 10⁵ × 6.63 × 10⁻²⁶/⁴.14 × 10⁻²/³ ≈ 1185 K. Substituting values gives 1200 K, which matches expected kinetic theory result, confirming mean free path λ = 1/(√2