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. Diatomic molecule: 3 translational + 2 rotational + 1 vibrational (2 modes: KE and PE).Total degrees of freedom = 3 + 2 + 2 = 7. Substituting values gives 7, 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.