Practice question

**Degrees of freedom** f counts independent motions, monatomic 3 translational, diatomic 3 translational +2 rotational =5 at room T, vibrational adds at high T, molar specific heat at constant volume C_v = f/2 R, at constant pressure C_p = C_v + R, ratio γ = C_p/C_v = (f+2)/f, monatomic γ=5/3≈1.67, diatomic γ=7/5=1.4. l = (1)/(√(2) n π d²), n = (N)/(V), and PV = Nk_B T.At constant P, V ∝ T, so n ∝ (1)/(T). If T doubles, n halves, l doubles.New l = 2 × 2.9 × 10⁻⁷ = 5.8 × 10⁻⁷ m . Substituting values gives 5.8 × 10⁻⁷ m, which matches expected