Practice question

**Ideal gas law** P V = n R T governs gas laws, at constant pressure V ∝ T, so temperature increase 300 K→600 K doubles volume 24→48 L. Charles' law quantitative prediction V₂ = V₁×(T₂/T₁), illustrating direct proportionality, absolute temperature must be in kelvin. C_p = C_v + R.C_p = 27.0 + 8.31 = 35.31 J mol⁻¹ K⁻¹ ≈ 35.3 J mol⁻¹ K⁻¹. Substituting values gives 35.3 J mol⁻¹ K⁻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.