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Question

A gas has a C_p of 33.24 J mol⁻¹ K⁻¹. What is its C_v? (R = 8.31 J mol⁻¹ K⁻¹)

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Explanation

**Partial pressure concept** for mixture of non-reacting gases, total pressure sum of partials, each gas behaves independently, kinetic theory still holds with effective n = Σ n_i, mean free path depends on total n and cross-sections, mixture properties weighted by mole tions. C_p - C_v = R, C_v = C_p - R.C_v = 33.24 - 8.31 = 24.93 J mol⁻¹ K⁻¹. Substituting values gives 24.93 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.

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