One mole of an ideal gas with the adiabatic exponent γ goes through a polytropic process as a result of which the absolute temperature of the gas increases τ-fold. The polytropic constant equals n. Th

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One mole of an ideal gas with the adiabatic exponent γ goes through a polytropic process as a result of which the absolute temperature of the gas increases τ-fold. The polytropic constant equals n. The entropy increment of the gas in this process is

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Polytropic relation TVⁿ⁻¹ = const gives V₂/V₁ = (T₁/T₂)^[1/(n−1)] = τ^[−1/(n−1)]. Then ΔS = Cᵥ,ₘ ln(T₂/T₁) + R ln(V₂/V₁) = [R/(γ−1)] ln τ − [R/(n−1)] ln τ = R ln τ × [(n−1) − (γ−1)]/[(n−1)(γ−1)] = (n−γ)R ln τ/[(n−1)(γ−1)]. Matches (a).

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