One mole of an ideal gas with the adiabatic exponent γ undergoes a polytropic process with polytropic constant n, as a result of which the volume of the gas increases ρ-fold. The entropy increment of

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One mole of an ideal gas with the adiabatic exponent γ undergoes a polytropic process with polytropic constant n, as a result of which the volume of the gas increases ρ-fold. The entropy increment of the gas in this process is

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

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