An ideal gas with the adiabatic exponent γ goes through a process: P = P₀ − αV, where P₀ and α are positive constants and V is the volume. At what volume will the gas entropy have the maximum value?

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For one mole S = Cᵥ,ₘ ln T + R ln V + const with T = (P₀V − αV²)/R. dS/dV = Cᵥ,ₘ(P₀ − 2αV)/(P₀V − αV²) + R/V = 0 gives P₀(Cᵥ,ₘ + R) = αV(2Cᵥ,ₘ + R). With Cᵥ,ₘ = R/(γ−1): Cᵥ,ₘ + R = γR/(γ−1) and 2Cᵥ,ₘ + R = (γ+1)R/(γ−1), so V = γP₀/[α(γ+1)]. Matches (b).

Chemistry - Thermodynamics - II Question with Solution | TestHub

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