One mole of an ideal gas undergoes a reversible process in which its entropy varies with absolute temperature T as: S = aT² + Cᵥ,ₘ ln T, where a is a positive constant. If T = T₀ at V = V₀, the volume

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One mole of an ideal gas undergoes a reversible process in which its entropy varies with absolute temperature T as: S = aT² + Cᵥ,ₘ ln T, where a is a positive constant. If T = T₀ at V = V₀, the volume of the gas as a function of temperature in this process is

TestHub · Accepted Answer

dS = (2aT + Cᵥ,ₘ/T) dT. For a reversible path dS = Cᵥ,ₘ dT/T + R dV/V, so R dV/V = 2aT dT. Integrating from (T₀, V₀): R ln(V/V₀) = a(T² − T₀²), i.e. V = V₀ e^[a(T²−T₀²)/R]. Matches (d).

Chemistry - Thermodynamics - II Question with Solution | TestHub

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