An ideal gas with the adiabatic exponent γ goes through a process: P = a − bV, where a and b are positive constants and V is the volume. At what volume does the entropy of the gas attain its maximum v

Question

An ideal gas with the adiabatic exponent γ goes through a process: P = a − bV, where a and b are positive constants and V is the volume. At what volume does the entropy of the gas attain its maximum value?

TestHub · Accepted Answer

For one mole S = Cᵥ,ₘ ln T + R ln V + const with T = (aV − bV²)/R. Setting dS/dV = Cᵥ,ₘ(a − 2bV)/(aV − bV²) + R/V = 0 gives a(Cᵥ,ₘ + R) = bV(2Cᵥ,ₘ + R). With Cᵥ,ₘ = R/(γ−1): Cᵥ,ₘ + R = γR/(γ−1), 2Cᵥ,ₘ + R = (γ+1)R/(γ−1), so V = γa/[b(γ+1)]. Matches (b).

Chemistry - Thermodynamics - II Question with Solution | TestHub

Options:

Doubts & Discussion