Answer Key # 2 The Entropy of Thermodynamics - Edubirdie

University:
Santa Fe College
Course:
PHY 2048 | General Physics 1 with Calculus
Academic year:

2024
Views:

464

Pages:

4
Author:

Jabin F.

Prob: The entropy of a thermodynamic system is defined as - S = CV^(1/4)U^(3/4), where C is Const and U, V have usual meaning. 1) Find the temp(T) and pressure(p) in terms of U,V & S 2) Find the Gibbs free energy of the system. Solution: TdS = dU + PdV => 1/T = (∂S/∂U)v, P/T = (∂S/∂V)u S = CV^(1/4)U^(3/4) → lnS = lnC + 1/4 lnV + 3/4 lnU do diff. → 1/S (∂S/∂U)v = 3/4 1/U → (∂S/∂U)v = 3/4 S/U = 1/T → T = 4/3 U/S → 1/S (∂S/∂V)u = 1/4 1/V → (∂S/∂V)u = 1/4 S/V = P/T → P = 1/3 U/V Solution (I): G = H-TS = U+PV-TS = U + 1/3U - 4/3U G = 0 [ques. 11. page 29] V = RT/P - b/T => P = RT/(V + b/T) => V + b/T = RT/P -(i) (∂V/∂T)p = R/P + b/T^2 (∂V/∂T)p = R/P (1 + bP/RT^2) ⇒ (∂P/∂T)v = ((V + b/T)R - RT(-b/T^2)) / (V + b/T)^2 = R(V + b/T + b/T) / (V + b/T)^2 from (i) = R (RT/P + b/T) / (RT/P)^2 = RRT/P(1 + Pb/RT^2) / (RT/P)^2 Cp - Cv = T(∂V/∂T)p (∂P/∂T)v put value = T R/P (1 + Pb/RT^2) * R (1 + Pb/RT^2) / (RT/P) Cp - Cv = R (1 + Pb/RT^2) (option-c)

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