hw13 - – 1 – Solutions to Homework Problem Set 12 Stowe...

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Unformatted text preview: – 1 – Solutions to Homework Problem Set 12 Stowe 11.40 (a) In this problem, we are supposed to find dS as a function of independent variables dT and dP . We may write dS = ∂S ∂T | P dT + ∂S ∂P | T dP . ∂S ∂T | P = 1 T T∂S ∂T | P = C P T . Using Maxwell relations, ∂S ∂P | T =- ∂V ∂T | P =- V β . Therefore, dS = C P T dT- V βdP . (b) By integrating the above equation over T and P independently, we get Δ S = integraltext dS = integraltext C P T dT- integraltext V βdP = C P ln ( T f /T i )- V β ( P f- P i ). With the numbers given, for mole of water, we get Δ S = 75 . 3J / K / mol ln 373K 273K- 1 . 8 × 10- 5 m 3 / mole × 2 . 1 × 10- 4 / K × 10000 × 1 . 013 × 10 5 Pa = 19 . 7J / K Reif 5.12 The system is thermally insulated and evolves quasi-statically, so the constraint can be written as dS = 0. In this problem, we may write dS as a function of dT and dP and then use the constraint to find the relationship between dT and dP . There is dS = ∂S ∂T |...
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