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Unformatted text preview: PHYS 253: Assignment 3 Problem 1 For this hydrostatic system, the first law is dU = dQ PdV dU = emf Â· I Â· dt p Â· dV Integrating, we get Î” U = emf Â· I Â· t p Â· ( nv o V ) Problem 2 a) We write the 1st law as Â¯ dQ = dU + PdV Keeping in mind that U = U ( P,T ), we can rewrite dU as dU = âˆ‚U âˆ‚T P dT + âˆ‚U âˆ‚P T dP and from the EOS, we write PdV as PdV = P âˆ‚V âˆ‚T P dT + âˆ‚V âˆ‚P T dP Regrouping the terms, we get Â¯ dQ = âˆ‚U âˆ‚T P + P âˆ‚V âˆ‚T P dT + âˆ‚U âˆ‚P T + P âˆ‚V âˆ‚P T dP b) setting P to be a constant, we rewrite the expression from a) as Â¯ dQ dT P = âˆ‚U âˆ‚T P + P âˆ‚V âˆ‚T P Rewriting the individual terms: Â¯ dQ dT P = C P and P âˆ‚V âˆ‚T P = PV Î² we finally get âˆ‚U âˆ‚T P = C P PV Î² â€“ 2 â€“ c) Starting from the expression in a), at constant V , we first use the result from b) to rewrite the âˆ‚U âˆ‚T  P term Â¯ dQ = C P dT + âˆ‚U âˆ‚P T + P âˆ‚V âˆ‚P T dP and now rewriting the âˆ‚V âˆ‚P  T using the definition of Îº , and dividing by dT , we get: Â¯...
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 Fall '10
 PeterGrutter
 Thermodynamics, Expression, Trigraph, SEPTA Regional Rail, Rewrite engine

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