Chapter 6. Thermodynamic properties of fluids

Chapter 6. Thermodynamic properties of fluids - Chapter 6...

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Chapter 6 Thermodynamic Properties of Fluids Purpose of this chapter: 1. Derive equations which allow calculation of entropy, enthalpy, from PVT, C P and C v etc 2. Discussion diagrams and tables for convenient use 3. Develop generalized correlations which provide estimates of property values in the absence of complete experimental information
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Property relations for homogeneous phases First law for a closed system of reversible process rev rev dW dQ dU + = The equation is derived from reversible process, but all terms are state functions so it can be applied to any process in a closed system (not necessarily reversible processes) with changes between equilibrium states. PV U H + The enthalpy: TS U A - The Helmholtz energy: TS H G - The Gibbs energy: (2.11) (6.2) (6.3) By definition: Where U and S are the energy and entropy of one mole or unit mass
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For one mole (or a unit mass), differentiation of PdV TdS dU - = SdT PdV dA - - = SdT VdP dG - = (6.8) Similarly, (6.7) (6.9) (6.10) PV U H +
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PdV TdS dU - = VdP TdS dH + = SdT PdV dA - - = SdT VdP dG - = V S S P V T - = P S S V P T = T V V S T P = T P P S T V - = Criterion of exactness for a differential expression: If F = F(x, y), then Comparing Eq(6.7) to Eq(6.11) We have Similar (6.13) (6.14) (6.15) (6.16) Maxwell’s equations which gave the relations among P, T, V, S
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If F = f(x,y) then dy y F dx x F dF x y + = Triple Product Rule If dF=0 (i.e. constant F) x F y y F y x x F + = 0 1 - = y x F x F F y y x Another useful relation F F F y z z x y x =
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Other useful equations dP P S dT T S dS T P + = S = f(T,P) T C T S P P = P T T V P S - = Maxwell dP T V dT T C dS P P - = (6.29) V=RT/P, for ideal gas P Rd T d C dP P R dT T C dS P P ln ln - = - = ) / ln( ) / ln( 1 2 1 2 P P R T T C S P - = Derive a general relation for entropy changes of any fluid with respect to temperature and pressure in terms of CP, CV, P, V, T and their derivatives. Entropy change with respect to T at constant P VdP TdS dH + = P P P V T S T T H + = P P P T S T C T H = = T C T S P P = If C P is a constant Similar T C T S V V =
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Because S = f(T,V) dV V S dT T S dS T V +
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This note was uploaded on 05/01/2011 for the course CHBE 2110 taught by Professor Gallivan during the Spring '08 term at Georgia Tech.

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Chapter 6. Thermodynamic properties of fluids - Chapter 6...

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