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The Advanced Chemical Engineering Thermodynamics The thermodynamics properties of fluids (I)

The Advanced Chemical Engineering Thermodynamics The thermodynamics properties of fluids (I). Q&A_-7- 10/27/2005(7) Ji-Sheng Chang. Property relations. The primary equation The first law of thermodynamics: d(nU) = dQ rev + dW rev

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The Advanced Chemical Engineering Thermodynamics The thermodynamics properties of fluids (I)

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  1. The Advanced Chemical Engineering ThermodynamicsThe thermodynamics properties of fluids (I) Q&A_-7- 10/27/2005(7) Ji-Sheng Chang

  2. Property relations • The primary equation • The first law of thermodynamics: d(nU) = dQrev + dWrev • The work of the reversible process for closed system: dWrev = -Pd(nV) • The second law of thermodynamics: dQrev = Td(nS)

  3. Property relations • To combine each terms: • d(nU) = Td(nS) – Pd(nV) • dU = TdS – PdV • For unit mole system • For the mathematic view for the internal energy: • U = f(S,V) or U = U(S,V)

  4. Property relations • dU = TdS – PdV • The total differential of the internal energy: dU = (U/S)VdS + (U/V)SdV • The partial differential term relation to the property: T = (U/S)V ; P = - (U/V)S

  5. Other energy functions • The enthalpy: H = U + PV; • The Helmholtz free energy: A = U – TS; • The Gibbs free energy: G = H – TS;

  6. Other energy functions • The enthalpy: • H = U + PV; • dH = dU + d(PV); • dH = dU + PdV + VdP; • dH = TdS + V dP; • H = H (S,P)

  7. Other energy functions • The Helmholtz free energy: • A = U – TS; • dA = dU – d(TS); • dA = dU – TdS – SdT; • dA = – SdT – PdV; • A = A (T,V)

  8. Other energy functions • The Gibbs free energy: • G = H – TS; • dG = dH – d(TS); • dG = dH – TdS – SdT; • dG = – SdT + VdP; • G = G (T,P)

  9. The Maxwell’s equations • dU = TdS – PdV, dU = (U/S)VdS + (U/V)SdV • T = (U/S)V ; P = – (U/V)S • Doing the next variable partial differential for each terms • (T/V)S = [2U/VS] ; • (P/S)V = - [2U/SV] • Then, (T/V)S = – (P/S)V ;

  10. The Maxwell’s equations • The Maxwell’s equation of each one that derived from internal energy. • (T/V)S = – (P/S)V • There have four Maxwell’s equations for a closed homogeneous system.

  11. Some definition • Some more useful and interested definition • Cp = (H/T)P; • Cv = (U/T)V; •  = [(V/T)P]/V; •  = – [(V/P)T]/V

  12. Enthalpy and entropy • Enthalpy and entropy as functions of T and P • H=H(T,P) • dH = (H/T)PdT + (H/P)TdP • In terms of PVT and Cp result in (6.20) • S=S(T,P) • dS = (S/T)PdT + (S/P)TdP • In terms of PVT and Cp result in (6.21)

  13. Internal energy and entropy • Internal energy and entropy as functions of T and V • U=U(T,V) • dU = (U/T)VdT + (U/V)TdV • In terms of PVT and Cv result in (6.32) • S=S(T,V) • dS = (S/T)VdT + (S/V)TdV • In terms of PVT and Cv result in (6.33)

  14. Generating function of Gibbs free energy • G = G(T,P) • In the view of classical mechanics • In the view of empirical thermodynamics • In the view of traditional thermodynamics

  15. Generating function of Gibbs free energy • G = G(T,P) • dG = VdP – SdT • d(G/RT) = (1/RT)dG – (G/RT2)dT • Using G = H – TS and dG = VdP – SdT • d(G/RT) = (V/RT)dP – (H/RT2)dT

  16. Generating function of Gibbs free energy • G/RT = f(T,P) • V/RT= [(G/RT)/P]T • H/RT= - T [(G/RT)/T]P • S = H/T - G/T • U = H - PV

  17. Generating function of Helmholtz free energy • A = A(T,V) • In the view of the quantum mechanics • In the view of the quantum physics • In the view of the statistical thermodynamics

  18. Generating function of Helmholtz free energy • A = A(T,V) • dA = – PdV – SdT • d(A/RT) = (1/RT)dA – (A/RT2)dT • Using A = U – TS and dA = – PdV – SdT • d(A/RT) = (P/RT)dV – (U/RT2)dT

  19. Generating function of Helmholtz free energy • A/RT = f(T,V) • P/RT= [(A/RT)/V]T • U/RT= - T [(A/RT)/T]V • H=U+PV • S = U/T - A/T

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