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The Advanced Chemical Engineering Thermodynamics The thermodynamics properties of fluids (II). Q&A_-10- 11/17/2005(10) Ji-Sheng Chang. Property relations. The residual Gibbs free energy The definition of residual properties M R (T,P) = M(T,P) - M IG (T,P) R: Residual property

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the advanced chemical engineering thermodynamics the thermodynamics properties of fluids ii

The Advanced Chemical Engineering ThermodynamicsThe thermodynamics properties of fluids (II)

Q&A_-10- 11/17/2005(10)

Ji-Sheng Chang

property relations
Property relations
  • The residual Gibbs free energy
    • The definition of residual properties
      • MR(T,P) = M(T,P) - MIG(T,P)
      • R: Residual property
      • IG : Ideal gas behavior property
    • MR(T,P) = M(T,P) - MIG(T,P),M are the properties as V, G, H, S, …
property relations3
Property relations
  • The residual properties
    • VR(T,P) = V(T,P) - VIG(T,P) = V - RT/P;Basic thermodynamics relationship for calculations
    • GR(T,P) = G(T,P) - GIG(T,P);More important in traditional Chemical Engineering Thermodynamics
    • HR(T,P) = H(T,P) - HIG(T,P)
property relations4
Property relations
  • Deriving the residual properties in terms of the PVT properties.
    • From the generating function of Gibbs free energy, VR/RT= [(GR/RT)/P]T,
    • Then d(GR/RT) = (VR/RT)dP,
    • to integrate from P=0 to P at constant T.
property relations5
Property relations
  • The integrated result in terms of PVT property as the formula (6.45)
property relations6
Property relations
  • The residual enthalpy, HR/RT= - T [(GR/RT)/T]P, The integrated result in terms of PVT property as the formula (6.46)
property relations7
Property relations
  • In previous section S = H/T - G/T, then the residual entropy SR/R = HR/RT - GR/RTThe result in terms of PVT property as the formula (6.48)
property relations8
Property relations
  • Using the independent property of T and V
    • More commonly as the form P=P(V,T) of the PVT equations of state, especially the cubic equations of state.
    • P = ZRT/V, P = ZRT; as  = 1/V
    • dP=RTd(Z)=RT(Zd+dZ) at constant T
property relations9
Property relations
  • dP/P=d/+dZ/Z,
  • as the formula (6.58)
  • the alternative form.
property relations10
Property relations
  • Calculating the residual properties
    • The PVT data, Using graphical integration method to calculate the residual Gibbs free energy from steam data.
phase diagram

PC,TC

Solid

Liquid

Gas

Phase diagram

1. PT phase diagram of water

2. The Solid/Liquid equilibrium curve

for water

for most component

200OC path

Critical properties

PC=220.55 bar

TC=647.1 K

TTri=273.16 K

vapor liquid equilibrium curve
Vapor/Liquid equilibrium curve
  • The Antoine equation
    • The constant of Antoine equation for water
      • A=16.3872
      • B=3056.96
      • C=217.625
property
Property
  • Critical properties of water
    • PC=220.55 bar
    • TC=647.1 K
    • PTri=0.611 kPa
    • TTri=273.16 K
    • Tn=373.15 K at P= 1.01325 bar = 1 atm
property relations14
Property relations
  • Problems
    • Calculate the residual Gibbs energy of the 200C superheat steam at 10 bar, using the PVT data from steam tables
example 1
Example 1
  • Calculating the residual properties
    • The PVT equations of state
      • Using the two term virial equation of states, estimate the molar volume, residual enthalpy, residual entropy, and residual Gibbs free energy of the carbon dioxide at the states of temperature of 25C and pressure of 1 bar.
deriving the formulas
Deriving the formulas
  • The equations of residual Gibbs free energy
  • Three type of the two term virial equation
  • The residual Gibbs free energy for a gas at each P and T
deriving the formulas20
Deriving the formulas
  • Second virial coefficient
    • From PVT data
    • From generalized correlation equations
    • Based molecular thermodynamic, it is integrated from potential function
example 2
Example 2
  • Calculating the residual properties
    • The PVT equations of state
      • Using the two term virial equation of states, estimate the molar volume, residual enthalpy, residual entropy, and residual Gibbs free energy of the methane at the states of temperature of 25C and pressure of 1 bar.
example 3
Example 3
  • Calculating the residual properties
    • The PVT equations of state
      • (?) Using the two term virial equation of states, estimate the molar volume, residual enthalpy, residual entropy, and residual Gibbs free energy of the benzene at the states of temperature of 25C and pressure of 1 bar.
theorem of corresponding states
Theorem of corresponding states
  • Two-parameter theorem of corresponding states
    • Given T and P
    • Finding Tc, Pc
    • Calculate Tr, Pr
    • Using Tr, Pr to finding the reduced properties from Table E.1 to E.16
theorem of corresponding states24
Theorem of corresponding states
  • Three-parameter theorem of corresponding states
    • Given T and P
    • Finding Tc, Pc, 
    • Calculate Tr, Pr
    • Using Tr, Pr,  to finding the reduced properties from Table E.1 to E.16
theorem of corresponding states25
Theorem of corresponding states
  • Based on the corresponding states principles
    • The Lee/Kesler generalized correlation tables, Appendix E at text books of pages from 695 to 711.
    • The properties of some pure species tables, Appendix B at text books of pages from 679 to 682.
example 4
Example 4
  • Application of the theorem of corresponding states to estimate the thermodynamics properties of the pure components.
    • At temperature of 25C and pressure of 1 bar, estimate the molar volume, residual enthalpy, residual entropy, and residual Gibbs free energy of the carbon dioxide.
example 5
Example 5
  • Application of the theorem of corresponding states to estimate the thermodynamics properties of the pure components.
    • At temperature of 25C and pressure of 1 bar, estimate the molar volume, residual enthalpy, residual entropy, and residual Gibbs free energy of the methane.
example 6
Example 6
  • Application of the theorem of corresponding states to estimate the thermodynamics properties of the pure components.
    • (?) At temperature of 25C and pressure of 1 bar, estimate the molar volume, residual enthalpy, residual entropy, and residual Gibbs free energy of the benzene.