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Chemical Engineering Thermodynamics II
• Dr. Perla B. Balbuena: JEB 240 [email protected] • Website:
http://research.che.tamu.edu/groups/Balbuena/Courses/CHEN%20354-Thermo%20II-%20Spring%2015/CHEN%20354-Thermo%20II-Spring%2015.htm
(use VPN from home)• CHEN 354-Fall 14
TA: Julius Woojoo Choi, [email protected]
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TAs office hours
• Julius Woojoo Choi, [email protected] • Office hours: Thursdays, 4-5pm, Office
613
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TEAMS
• Please group in teams of 4-5 students each
• Designate a team coordinator • Team coordinator: Please send an
e-mail to [email protected] stating the names of all the students in your team (including yourself) no later than next Monday
• First HW is due January 28.
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Introduction to phase equilibrium
Chapter 10 (but also revision from Chapter 6)
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Equilibrium
• Absence of change• Absence of a driving force for change• Example of driving forces– Imbalance of mechanical forces =>
work (energy transfer)– Temperature differences => heat
transfer– Differences in chemical potential =>
mass transfer
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Energies
• Internal energy, U
• Enthalpy H = U + PV
• Gibbs free energy G = H – TS
• Helmholtz free energy A = U - TS
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Phase Diagram Pure Component
a
d
c
b
e
What happens from (a) to (f) as volume is compressed at constant T.
f
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P-T for pure component
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P-V diagrams pure component
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Equilibrium condition for coexistence of two phases
(pure component)
• Review Section 6.4
• At a phase transition, molar or specific values of extensive thermodynamic properties change abruptly.
• The exception is the molar Gibbs free energy, G, that for a pure species does not change at a phase transition
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Equilibrium condition for coexistence of two phases
(pure component, closed system)
d(nG) = (nV) dP –(nS) dT
Pure liquid in equilibrium with its vapor, if a differential amount of liquid evaporates at constant T and P, then
d(nG) = 0
n = constant => ndG =0 => dG =0
Gl = Gv
Equality of the molar or specific Gibbs free energies (chemical potentials) of each phase
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Chemical potential in a mixture:
• Single-phase, open system:
i
i
nTPinPnT
dnn
nGdT
T
nGdP
P
nGnGd
j,,,,
)()()()(
i :Chemical potential of component i in the mixture
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Phase equilibrium: 2-phases and n components
• Two phases, a and b and n components:
Equilibrium conditions:
ia = i
b (for i = 1, 2, 3,….n)
Ta = Tb
Pa = Pb
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A liquid at temperature T
The more energetic particles escape
A liquid at temperature T in a closed container
Vapor pressure
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Fugacity of 1 = f1 Fugacity of 2 = f2
222̂ fxf id
111̂ fxf id
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For a pure component
=
iiii fRTTG ln)(
For a pure component, fugacity is a function of T and P
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For a mixture of n components
i = i
for all i =1, 2, 3, …n
in a mixture:
iii fRTT ˆln)(
Fugacity is a function of composition,T and P
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Lets recall Raoult’s law for a binary
lv
lv
ff
ff
22
11
ˆˆ
ˆˆ
We need models for the fugacity in the vapor phase and in the liquid phase
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Raoult’s law
• Model the vapor phase as a mixture of ideal gases:
• Model the liquid phase as an ideal solution
ivi Pyf ˆ
isati
li xPf ˆ
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VLE according to Raoult’s law:
222
111
xPPy
xPPysat
sat
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Homework # 1
download from web site
Due Wednesday, 1/28