Chemical Engineering 713
Advanced Chemical Engineering Thermodynamics
Lecture 1
Organization of Course and Introduction:
The Phase Equilibrium Problem
NC STATE UNIVERSITY
Organization
• Instructor:
Keith E. Gubbins
2-088A Engineering Building I
Phone: 513-2262
Email: keg@ncsu.edu
Office Hours: Tu 4:30 – 6:30 PM
or by email or phone appointment
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Organization
Guest Lecturer
Dr. Liangliang (Paul) Huang
2-029 Engineering Building I
Phone: 513-2051
Email: lhuang4@ncsu.edu
Office Hours:
by e-mail or phone
appointment
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Organization
Teaching Assistants
•
Cody Addington (on campus)
2-029 Engineering Building I
Phone: 513-2051
Email: CHE713TA@gmail.com
Office Hours: by e-mail or phone appointment
•
Ahmed M. Gomaa (distance EOL class)
2-106 Partners II
Phone: 515-8395
Email: aamahmo2@ncsu.edu
Office Hours: e-mail or phone appt
.
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Course Outline
• 1/3 Classical Thermodynamics
• 2/3 Statistical Thermodynamics
Recommended Texts:
– Prausnitz, J.M., Lichtenthaler, R.N., and E. Gomes de
Azevedo, “Molecular Thermodynamics of FluidPhase Equilibria”, third edn., Prentice Hall,
Englewood Cliffs (1999)
– A.R. Leach, “Molecular Modeling: Principles and
Applications”, 2nd edition, Prentice Hall, (2001)
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Course Outline
• Grading:
– 2 in-term exams 50 % (25 % each)
Dates:
Thursday, October 17
Thursday, November 21
– Term paper 30 %
(Details including topic list will be given on
web site)
– Weekly problems 20 %
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Course Objectives
By the end of the course the attendees should be able to
perform the following:
• Use the full set of thermodynamic functions for non-ideal
gas and liquid systems to carry out thermodynamic
calculations, including those for gas-liquid, liquid-liquid and
supercritical extraction equilibria.
• Understand binary phase diagrams, including the high
pressure regions.
• Understand the probability distribution law and partition
function for canonical, microcanonical and grand canonical
variables, and how the various thermodynamic functions are
related to these. Understand the Second Law & statistical
interpretation of entropy and its significance.
• Be able to carry out thermodynamic calculations for gases
and liquids, including complex fluids such as associating
liquids, using statistical thermodynamics.
• Understand the basis of molecular simulation, including
Molecular Dynamics and Monte Carlo methods.
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Recommended Texts
Classical Thermodynamics
*Prausnitz, J.M., Lichtenthaler, R.N. and Gomes de Azevedo, E., “Molecular Thermodynamics of
Fluid-Phase Equilibria”, third edn., Prentice-Hall, Englewood Cliffs (1999)
Denbigh, K.G., “The Principles of Chemical Equilibrium”, Cambridge Univ. Press
Tester, J. and Modell, M., “Thermodynamics and its Applications”, 3rd edn., Prentice-Hall, Englewood
Cliffs (1998)
J.S. Rowlinson and F.L. Swinton, “Liquids and Liquid Mixtures”, 3rd edition, Butterworth Scientific,
London (1982). ISBN 0-408-24192-6.
J.P. O’Connell and J.M. Haile, “Thermodynamics. Fundamentals for Applications”, Cambridge
University Press (2005)
R. Koningsveld, W.H. Stockmayer and E. Nies, “Polymer Phase Diagrams”, Oxford University Press,
Oxford (2001)
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Recommended Texts
Statistical Thermodynamics
K.A. Dill and S. Bromberg, “Molecular Driving Forces. Statistical Thermodynamics in
Chemistry and Biology”, Garland Science, New York (2003)
*
Hill, T.M., “An Introduction to Statistical Thermodynamics”, Addison-Wesley,
Reading (1960)
Gray, C.G. and Gubbins, K.E., “Theory of Molecular Fluids. Volume 1.
Fundamentals”, Oxford University Press, Oxford (1984)
Gray, C.G., Gubbins, K.E. and Joslin, C.G., “Theory of Molecular Fluids. Volume 2.
Applications”, Oxford University Press, Oxford (2011).
McQuarrie, D.A., “Statistical Mechanics”, Harper & Row, New York (1976)
Reed, T.M. and Gubbins, K.E., “Applied Statistical Mechanics”, McGraw-Hill, New
York (1973)
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Recommended Texts
Molecular Simulation
Allen, M.P. and Tildesley, D.J., “Computer Simulation of Liquids”, Clarendon
Press, Oxford (1987)
Frenkel, D. and Smit, B., “Understanding Molecular Simulation”, second
edition, Academic Press, San Diego (2002)
A.R. Leach, “Molecular Modeling: Principles and Applications”, 2nd edition,
Prentice Hall, ISBN 0-582-38210-6 (2001)
E.B. Tadmoor and R.E. Miller, “Modeling Materials”, Cambridge University
Press, Cambridge (2011)
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Course Outline
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Date
08/22/13
08/27/13
08/29/13
09/03/13
09/05/13
09/10/13
09/12/13
09/17/13
09/19/13
09/24/13
09/26/13
10/01/13
10/03/13
10/08/13
• 10/10/13
Topic
Reading*
Introduction. The Phase Equilibrium Problem
PLG1
Energy eqns. Chemical potential, phase eqbm.
PLG2
Equilibrium and stability
Notes
Fugacity
PLG 2,3
Volumetric properties
PLG 3
Gas mixtures. Fugacity, virial eqn. of state
PLG 5
Solubility of solids in compressed gases
PLG 5
Liquid mixtures and phase equilibria
PLG 6
Vapor-liquid equilibria, gas solubility
PLG 6,10
High pressure phase diagrams
GGJ7,PLG 12, KSN 3,4
Statistical mechanics. Distribution law
PLG B; D 11, RG 1,2, H 1
Thermodynamic property expressions
PLG B, GG3.1
Microcanonical ensemble. Second Law, entropy
Notes, H1
Classical statistical mechanics
PLG B, RG 2, H6
FALL BREAK
* PLG=Prausnitz, Lichtenthaler, Gomes de Azevedo; RG= Reed &
Gubbins; GG = Gray & Gubbins; GGJ = Gray, Gubbins,Joslin; KSN =
Koningsveld, Stockmayer& Nies; GQ=Gubbins & Quirke; L=Leach;
D=Denbigh, H=Hill; FS = Frenkel & Smit.
NC STATE UNIVERSITY
Course Outline
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Date
10/15/13
10/17/13
10/22/13
10/24/13
10/29/13
10/31/13
11/05/13
11/07/13
11/12/13
11/14/13
11/19/13
11/21/13
11/26/13
11/28/13
12/03/13
12/05/13
Topic
Reading
Molecular Simulation. General Features
Molecular Simulation: Molecular Dynamics
Molecular Simulation: Monte Carlo
Molecular Simulation: MC in different ensembles
Ideal gas
Intermolecular forces and potentials
Virial equation of state
Corresponding states theory
Distribution functions. Perturbation theory
Perturbation theory
Ideal Solutions
Simple liquid mixtures
GGJ
Simple liquid mixtures
THANKSGIVING HOLIDAY
Associating liquids (H-bonded liquids, etc.)
Polymer solutions
GQ1, L6, Notes
GQ1, L7, FS4, Notes
GQ1, L8, FS3, Notes
Notes, FS5
RG 3, H 4,8,9
PLG4, RG 4,5
PLG 5, RG 7, H15
RG 11, PLG 4
PLG H, GG 4, Notes
GG 4, Notes
GGJ 7, Notes
7, Notes, PLG 7, H20
GGJ 7, Notes, PLG 7
GGJ 7, PLG 7
PLG 8, H21
* PLG=Prausnitz, Lichtenthaler, Gomes de Azevedo; RG= Reed & Gubbins; GG = Gray & Gubbins;
GGJ = Gray, Gubbins,Joslin; KSN = Koningsveld, Stockmayer& Nies; GQ=Gubbins & Quirke;
L=Leach; D=Denbigh, H=Hill; FS = Frenkel & Smit.
NC STATE UNIVERSITY
Heros of Thermodynamics
Major game changers in thermo:
• Nicolas Léonard Sadi Carnot 1796-1832),
French military engineer.
• J. Willard Gibbs (1839-1903), Professor at
Yale University
• J.D. Van der Waals (1837-1923),
University of Amsterdam
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Nicolas Léonard Sadi Carnot
A French military engineer
In1824 he published his “Reflections on the
Motive Power of Fire ”, the first successful
theoretical account of heat engines,
now known as the Carnot cycle, thereby
laying the foundations of the second law of
thermodynamics.
 Sometimes described as the "Father of
Thermodynamics", being responsible for
such concepts as Reversibility, Carnot
Nicolas Léonard Sadi Carnot
efficiency, Carnot theorem, Carnot heat engine.
 His work was elaborated upon by Clausius and Kelvin,
who together derived from it the notion of entropy and
the second law of thermodynamics.
http://en.wikipedia.org/wiki/Nicolas_Léonard_Sadi_Carnot
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History of Thermodynamics
•
•
1810 – 1860: Science of heat engines
(Rankine, Otto, Carnot, Watt)
1873 – 1903: J. Willard Gibbs
J. Willard Gibbs
a) Extended thermodynamics to other
problems, especially chemical and
phase equilibria
b) Developed statistical mechanics,
various ensembles
c) Introduced G and μ and showed how
these determine equilibrium
http://concise.britannica.com/ebc/art-11046
d) Developed vector analysis
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History of Thermodynamics
•
More on Gibbs
–
–
–
–
–
First professor of mathematical physics at Yale
in 1871 (before he published his fundamental
work)
At Yale he laid the foundations of chemical
thermodynamics (1873-75)
Yale paid no salary as professorship was such
an honor. Later John Hopkins University tried
to attract him; Yale relented and paid a salary
Lost his parents at a young age and inherited a
family home and modest fortune with his two
sisters
Remained a bachelor his whole life living later
with his sister’s family
J. Willard Gibbs
http://concise.britannica.com/ebc/art-11046
Source:
http://www.britannica.com/eb/article-9036747
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History of Thermodynamics
•
1873 - ~ 1910: J.D. van der Waals
a) Developed first realistic equation of
state
b) Corresponding states principle
c) Phase equilibria for mixtures
d) High pressure phase behavior
Pv
v
a


RT v  b RTv
J. D. van der Waals
http://nobelprize.org/nobel_prizes/physics/laureates/1910/
waals-bio.html
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History of Thermodynamics
•
More on van der Waals
–
–
–
–
–
–
1910 Nobel Prize Winner in Physics
From the Netherlands
Originally only finished elementary
education (prerequisite to academic
examinations was a classical language – he
had no knowledge)
J. D. van der Waals
Originally a schoolteacher but continued
studies at the University of Leyden
A change in the law in the Netherlands
finally allowed him to sit for academic
examinations and he achieved his doctorate
in 1873
He put forth his famous EOS in his thesis
Became first professor of physics at
Athenaeum Illustre of Amsterdam and made
the university famous together with van’t
Hoff (1901 Nobel Prize in Chemistry)
http://nobelprize.org/nobel_prizes/physics/laureates/1910/
Source :
http://nobelprize.org/nobel_prizes/physics/laureates/1910/
waals-bio.html
waals-bio.html
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Problems Dealt with in Thermodynamics
1. Phase Equilibrium: Fundamentals & Applications
2. Approaches to Phase Equilibria
3. Chemical Reaction Equilibria
4. Property Prediction Using Statistical Thermodynamics
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Pure Component Phase Equilibria
Sandler, S.I., Chemical, Biochemical, and Engineering
Thermodynamics, 4th Ed, John Wiley & Sons,
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Pure Component Phase Equilibria
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Binary Phase Equilibria
Class I: Ar/Kr
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Binary Phase Equilibria
Class II: n-hexane/aniline (no azeotrope)
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Binary Phase Equilibria
Class III: ethane/methanol
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Binary Phase Equilibria
Class VI: 3-methylpyridine/water
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1) Problems: Phase Equilibrium
• Phase Equilibrium: Fundamentals & Applications:
 x1 , x2 ,...xM
 x1 , x2 ,...xM
 x1 , x2 ,...xM



See Prausnitz, Lichtenthaler, Gomes de Azevedo, Appendix A
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1) Problems: Phase Equilibrium
• Gibbs showed that phase equilibrium is governed by this set of
 M  2   1 equations
i depends on
i
T a , Pa , x1a , x2a , xaM -1 , i.e. on (M + 1) variables.
b
b
b
b
b
T
,
P
,
x
,
x
,
x
depends on
1
2
M -1 , i.e. on (M + 1) variables.
PROBLEM:
Given the state of one phase,  , find the state (composition) of the
other phases at equilibrium
SOLUTION:
Gibbs derived the condition of equilibrium and defined thermodynamic
functions (G, the Gibbs free energy and i , the chemical potential)
useful in obtaining a solution.
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1) Problems: Phase Equilibrium
• To solve the set of thermodynamic equations we need an
“equation of state” for our mixture, a function that relates P andi
to T , , x1, x2 , xM 1
P= P (T , r , x1 , x2 ,
x M -1 )
mi = mi (T , r , x1 , x2 , x M -1 )
• Note that P and
i
 A 
P  


V

T , N
are related, so this is really one EOS
 A 
i   
 ni T ,V ,n'
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1) Problems: Phase Equilibrium
• Gibb’s Phase Rule:
– To help keep the variable straight in such problems Gibbs derived the
Phase Rule (1874)
• Consider a simple mixture - no chemical reactions or external fields
(electrical, magnetic, gravitational, etc.)
# of variables
(T
a
, Pa , xa , xa ,
Total # of variables for
1
2
xaM -1
)
for one

phase
  M  1
 phases    M  1
# of constraint equations   M  2   1

# of independent variables
 F  number of degrees of freedom 
   M  1   M  2   1
Gibbs phase rule
 M   2
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1) Problems: Phase Equilibrium
•
Gibb’s Phase Rule Examples:
1.
One component vapor-liquid mixture:
M  1,   2, F  1
If the pressure is set, the temperature is fixed or if the temperature is set the
pressure is fixed (only 1 degree of freedom)
2.
Two component vapor-liquid mixture:
M  2,   2, F  2
The values of two state parameters must be set to determine the state of this
mixture. For example, at a fixed pressure the boiling temperature of the
mixture is a function of composition.
3.
Three component, 4 phase mixture:
M  3,   4, F  1
Fixing any singe state parameter will set the state of the mixture.
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2) Problems: Approaches to Phase Equilibria
Approaches to Phase Equilibria
•
Use a single EOS for both phases. Usually the EOS is based on an ideal
gas as a reference
Advantage: thermodynamic consistency, should be valid for all T,P,X
Disadvantage: difficult to find a sufficiently accurate EOS for both gas
and liquid phases, especially for complex fluids (ionic, H-bonded, etc.)
B.
Use different EOS for gas and liquid phases
Gas – relate to ideal gas as reference
Liquid – relate to ideal liquid solution as reference
Advantage: EOS more accurate since the density range is small
Disadvantage: Inconsistency near the critical points
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3) Problems: Chemical Reaction Equilibria
x1o , x2o ,
, xMo
Rx
x1e , x2e ,
T o , Po
T e , Pe
t=0
t→∞
, xMe
Problem: Given the initial composition, temperature and pressure of the
system, find the equilibrium composition, temperature and pressure.
•The reaction can be carried out isothermally or adiabatically or along some
other path.
•The only new feature is that molecules can change into new species.
•This introduces stoichiometry of the reaction into the equations – a new
constraint equation.
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3) Problems: Chemical Reaction Equilibria
How do reactions change the Gibbs Phase Rule?
Example: A vapor-liquid mixture of ortho, meta, and
para-xylenes and ethylbenzene at temperature high
enough that the xylenes can undergo isomerization
For nonreacting systems with no external fields
F  # components - # phases +2  M    2
But in general we said:
 number of unknown 
   number of independent relations 
F   thermodynamic
  among the unknown parameters 

 parameters
 


Each independent chemical reaction will add to the number of
independent relations (constraints)
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3) Problems: Chemical Reaction Equilibria
How does this change the Gibbs Phase Rule?
Example: A vapor-liquid mixture of ortho, meta, and para-xylenes and
ethylbenzene at temperature high enough that the xylenes can undergo
isomerization
Let R be the number of independent reactions.
Our phase rule becomes:
F  M    R  2 (for reactive systems)
There are three independent reactions in the above example. One
possible set is:
m-xylene  o-xylene
m-xylene  p-xylene
m-xylene  ethylbenzene
F  M    R  2  4- 2-3  2  1
Setting one state variable (temperature, pressure, or composition)
completely fixes the two-phase state of this mixture!
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4) Problems: Property Predictions using Statistical
Thermodynamics
•
Statistical Thermodynamics relates thermodynamic
properties to molecular properties through exact
equations
•
Molecular properties include:
•
•
•
•
•
Molecular mass
Moment of inertia
Bond lengths, angles, vibrations
Intermolecular forces
Foundation primarily given by Gibbs
•
For any given ‘ensemble’ or set of independent state
variables (e.g. T,P,x) he derived equations relating
thermodynamic properties to a ‘partition function’
•
•
•
•
Internal energy, U
Enthalpy, H
Pressure, P
Gibbs free energy, G, etc.
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Statistical Thermodynamics: What will we cover?
1. Basic statistical mechanics
(Canonical, Microcanonical and Grand Canonical
Ensembles)
1. Ideal gas properties, ~1910 – 1940
2. Real gases, Virial EOS,~1940 – 1965
3. Corresponding states theory, ~ 1950 – 1970
4. Perturbation theory, ~1950s – 1980s
5. Theory of liquid mixtures, ~1910 - present
6. Molecular simulation, ~1953 - present
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