Aug 22, 2013 ... Chemical Engineering 713. Advanced Chemical Engineering Thermodynamics
..... Sandler, S.I., Chemical, Biochemical, and Engineering.
Chemical Engineering 713 Advanced Chemical Engineering Thermodynamics
Lecture 1 Organization of Course and Introduction: The Phase Equilibrium Problem
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Organization
• Instructor: Keith E. Gubbins 2-088A Engineering Building I Phone: 513-2262 Email:
[email protected] 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:
[email protected] Office Hours: by e-mail or phone appointment NC STATE UNIVERSITY
Organization Teaching Assistants •
Cody Addington (on campus) 2-029 Engineering Building I Phone: 513-2051 Email:
[email protected] Office Hours: by e-mail or phone appointment
•
Ahmed M. Gomaa (distance EOL class) 2-106 Partners II Phone: 515-8395 Email:
[email protected] 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. NC STATE UNIVERSITY
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) NC STATE UNIVERSITY
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) NC STATE UNIVERSITY
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) NC STATE UNIVERSITY
Course Outline • • • • • • • • • • • • • •
# 1 2 3 4 5 6 7 8 9 10 11 12 13 14 .
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.
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Course Outline # 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
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.
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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 NC STATE UNIVERSITY
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 NC STATE UNIVERSITY
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. NC STATE UNIVERSITY
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 andi 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' NC STATE UNIVERSITY
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 NC STATE UNIVERSITY
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. NC STATE UNIVERSITY
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) NC STATE UNIVERSITY
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! NC STATE UNIVERSITY
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. NC STATE UNIVERSITY
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 NC STATE UNIVERSITY
