27
Dimitrios P. Tassios
Applied Chemical Engineering Thermodynamics
extras.springer.com
Springer-Verlag
Berlin Heidelberg GmbH
Prof. Dimitrios P. Tassios National Technical University of Athens Zographou Campus 15780 Zographos Athens, Greece
Fonnerly: New Jersey Institute of Technology 323 Dr. Martin Luther King Jr. Blvp. Newark, N.J., 07102, USA
Additional material to this book can be downloaded from http:/lcxtras.springer.com
ISBN 978-3-662-01647-3 ISBN 978-3-662-01645-9 (eBook) DOI 10.1007/978-3-662-01645-9
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© Springer-Verlag Berlin Heidelberg 1993 Originally published by Springer-Verlag Berlin Heidelberg New York in 1993
The use of general descriptive names, registered names, trademarks. etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
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To my students,
Past, Present, and Future
The Hazards of Literary Life
"The hardships endured by authors are typified by a letter bound inside the flyleaf of a volume in exhibition of annotated rare books on view at the Smithsonian Institution . .... .
The book in question is "History and Progress of the Steam Engine", published in London in 1837. It was written by civil engineer Elijah Galloway, who addressed the letter inside to Charles Manby, a prominent English engineer. It reads: 'Dear Sir:
I am just on the eve of completing a new work on "The Mechanic Powers and Their Application to Machinery". But literary work is only paid for when the Manuscript is completed and what with ill health and the all absorbing nature of this kind of labor I am in the awful predicament of wanting a bit of bread!
I have by me an only copy of my well known "History of the Steam Engine", which Mrs Galloway will herewith hand you. Will you in charity purchase it of her? This is the only legitimate source by which I can avert the horror of hunger and cold for we have neither food,fire, nor a penny in the world!
I am, Dear Sir, Your ever Obliged E. Galloway."'
(Chern. & Eng. News, Nov. 10, 1986, p.40.)
This is by way of expressing my appreciation to NJIT for granting me a Sabbatical leave for the 1985-1986academic year, during which most of this book was written.
Preface
There are many excellent books on Chemical Engineering Thermodynamics, but their use in teaching the subject in the classroom leads to two serious difficulties:
First, most books tend to concentrate either on undergraduate or graduate level material only. This creates problems in the review of undergraduate material, which I have found essential for an effective graduate course.
Second, their presentation of the subject is too extensive for the number of credits allocated to it (about six semester hours in the undergraduate level and three in the graduate one). As a result, Chapters - or Sections of them- must be skipped, making the subject- that is by its very nature complex - still more difficult for the students to comprehend. Thus, not only learning suffers, but a fear of Thermodynamics is embedded into the student's mind, which hinders his or her future learning and use of the subject. (This fear is apparent to anyone teaching the graduate level course; and felt by many practicing engineers and chemists, leading a well known thermodynamicist to state a few years ago: "The most underutilized subject in the chemical and petroleum industries is Thermodynamics.")
These problems are, hopefully, avoided with this book for the material included in it covers both levels and can be presented in the aforementioned semester hours.
Obviously, less material is thus presented, but the book does provide the undergraduate and graduate student with the material needed in industrial practice and for future study; in addition, through the extensive list of pertinent references, it provides for: * a more in depth study of the different subjects; * practical applications; * the development of awareness of data sources, and * making the student appreciate the importance of using the literature in
problem solving. The emphasis is, of course, placed on covering the undergraduate level
material, while that for the graduate one is presented in Sections of Chapters 3,5, 7, 8, and 12, with the Problems numbered over 50 assigned to it; and in Chapters 10, 16 and 17. The presentation is made in such a fashion, however, that minimizes any loss of continuity in the undergraduate material, while the latter's review in the graduate course is facili-
X
tated with the assignment of some of the aforementioned Problems (51, 52 ... ).
The short length of the book should also make it useful to the practicing engineer and chemist that needs a relatively quick review of the subject, as well as references for a more detailed study of items of his/her interest.
The development of the subject is based on the Laws of Thermodynamics, i.e. it follows the historical approach, which seems easier for most students to understand than the postulatory one. (The latter is based on a small number of postulates, that cannot be proved but only disproved by showing that consequences resulting from them are in disagreement with experimental evidence, and from which the laws of thermodynamics can be derived.)
We start the presentation of Chemical Engineering Thermodynamics by taking a Glimpse at the Subject and proceed with a discussion of its Laws, followed by a brief Historical Account of its development. (A Nation cannot exist without a sense of its history, why should a field of Science and Technology?)
We continue with a discussion of Efficient Energy Utilisation - a subject of immense importance that became, unfortunately, apparent only after the energy crisis of th·e early 1970's - followed by a brief presentation of the Broader Implications of the Second Law. (We are educating the technological leaders of tomorrow, not just technologists.)
We proceed with a limited discussion of Intermolecular Forces, which will help in understanding the Physical and Thermodynamic Properties of Pure Fluids which are considered next and, of course, the rest of the subject matter.
Cubic Equations of State are then considered for they have become a major tool in describing quantitatively the properties of Pure Fluids, as well as those of Mixtures, which are discussed next.
We continue with a discussion of Equilibrium and Stability, that prepares the ground for the ensuing presentation of the two topics of paramount importance to chemical engineers: Phase and Chemical Reaction Equilibria.
We close with a brief discussion of Statistical Mechanics that should prepare the student for further ·study in this area, which is becoming progressively more and more important in applied thermodynamics.
The inclusion of computer Programs in the enclosed diskette should help the students in developing familiarity with the determination of fluid properties and phase equilibria calculations.
The presentation of the material has been influenced by the excellent books of Professors K. Denbigh (The Principles of Chemical Equilibrium, 4th Ed., Cambridge University Press, 1981), J.M. Prausnitz (with R.N.
XI
Lichtenthaler and E.G. de Azevedo, Molecular Thermodynamics of Fluid Phase Equilibria, 2nd Ed., Prentice Hall, 1986) and H.C. Van Ness (with J .M. Smith, Introduction to Chemical Engineering Thermodynamics, 4th Ed., McGraw-Hill, 1987), that are often mentioned in the book. The philosophy of presentation, however, has been shaped by many students, who always want to know the why and the relevance of what they are taught, and to whom this book is dedicated; and from my own conviction, that we should strive to make the topic more attractive to students by exposing them to the broader world of Thermodynamics. If they like this book, the effort will have been more than worthwhile.
In closing I would like to gratefully acknowledge: Professor D. Cardwell for permitting the use of material from his book: From Watt to Clausius; Professor H. Van Ness for providing the program that generates the Steam Tables; and Academic Press for permitting the use of material from W. Kenney's book Energy Conservation in the Process Industries; and, of course, to express my appreciation to NJIT for granting me a Sabbatical leave for the 1985-1986 academic year, during which most of this book was written.
Dimitrios P. Tassios Athens, 1992
Contents
1 A Glimpse at Thermodynamics 1
1.1 Introduction 1 1.2 Objective and Approach 2 1.3 The Vocabulary of Thermodynamics 2 1.4 Pressure, Temperature and Volume 4 1.5 Work 5
1.5.1 Definition 5 1.5.2 Example 1.1 5 1.5.3 Example 1.2 6
1.6 Energies 7 1.6.1 Potential 7 1.6.2 Kinetic 8 1.6.3 Internal 8 1.6.4 Enthalpy 8 1.6.5 Helmholtz and Gibbs Free Energies 8
1.7 Heat 9 1.8 System, Surroundings, and Related Terms 10
1.8.1 System and Surroundings 10 1.8.2 Modes of Interaction Between Them 10 1.8.3 State 10 1.8.4 Process 11 1.8.5 Equilibrium: Internal and External 11
1.9 Internal Energy and Molecular Energy 11 1 . 10 Entropy 12 1.11 State Properties 12 I . 12 Reversibility 13 1.13 Auxiliary Terms 15
XIV Contents
I .13.1 Heat Capacity 15 1.13.2 Ideal Gas 15 1.13.3 Real Fluid versus Ideal Gas 16 1. I 3.4 Ideal Solution 16 1. I3.5 Real versus Ideal Solution 17 1. I3.6 Activity Coefficient 17 I. I 3. 7 Chemical Potential and Fugacity 18 I. I 3. 8 Intensive and Extensive Properties 18
I .14 The Foundations of Thermodynamics 18 1.14.1 The Laws of Thermodynamics 18 1.14.2 The Thermophysical Data 20
1.15 The Purpose of Chemical Engineering Thermodynamics 20 1.15.1 Feasibility of Processes and Efficient Energy Utilization 21 I. 15.2 Thermophysical Properties 22 1.15.3 Chemical and Phase Equilibrium 23
1.16 Examples 1.3 through 1.9 24
2 The Zeroth and First Laws of Thermodynamics 35
2.1 Introduction 35 2.2 Objective and Approach 36 2.3 The Zeroth Law and the Ideal Gas Temperature 36
2.3.1 The Statement 36 2.3.2 Is it Really a Law? 37 2.3.3 Temperature: the Common Property of Systems in Thermal
Equilibrium 2.3.4 The Ideal Gas Temperature Scale 2.3.5 Example 2.1
2.4 The First Law
37 38 40 41
2.4.1 Background and Statement 41 2.4.2 The Analytical Expression 43 2.4.3 Comments 44 2.4.4 Example 2.2 44 2.4.5 Example 2.3 45
2.5 The First Law Expression for a Steady-State Flow Process 46 2.5.1 The Problem 46 2.5.2 Development of the Expression 46 2.5.3 Comments
2.6 Thermodynamic Relationships of the Ideal Gas 2.6. 1 Importance of Ideal Gases
47 48 48
Contents XV
2.6.2 Equation of State 48 2.6.3 Internal Energy and Enthalpy Changes Due to Heating or
Cooling 49 2.6.4 The Difference in Heat Capacities 49 2.6.5 The P-Y-TRelationship for an Adiabatic and Reversible
Change 49 2.6.6 Comments 50
2.7 Examples 2.4 through 2.7 51 2.8 Concluding Remarks 56
3 The Second Law of Thermodynamics 61
3. 1 Introduction 61 3.2 Rationale for a Second Law 62
3.2.1 The Direction of Natural Phenomena 62 3.2.2 The Feasibility of Processes 62 3.2.3 The Big Question: Where is the Energy Gone? 63 3.2.4 Summary 63
3. 3 Objective and Approach 64 3.4 Second Law: The Verbal Statement 65
3.4.1 Statements 65 3.4.2 Example 3.1 65
3.5 The Carnot Cycle 66 3.5.1 Description 66 3.5.2 The Expression for the Thermal Efficiency 67 3.5.3 The Maximum Thermal Efficiency 69 3.5.4 Comments 70 3.5.5 Example 3.2 72 3.5.6 Example 3.3 72
3.6 A Real Heat Engine: A Simple Power Plant 73 3.6.1 Description 73 3.6.2 The Expression for the Thermal Efficiency 74 3.6.3 Comments 74
3.7 Second Law: The Analytical Statement 75 3.8 Proposition I 76 3. 9 Proposition II 77
3. 9. I Approach 77 3.9.2 j(tpt2) = j(t1)/f(t2) 77 3.9.3 The Thermodynamic Temperature 79
3. 10 Proposition III 79
XVI Contents
3 0 11 Proposition IV 81 3011.1 Objective 81 3 0110 2 Entropy Change of a System Undergoing a Spontaneous
Process 81 3011.3 The Total Entropy Change 82
3 0 12 Entropy Change Calculations 82 3 0 12 0 I The Problem and Approach 82 301202 Isothermal Removal or Addition of Heat 83 301203 Heating or Cooling of a Body from T1 to T2 83 3012.4 Entropy Changes of an Ideal Gas 83 301205 Entropy of Mixing 84
3013 A Molecular Interpretation of Entropy 85 3014 Examples 304 through 3012 88 3015 Steam Power Plants 97
3 015 01 Operating Conditions 97 3o15o2 Comments 99 301503 Example 30130 A look at Example 1.9 101
3 0 16 Concluding Remarks 102
4 Thermodynamics: A Historical Perspective 107
401 Introduction 107 402 Objective and Approach 108 403 The Power of Heat: Early Recognition 109 4.4 The Steam Engine 110
4.401 James Watt 112 4.402 Richard Trevithick and the Railway Locomotive 113
405 The Science of Heat 114 40501 The Thermometer 115 40502 The Nature of Heat 116 40503 The Conservation of Fire 117 405.4 The Differentiation of Heat and Temperature 118 40505 The Conservation of Heat 119 40506 The Caloric Theory and its Problems 120
406 The Establishment of Thermodynamics 121 407 Sadi Carnot 123
40701 Motivation 124 40702 Arguments 124 40703 Conclusions 125 407.4 The Acceptance of his Work 126
Contents XVll
4.8 Emile Clapeyron 127 4.8.1 Contributions 128 4.8.2 The Efficiency of the Camot Cycle 129 4.8.3 Example 4.1. The Clapeyron Equation 130 4.8.4 Example 4.2. Evaluation of the Camot Factor C 131
4.9 The Conversion of Work to Heat 132 4.9.1 J.R. Mayer 132 4.9.2 J.P. Joule 133 4.9.3 Early Experimental Work 134 4.9.4 The Expansion/Compression of Gases and Later Work 135
4.10 Kelvin, Clausius, and the Establishment of the First and Second Laws 137 4.10.1 Lord Kelvin 137 4.10.2 R.J .E. Clausius 139
4.11 The Absolute Temperature and the Analytical Expression of the Second Law 142 4.11.1 The Absolute Temperature 142 4.11. 2 The Analytical Statement of the Second Law: Reversible
Processes 142 4. 11.3 Real Life Processes and Entropy: Irreversible Processes 143
4.12 Thermodynamic Properties of Matter 144 4.12.1 J.W. Gibbs 145 4.12.2 EquationsofState 147 4.12.3 Activity Coefficients 149 4.12.4 The Third Law of Thermodynamics 150 4.12.5 OtherContributors 151
5 Efficient Energy Utilization: Energy Conservation 155
5. 1 Introduction 155 5.2 Objective and Approach 156 5.3 Ideal Work 158
5.3.1 Definition 158 5.3.2 Example 5.1 159 5.3.3 Evaluation of Ideal Work: the General Expression 160 5.3.4 Example 5.2 162 5.3.5 Example 5.3 162
5. 4 Useful Energy 163 5.4.1 Definition 163
XVIII Contents
5.4.2 Example 5.4 164 5.5 Exergy 165
5.5.1 Maximum Obtainable Useful Energy from a System 165 5.5.2 Definition 166
5.6 Evaluation of Exergy 166 5.6.1 Exergy of a System at T and P 166 5.6.2 Example 5.5 167 5.6.3 Example 5.6 167 5.6.4 Exergy of Thermal Energy Available at a Temperature T 168 5.6.5 Exergy of Any Energy Except Thermal 168 5.6.6 Summary 170
5. 7 First and Second Law Efficiencies 171 5. 7.1 Definitions 171 5. 7.2 Example 5. 7 172 5.7.3 Example5.8 173 5. 7.4 Comments 173
5.8 Cogeneration 174 5.8.1 Rationale 174 5.8.2 Example 5.9 175 5.8.3 Example5.10 179
5. 9 Limitations of Cogeneration 181 5.10 Energy Conservation: The Favorable Economics
and the Institutional Barriers 181 5.11 Concluding Remarks 185
6 Second Law and Entropy: A Broader View 191
6.1 Introduction 191 6.2 Objective and Approach 192 6.3 Material Dissipation and the 'Fourth' Law 192 6.4 Second Law and World History 193
6.4.1 Common Threads in World History 193 6.4.2 Entropy Watersheds and the Main Transitions in World
History 194 6.5 Energy Demand and Supply in the Future 197
6.5.1 The Energy Crisis of the Early 1970's: Was it a Warning? 197 6.5.2 The U.S. Oil Demand and Supply to the Year 2000 198 6.5.3 Global Energy Demand and·Supply in the Future 200
6.6 Meeting the Energy Demand in the Future: Problems 203 6.6.1 Cost 203
Contents
60602 Environmental 60 7 So, Is There a Third Entropy Watershed Coming?
60 7 01 The Magnitude of the Problem 60702 Life After This Entropy Watershed 6o 1o3 Comments
608 Concluding Remarks
7 Intermolecular Forces
7 01 Introduction 702 Objective and Approach 703 Intermolecular Forces and Potential Energy 7.4 Origin and Types of Intermolecular Forces
7.401 Attractive Forces 70402 Repulsive Forces
705 Physical Attractive Forces 70501 Dipole-DipoleForces 70502 Dipole-Induced Dipole Forces 70503 Dispersion Forces 70504 Example 7010 Comparison of Attractive Forces 70505 Comments
706 Intermolecular Potentials 70601 The Mie Potential 70602 The Lennard-lones Potential 70603 Comments 706.4 Example 7020 The Origin of the 'Geometric Mean'
707 Chemical Forces 70 701 Hydrogen Bonding 70 702 Weaker Forces 7 0 7 0 3 Applications 707.4 Example 703
708 Concluding Remarks
8 Physical Properties of Pure Fluids
801 Introduction 802 Objective and Approach 803 The Volumetric Behavior of Pure Gases
80301 The Origin of Fluid Pressure
Rule
XIX
204 208 209 209 211 211
217
217 217 218 219 219 220 221 221 221 222 223 224 225 225 226 227 228 229 229 231 231 231 233
237
237 238 239 239
XX Contents
8.3.2 Pressure-Volume Isotherms 240 8.4 The Volumetric Behavior of Pure Vapors and Liquids 240
8.4.1 Pressure-Volume Isotherms 240 8.4.2 Terminology 241 8.4.3 Phase Diagrams 243
8.5 Volumetric Behavior Common to All Pure Fluids 244 8.6 The Volumetric Behavior of Pure Fluids: Quantitative
Treatment 245 8.6.1 The Compressibility Factor 245 8.6.2 Determination of the PVT Behavior 246
8. 7 The Corresponding States Principle 246 8. 7.1 The Two-Parameter Version 246 8.7.2 The Three-Parameter Version 248 8.7.3 Example 8.1 250 8. 7. 4 Comments 250 8. 7.5 Example 8.2. The Molecular Theory of the
Corresponding States Principle 251 8.8 Equations of State: General Remarks 251
8. 8. 1 The Purpose of an Equation of State 251 8.8.2 Classification of Equations of State 252
8.9 The Virial Equation of State 252 8.9.1 The Expression 252 8.9.2 Evaluation of Virial Coefficients 253 8.9.3 Example 8.3. The Relationship Among the Coefficients
of the Volume and Pressure Series Expansions 255 8.9.4 Example 8.4 255 8.9.5 Example 8.5. Estimation of Second Virial Coefficients:
Nonpolar Compounds 257 8.9.6 Example 8.6. Estimation of Second Virial Coefficients:
Polar Compounds 260 8. 9. 7 Comments 260
8.10 Cubic Equations of State 261 8. 10.1 Development of a Cubic Equation of State 261 8.10.2 Example 8. 7 262 8.10.3 Example 8.8 262 8.10.4 The Redlich-Kwong Equation of State 263 8.10.5 Example 8.9 264 8.10.6 The SRK, PR, and vdW-711 Equations of State 264 8.10.7 Example8.10 265 8.10.8 Comments 267
8.11 The Benedict-Webb-Rubin (BWR) Equation of State 270
Contents XXI
8.12 Recommendations for the Estimation of the Volumetric Behavior of Pure Fluids 270
8.13 Vapor Pressures 271 8. 13. 1 Correlation of Vapor Pressure Data 2 71 8.13.2 Estimation of Vapor Pressures 273 8.13.3 Comments 273
8.14 Enthalpies of Vaporization 274 8.14.1 Determination and Prediction 275 8.14.2 Example 8.11 276
8.15 Heat Capacities 276 8.15.1 Determination 277 8.15.2 Example 8.12 278
9 Thermodynamic Properties of Pure Fluids 285
9. 1 Introduction 285 9.2 Objective and Approach 286 9.3 The Fundamental Equations: Closed Systems 286
9.3.1 The Fundamental Equation for the Internal Energy 287 9.3.2 The Fundamental Equation for H, A, and G 288 9.3.3 Example 9.1 290
9.4 The Fundamental Equations: Open Systems 290 9.5 Evaluation of Thermodynamic Properties of Pure Fluids 293
9.5.1 The Problem 293 9.5.2 The Approach 293
9.6 The Maxwell Relations 296 9. 7 Departure Functions 297
9. 7.1 The Approach 297 9.7.2 Example 9.2 298 9.7.3 Example 9.3 300 9. 7.4 Evaluation of Departure Functions 301 9.7.5 Evaluation of Enthalpy and Entropy Differences 302 9. 7.6 Development of Enthalpy and Entropy Tables and Charts 303
9. 8 Estimation of Departure Functions 303 9.8.1 The Methods 303 9.8.2 Example 9.4 304 9.8.3 Example 9.5 305 9.8.4 Example 9.6 305 9.8.5 Comments on the Estimation of Entropy and Enthalpy
Departures 306
XXII Contents
9. 9 The Chemical Potential 307 9. I 0 Fugacity 308
9.10.1 Definition 308 9.10.2 A Physical Interpretation 309
9. 11 Evaluation of Fugacities from Experimental Data 310 9.11.1 The Mathematical Formulation 310 9.11.2 Evaluation of Fugacities with an Equation of State 311 9.11.3 Example 9.7 312 9.11.4Example 9.8 312 9.11.5 Liquid Phase Fugacities 313 9.11.6 Example 9.9 314
9. 12 Estimation of Fugacities 315 9.12.1 The Methods 315 9.12.2Example9.10 315 9.12.3 Comments 316
9.13 Summary 317
10 Cubic Equations of State 323
10.1 Introduction 323 10.2 Objective and Approach 324 10.3 Evaluation of Vapor Pressures with an Equation of State 324
10.3.1 The Problem 324 10.3.2 Example 10.1 325 10.3.3 Comments 326
10.4 Development of a Cubic Equation of State for Vapor Pressure Prediction 326 10.4.1 The Approach 326 10.4.2 The Dependency of Alpha on Temperature 327 10.4.3 Generalization of the EoS 328
10.5 Prediction of Saturated Liquid Volumes 328 10.5.1 The Problem 328 10.5.2 Methodology and Results 329
10.6 Comments 331 10.7 Concluding Remarks 336
11 Properties of Mixtures 339
11.1 Introduction 339
Contents
11.2 Objective and Approach 11.3 Partial Molar Properties
11.3.1 Definition 11.3.2 Example 11.1
11.4 Mixture Properties from Partial Molar Properties 11.4.1 The Problem 11.4.2 The Approach 11.4.3 Comments
11.5 Partial Molar Properties from Mixture Properties 11.5.1 The Analytical Expression 11.5.2 Example 11.2
11.6 Interdependency of the Partial Molar Properties 11.6.1 The Gibbs-Duhem Equation 11.6.2 Example 11.3 11.6.3 Example 11.4
11.7 Evaluation of Mixture Properties II. 7.1 The Problem and Approach II. 7.2 The Virial Equation 11.7. 3 The Pitzer Corresponding States Correlation 11.7 .4 Cubic Equations of State 11.7 .5 Example 11.5 11.7 .6 Example 11.6 11.7.7 Example 11.7 11.7. 8 Comments on the Estimation of Mixture Properties
11.8 Fugacities in Mixtures 11.8.1 Fugacity of the Components of a Mixture 11.8.2 Relationship Betweenfand};
11.8.3 The Case of an Ideal Solution 11. 8.4 Comments
11.9 Fugacities with Equations of State 11.9.1 Fugacities with the Virial Equation 11.9. 2 Fugacities with Cubic Equations of State 11.9.3 Example 11.8
11.10 Fugacities with the Standard State Method 11.10.1 The Problem and Approach 11.10.2 The Standard State Fugacity for a Condensable
Component 11.10.3 Example 11.9 11.10.4 The Standard State Fugacity for a Noncondensahle
Component 11.10.5 Example 11.10
XXITI
340 341 341 342 343 343 343 344 344 344 345 347 347 348 349 349 349 350 353 354 356 357 358 359 360 360 361 362 363 365 365 366 367 368 368
369 370
371 373
XXIV
11.11 An Application of Fugacities: Solubility of Solids and Liquids in Gases 11.11.1 Solids 11.11.2 Comments 11. 11.3 Liquids
11 . 12 Property Changes of Mixing 11.12.1 Definition 11.12. 2 The Case of an Ideal Solution
11. 13 Excess Properties 11.13.1 Definition 11.13.2 The Excess Gibbs Free Energy and the Activity
Coefficient 11. 14 Concluding Remarks
12 Equilibrium and Stability
Contents
374 374 375 377 378 378 378 380 380
381 382
393
12.1 Introduction 393 12.2 Objective and Approach 394 12.3 The Thermodynamic Criteria of Equilibrium 394
12.3.1 A Closed System of Constant Internal Energy and Volume 395 12.3.2 Example 12.1 396 12.3.3 A Closed System of Constant Temperature and Pressure 397 12.3.4 Example 12.2 398
12.4 The Basis for Phase Equilibrium Calculations at Constant Temperature and Pressure 400 12.4.1 The Equality of Chemical Potentials 400 12.4.2 Example 12.3 401 12.4.3 Example 12.4. The Clapeyron Equation 401 12.4.4 The Equality of Fugacities 402 12.4.5 Comments 402
12.5 The Basis for Chemical Reaction Equilibrium Calculations at Constant Temperature and Pressure 403 12.5.1 The Problem and Approach 403 12.5.2 Stoichiometric Coefficients and Numbers 403 12.5.3 The Progress of the Reaction Variable 404 12.5.4 Example 12.5 405 12.5.5 Example 12.6 405 12.5.6 Evaluation of Gi: The Standard State Fugacity and
Gibbs Free Energy 406 12.5. 7 The Expression for the Equilibrium Constant K 407
Contents XXV
12.5.8 Example 12.7 408 12.5.9 Comments 408
12.6 The Basis for Mu1tiphase/Multireaction Equilibrium Calculations at Constant Temperature and Pressure 409 12.6.1 Three-Phase Equilibrium 409 12.6.2 Multiple Reactions in a Single-Phase System 410 12.6.3 Multiple Reactions in a Two-Phase System 411 12.6.4 Comments 412
12.7 The Complete Specification of an Equilibrium System 412 12.7 .1 The Phase Rule 413 12.7.2 The Duhem Theorem 414 12.7.3 Example 12.8 414 12.7.4 A Multiphase, Multireaction System 415
12.8 Stability in Thermodynamic Systems 416 12.8.1 Stability Criteria 416 12.8.2 Comments 417 12.8.3 Example 12.9 418
12.9 Phase Transitions 419 12.9.1 The Unstable Region 420 12.9.2 The Metastable Region 420 12.9.3 Comments 422
12.10 Liquid-Liquid Equilibrium in Binary Systems 424 12.10.1 The Mixing of Two Pure Liquids 424 12.10.2 Evaluation of the Miscibility Limits 425 12.10.3 The Metastable and Unstable Regions 426 12.10.4 The Effect of Temperature on Mutual Solubility 427 12.10.5 Example 12.10 428 12.10.6 Comments 429
12.11 Concluding Remarks 430
13 Low Pressure Vapor-Liquid Equilibrium 435
13.1 Introduction 435 13.2 Objective and Approach 436 13.3 The Vapor-Liquid Equilibrium Problem 437 13.4 Methodology 438 13.5 Activity Coefficients: Determination from Vapor-Liquid
Equilibrium Measurements 440 13.5.1 Experimental Measurements 441 13.5.2 Evaluationofthe Activity Coefficient 441
XXVI
13.5.3 Example 13.1 13.5.4 Comments
13.6 Ideal Solutions 13.6.1 Raoult's Law 13.6.2 Example 13.2 13.6.3 Example 13.3 13.6.4 Example 13.4 13.6.5 Example 13.5 13.6.6 Example 13.6 13.6.7 Example 13.7 13.6.8 Summary
13.7 Activity Coefficients: Qualitative Remarks 13.7.1 The Effect of Composition 13.7. 2 The Effect of Molecular Nature 13. 7.3 Summary
13.8 Activity Coefficients: The Effect of Pressure and Temperature 13.8.1 Pressure 13. 8. 2 Temperature
13.9 Thermodynamic Consistency of Experimental Data 13.9.1 The Interrelationship Among Activity Coefficients 13.9.2 Binary Systems 13.9.3 Comments 13.9.4 Example 13.8
13.10 Activity Coefficients and Composition: Analytical Expressions 13.10.1 Procedure 13.10.2 Comments
13.11 The Wohl Type Expressions 13. II. I The General Expression for a Binary System 13 .11. 2 The van Laar Equation 13. II. 3 The Margules Equation 13.11.4 Evaluation of the Parameters 13.11.5 Example 13.9
13.12 The Local Composition Expressions 13 .12. I The Concept of Local Compositions 13.12.2 The Wilson Equation 13.12.3 The NRTL Equation 13.12.4 The UNIQUAC Equation 13.12.5 Comments 13.12.6 Example 13.10
Contents
442 443 445 445 446 448 448 449 450 450 451 452 452 452 457
458 458 458 460 460 460 461 462
463 463 464 465 465 466 466 467 467 469 469 470 471 472 473 474
Contents
13.13 Advantages of the Local Composition Models 13. 13.1 Correlation of Binary Data 13.13.2 Temperature Dependency of the Parameters 13.13.3 Prediction of Multicomponent VLE Behavior
13.14 Single-Parameter Expressions 13.15 Evaluation of Vapor Phase Composition from Liquid
Composition-Total Pressure Data 13.15.1 The Approach 13.15.2 Example 13.11
13.16 Bubble and Dew Point Calculations 13. 16.1 Bubble Point 13.16.2 Dew Point
13.17 Prediction of Multi component VLE Behavior from Binary Data 13.17. 1 The Effect of the Method for Evaluating
Binary Parameters 13.17. 2 The Effect of the Quality of the Binary Data 13.17. 3 The Effect of Temperature 13.17.4 The Effect of System Type 13.17.5 Example 13.12
13.18 Estimation of Vapor-Liquid Equilibrium 13.18.1 The Group-Contribution Concept 13.18.2 The UNIFAC Model 13.18.3 Comments
13.19 Concluding Remarks
14 High Pressure Vapor-Liquid Equilibrium
14 .I Introduction 14.2 Objective and Approach 14.3 Qualitative Behavior
14.3.1 Bubble, Dew, and Critical Points of Mixtures 14.3. 2 Comments 14.3. 3 Equilibrium Compositions as Functions of Pressure
and Temperature 14.4 Quantitative Description 14.5 Graphical Methods: The K-Charts
14.5.1 Charts Using P and T Only 14.5.2 Charts Using the Convergence Pressure
14.6 The Chao-Seader Method
XXVII
475 475 476 478 479
481 481 482 483 484 485
487
487 490 492 492 493 494 495 495 497 498
511
511 511 512 512 514
516 516 518 518 519 520
XXVIII
14.6.1 The Method 14.6.2 Comments
14.7 The Equation of State Approach 14.7 .I Required Information 14. 7.2 Comments 14.7. 3 Polar Systems
14.8 Bubble Point, Dew Point, and Flash Calculations 14.8.1 Bubble and Dew Points 14.8.2 Example 14.1 14.8.3 Example 14.2 14.8.4 Example 14.3 14.8.5 Flash Calculations 14.8.6 Example 14.4
14.9 Concluding Remarks
15 Chemical Reaction Equilibrium
15.1 Introduction 15.2 Objective and Approach 15.3 The Dependency of K on Temperature
15.3.1 The Problem 15.3.2 The Variation of K with the Enthalpy of the Reaction
15.3.3 The Temperature Dependency of i!H 0
15.3.4 The Expression for K(T)
15.3.5 Comments 15.3.6 Example 15.1 15.3.7 Example 15.2 15.3.8 Example 15.3 15.3.9 Example 15.4
15.4 Equilibrium Conversion: Gas-Phase Reactions 15.4.1 Kin Terms of Composition 15.4.2 Evaluation of the Equilibrium Conversion
15.4.3 Example 15.5 15.4.4 Example 15.6 15.4.5 Adiabatic Reactions
15.5 Equilibrium Conversion: Liquid-Phase Reactions 15.6 Factors Effecting the Equilibrium Conversion
15.6.1 Temperature 15.6.2 Pressure 15.6.3 Inert Components
Contents
52{) 521 522 522 523 528 529 529 531 531 532 533 535 536
545
546 546 548 548 548 550 552 552 553 554 555 556 558 558 558 559 560 561 562 564 564 564 564
Contents
15.6.4 Excess Reactant in Feed 15.6.5 Example 15.7. The Ammonia Synthesis 15.6.6 Example 15.8
15.7 The Phase Rule and the Duhem Theorem for
XXIX
565 565 567
Reacting Systems 567 15.7 .1 The Phase Rule and the Number of Independent
Reactions 568 15.7.2 Example 15.9 569 15.7.3 Example 15.10 569 15.7.4 Example 15.11 570 15.7.5 The Duhem Theorem 570
15.8 Equilibrium Conversion: Heterogeneous Systems 571 15.8.1 The Equilibrium Constant in Terms of Composition
for a Gas(g)-Solid(s) Reaction 571 15. 8.2 Example 15.12. Solid """Solid + Gas 572 15.8.3 Example 15.13. Solid + Gas ,... Solid + Gas 572
15.9 Multiple Reactions 573 15.9.1 The Problem 573 15.9.2 Example 15.14 574 15.9.3 Example 15.15 575 15.9.4 Example 15.16 575
15.10 Concluding Remarks 576
16 Elements of Statistical Mechanics 585
16.1 Introduction 585 16.2 Objective and Approach 586 16.3 Description of the Molecular Behavior 587
16.3.1 Classical Mechanics 588 16.3.2 Quantum Mechanics 588
a. Introductory Remarks 589 b. The Schrodinger Equation 590
16.3.3 Comments 592 16.3.4 Example 16.1 592 16.3.5 Example 16.2 593
16.4 The Translational Wave Function of a Single Particle 594 16.4.1 The General Solution 594 16.4.2 Quantum Numbers, Permissible Energy Levels, and
the Wave Function 595 16.4.3 Comments 596
XXX Contents
16.5 The Averaging Process 596 16.5.1 The Problem 596 16.5.2 The Statistical Postulate 597 16.5.3 Ensembles 598
16.6 The Canonical Ensemble 598 16.6.1 The Characteristic Property of the Probability Function 598 16.6.2 Example 16.3 599 16.6.3 The Partition Function 600
16.7 Thermodynamic Properties from the Partition Function 601 16.8 The Partition Function of an Ideal Gas 602
16. 8.1 In Terms of the Molecular Partition Function 602 16.8.2 Factoring the Molecular Partition Function 603 16.8.3 The Translational Partition Function 604
16.9 The Description of an Ideal Gas 605 16.9.1 Equation of State 605 16.9.2 Thermodynamic Properties 606
16.10 Concluding Remarks 607 16.10.I A Rigorous Development of the Second Law 607 16.10.2 A Philosophical Insight into the Second Law 608
17 Statistical Mechanics: Application to Real Fluids 615
17. 1 Introduction 615 17.2 Objective and Approach 615 17.3 The Partition Function of a Real Fluid 616
I 7. 3. I The Configuration Integral 616 17.3.2 Comments 617 17.3. 3 Example 17 .1. Thermodynamic Properties from the
Configuration Integral 619 17.4 The Radial Distribution Function and Thermodynamic
Properties 620 17 .4. 1 The Radial Distribution Function g(r) 620 17 .4.2 Thermodynamic Properties from g(r) and f(r) 621 17.4.3 Comments 623
17.5 Low Densities: The Virial Equation 624 17 .5.1 The Vi rial Equation 624 17.5.2 Comments 624 17.5.3 Example 17.2. The Second Virial Coefficient of the
Hard-Sphere Fluid 625
Contents XXXI
17.6 High Densities: The Approaches 626 17.7 Molecular Simulation 627
17.7.1 Monte Carlo (Metropolis et al, 1953) 627 17.7.2 Molecular Dynamics (Alder and Wainwright, 1959b) 628 17.7. 3 Comments 628 17.7 .4 The Hard-Sphere Fluid 629
17.8 Perturbation 631 17.9 Equations of State with the Semiempirical Approach 632
17.9.1 The Generalized van der Waals Partition Function 632 17.9.2 The van der Waals Equation of State 633 17.9.3 The Camahan-Starling-vdWand -RK Equations of State 634 17.9 .4 Rotational ami Attractive Contributions 635 17.9.5 Comments 636
17. I 0 Concluding Remarks 638
Appendices
A Conversion Factors B Steam Tables C Physical Properties for Selected Compounds D Lee-Kesler Tables E Computer Programs
Mollier h,s Diagram
Index
643 644 672 677 695
696
699
