THERMODYNAMICS Fundamentals for Applications Other Books by the Authors J. P. O’Connell Computer Calculations for Multicomponent Vapor-Liquid Equilibria (coauthor) Computer Calculations for Multicomponent Vapor-Liquid and Liquid- Liquid Equilibria (coauthor) The Properties of Gases and Liquids (coauthor of 5th edition) J. M. Haile Molecular-Based Study of Fluids (coeditor) Chemical Engineering Applications of Molecular Simulation (editor) Molecular Dynamics Simulation Technical Style: Technical Writing in a Digital Age Lectures in Thermodynamics: Heat and Work Analysis of Data THERMODYNAMICS Fundamentals for Applications J. P. O’Connell University of Virginia and J. M. Haile Macatea Productions cambridge university press Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge cb2 2ru,UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521582063 ©J.P.O'ConnellandJ.M.Haile2005 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2005 isbn-13 978-0-511-11533-2 eBook (NetLibrary) isbn-10 0-511-11533-4 eBook (NetLibrary) isbn-13 978-0-521-58206-3 hardback isbn-10 0-521-58206-7 hardback Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guaranteethatanycontentonsuchwebsitesis,orwillremain,accurateorappropriate. If it were easy … it cannot be educational. In education, as elsewhere, the broad primrose path leads to a nasty place. Alfred North Whitehead “The Aims of Education,” in Alfred North Whitehead, An Anthology, F. S. C. Northrop and M. W. Gross, eds., Macmillan, New York, 1953, p. 90. remarkable things occur in accordance with Nature, the cause of which is unknown; others occur contrary to Nature, which are produced by skill for the benefit of mankind. Mechanica, Aristotle (384–322 BCE) Many scholars doubt that the Mechanica, the oldest known textbook on engineering, was written by Aristotle. Perhaps it was written by Straton of Lampsacus (a.k.a. Strato Physicus, died c. 270 BCE), who was a graduate student under Aristotle and who eventually succeeded Theophrastus as head of the Peripatetic school. CONTENTS Preface, xiii Acknowledgments, xvi 0. Introduction, 1 0.1 Natural Phenomena, 1 0.2 Thermodynamics, Science, and Engineering, 2 0.3 Why Thermodynamics Is Challenging, 5 0.4 The Role of Thermodynamic Modeling, 7 Literature Cited, 8 PART I. THE BASICS, 9 1. Primitives, 10 1.1 Primitive Things, 10 1.2 Primitive Quantities, 15 1.3 Primitive Changes, 20 1.4 Primitive Analyses, 24 1.5 Summary, 26 Literature Cited, 27 Problems, 28 2. The First and Second Laws, 32 2.1 Work, 34 2.2 The First Law, 43 2.3 The Second Law, 48 2.4 Thermodynamic Stuff Equations, 55 2.5 Summary, 63 Literature Cited, 64 Problems, 64 x CONTENTS 3. Fundamental Relations, 69 3.1 State of Single Homogeneous Phases, 70 3.2 Fundamental Equations, 74 3.3 Response to a Change in T, P, or V,80 3.4 Response to a Change in Mole Number, 88 3.5 Differential Relations Between Conceptuals and Measurables, 96 3.6 Generalized Stuff Equations, 98 3.7 General Expressions for Heat and Work, 104 3.8 Summary, 111 Literature Cited, 113 Problems, 113 PART II. SINGLE-PHASE SYSTEMS, 119 4. Properties Relative to Ideal Gases,120 4.1 Ideal Gases, 121 4.2 Deviations from Ideal Gases: Difference Measures, 133 4.3 Deviations from Ideal Gases: Ratio Measures, 137 4.4 Conceptuals from Measurables Using Equations of State, 146 4.5 Simple Models for Equations of State,15 2 4.6 Summary, 174 Literature Cited, 175 Problems, 177 5. Properties Relative to Ideal Solutions, 184 5.1 Ideal Solutions, 185 5.2 Deviations from Ideal Solutions: Difference Measures, 189 5.3 Excess Properties from Residual Properties, 194 5.4 Deviations from Ideal Solutions: Ratio Measures, 200 5.5 Activity Coefficients from Fugacity Coefficients, 208 5.6 Simple Models for Nonideal Solutions, 211 5.7 Summary, 219 Literature Cited, 221 Problems, 222 6. Relations Among Relations, 228 6.1 Effects of External Constraints on System States, 229 6.2 Symmetry in Routes to Conceptuals, 231 6.3 Physical Interpretations of Selected Conceptuals, 239 6.4 Five Famous Fugacity Formulae, 243 6.5 Mixing Rules from Models for Excess Gibbs Energy, 247 6.6 Summary, 249 Literature Cited, 250 Problems, 251 CONTENTS xi PART III. MULTIPHASE AND REACTING SYSTEMS, 255 7. Transfers, Transformations, and Equilibria, 256 7.1 The Laws for Closed Nonreacting Systems, 257 7.2 The Laws for Open Nonreacting Systems, 269 7.3 Criteria for Phase Equilibrium, 279 7.4 The Laws for Closed Reacting Systems, 286 7.5 The Laws for Open Reacting Systems, 300 7.6 Criteria for Reaction Equilibrium, 303 7.7 Summary, 305 Literature Cited, 307 Problems, 307 8. Criteria for Observability, 310 8.1 Phase Stability in Closed Systems, 311 8.2 Pure Substances, 320 8.3 Phase Stability in Open Systems, 336 8.4 Fluid Mixtures, 340 8.5 Summary,35 6 Literature Cited, 359 Problems, 360 9. Phase Diagrams for Real Systems, 366 9.1 Thermodynamic State for Multiphase Systems, 367 9.2 Pure Substances, 371 9.3 Binary Mixtures of Fluids at Low Pressures, 375 9.4 Binary Mixtures Containing Solids, 393 9.5 Binary Mixtures of Fluids at High Pressures, 399 9.6 Ternary Mixtures, 405 9.7 Summary, 410 Literature Cited, 412 Problems, 414 PART IV. ENGINEERING CALCULATIONS, 419 10. Options for Equilibrium Calculations, 420 10.1 Basic Phase-Equilibrium Relations, 421 10.2 Choices for Standard States in Gamma Methods, 428 10.3 Basic Reaction-Equilibrium Relations, 443 10.4 Preliminaries to Reaction-Equilibrium Calculations, 456 10.5 Choosing an Appropriate Form in Applications, 468 Literature Cited, 470 Problems, 471 xii CONTENTS 11. Elementary Computational Procedures, 477 11.1 Phase-Equilibrium Calculations, 478 11.2 One-Phase Reaction-Equilibrium Calculations, 499 11.3 Multiphase Reaction-Equilibrium Calculations, 511 11.4 Summary, 519 Literature Cited, 521 Problems, 522 12. Selected Applications, 529 12.1 Phase Equilibria, 529 12.2 Solubilities, 542 12.3 Independent Variables in Steady-Flow Processes, 550 12.4 Heat Effects in Steady-Flow Processes, 555 12.5 Response of Selected Properties, 571 12.6 Summary, 577 Literature Cited, 579 Problems, 579 AFTERWORD, 585 APPENDICES, 589 A. Tools from the Calculus, 590 B. Elements of Linear Algebra, 606 C. Solutions to Cubic Equations, 620 D. Vapor Pressures of Selected Fluids, 622 E. Parameters in Models for G Excess, 623 F. A Stability Condition for Binaries, 627 G. Notation in Variational Calculus, 629 H. Triangular Diagrams, 631 I. Lagrange Multipliers, 634 J. NRTL Model, 636 K. Simple Algorithms for Binary VLLE, 639 Notation, 641 Index, 646