THERMODYNAMICS. Second Edition

THERMODYNAMICS Second Edition

THERMODYNAMICS Second Edition N. A. Gokcen, Sc.D. Albany, Oregon R. G. Reddy, Ph.D. The University of Alabama Tuscaloosa, Alabama Springer Science+Business Media, LLC

On file Library of Congress Cataloging-in-Publication Data If your diskette is defective in manufacture or has been damaged in transit, it will be replaced at no charge if returned within 30 days of receipt to Managing Editor, Springer Science+Business Media, LLC. The publisher makes no warranty of any kind, expressed or implied, with regard to the software reproduced on the diskette or the accompanying documentation. The publisher shall not be liable in any event for incidental or consequential damages or loss in connection with, or arising out of, the furnishing, performance, or use of the software. Additional material to this book can be downloaded from http://extras.springer.com ISBN 978-1-4899-1375-3 ISBN 978-1-4899-1373-9 (ebook) DOI 10.1007/978-1-4899-1373-9 Springer Science+Business Media New York 1996 Originally published by Plenum Press, New York in 1996 Softcover reprint of the hardcover 1st edition 1996 All rights reserved 10 98765432 1 No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the Publisher The first edition of this book was published by Techscience, Inc., Hawthorne, California, 1975

To Emel Gokcen and Rama Reddy with devotion and dedication

PREFACE This edition of Thermodynamics is a thoroughly revised, streamlined, and corrected version of the book of the same title, first published in 1975. It is intended for students, practicing engineers, and specialists in materials sciences, metallurgical engineering, chemical engineering, chemistry, electrochemistry, and related fields. The present edition contains many additional numerical examples and problems. Greater emphasis is put on the application of thermodynamics to chemical, materials, and metallurgical problems. The SI system has been used throughout the textbook. In addition, a floppy disk for chemical equilibrium calculations is enclosed inside the back cover. It contains the data for the elements, oxides, halides, sulfides, and other inorganic compounds. The subject material presented in chapters III to XIV formed the basis of a thermodynamics course offered by one of the authors (R.G. Reddy) for the last 14 years at the University of Nevada, Reno. The subject matter in this book is based on a minimum number of laws, axioms, and postulates. This procedure avoids unnecessary repetitions, often encountered in books based on historical sequence of development in thermodynamics. For example, the Clapeyron equation, the van't Hoff equation, and the Nernst distribution law all refer to the Gibbs energy changes of relevant processes, and they need not be presented as radically different relationships. The manuscript and galley proofs were corrected not only by the authors, but also by Dr. J.A. Sommers, whose diligent efforts are gratefully acknowledged. Criticisms and suggestions during the past two decades from Professors E.F. Westrum, Jr., Y.K. Rao, D.A. Stevenson, G.R. St. Pierre, A.E. Morris, D.C. Lynch, L. Brewer, and Dr. M. Blander are also acknowledged. Help rendered by Professors SJ. Louis, F.C. Harris, Jr., and their students in developing the software package for thermodynamic calculations is greatly appreciated. They are not responsible for the content of the text, and the responsibility rests entirely with the authors who welcome further comments and criticism from readers. Finally, we thank our families for their patience, support, and encouragement throughout the preparation of this book. N.A. Gokcen Albany, Oregon R.G. Reddy Tuscaloosa, Alabama vii

CONTENTS CHAPTER I. INTRODUCTION AND DEFINITIONS.... Introduction.... Terms and Symbols...................................... 1 Thermodynamic State of a System............................ 4 Boundaries of a System................................... 5 Temperature........................................... 5 Work and Energy... 8 Equilibrium........................................... 9 Objectives of Thermodynamics.............................. 9 Problems............................................. 9 CHAPTER II. DIFFERENTIATION, INTEGRATION, AND SPECIAL FUNCTIONS.................................. 11 Differentials and Derivatives................................ 11 Second Derivatives... 14 Useful Differentials...................................... 14 Maxima, Minima and Inflection Points......................... 15 L'Hopital's Theorem..................................... 16 Homogeneous Functions... 17 Euler's Theorem on Homogeneous Functions... 17 Homogeneous Thermodynamic Functions....................... 18 Integrals.............................................. 20 Exact Differentials....................................... 21 Line Integrals.......................................... 23 A Graphical Example..................................... 24 Cross Differentials....................................... 25 Lagrange's Method of Undetermined Multipliers.................. 26 Change of Independent Variables............................. 27 Representation of Data.................................... 28 Determinants... 31 ix

x Contents Useful Series... 32 Problems............................................. 33 CHAPTER III. THE FIRST LAW OF THERMODYNAMICS....... 37 Work of Compression and Expansion.......................... 38 Heat................................................ 39 Reversible Processes in Closed Systems........................ 40 Application of the First Law to Ideal Gases.................... 40 Energy of Ideal Gases... 40 Heat Capacity.......................................... 42 Processes with Ideal Gases................................. 42 Simple Kinetic Theory of Ideal Gases.......................... 45 Real Gases, Liquids and Solids............................. 47 Compressibility Factor.................................... 47 van der Waals Equation................................... 48 Other Equations of State................................... 51 Liquids and Solids....................................... 53 Enthalpy and Heat Capacity............................... 53 Heat Capacity of Solids................................... 54 Empirical Representation of Heat Capacity...................... 57 Relationship between C and ~ H -~ H ~ 9... 8 57 Enthalpy Change of Phase Transformations... :.......... 58 Thermochemistry... 60 Variation of /}., HI- with Temperature.......................... 63 Bond Energies... 65 Adiabatic Flame Temperature............................... 66 Problems............................................. 67 CHAPTER IV. THE SECOND LAW OF THERMODYNAMICS..... 71 The Second Law of Thermodynamics.......................... 71 Carnot Engine.......................................... 72 Carnot Theorem........................................ 74 Kelvin Temperature Scale.................................. 75 Carnot Engine with an Ideal Gas............................. 77 Refrigeration Engine..................................... 79 Spontaneous Processes.................................... 79 Reversible Cyclic Processes................................ 79 Entropy Change in Reversible Processes........................ 83 Entropy Change in Irreversible Processes....................... 83 Method of Caratheodory................................... 85 The Second Law of Thermodynamics.......................... 87 Problems............................................. 88

Contents Xl CHAPTER V. ENTROPY AND RELATED FUNCTIONS......... 89 Entropy Change... 89 Entropy of Mixing of Ideal Gases... 91 Entropy of Phase Change and Chemical Reactions................. 92 Entropy, Randomness and Probability.......................... 93 Thermodynamic Equations of State........................... 94 Difference Between C p and C v.............................. 96 Variation of C p and C v with P and V... 97 Joule-Kelvin Expansion of Gases............................. 97 Problems............................................. 99 CHAPTER VI. HELMHOLTZ AND GIBBS ENERGIES.......... 101 Introduction and Definitions................................ 101 Partial Differential Relations................................ 103 Isothermal Changes in A and G.............................. 104 Criteria for Reversibility and Irreversibility...................... 105 Examples............................................. 107 Problems............................................. 108 CHAPTER VII. THE THIRD LAW OF THERMODYNAMICS...... 109 Introduction........................................... 109 The Third Law of Thermodynamics........................... 111 Entropy from Statistical Mechanics... '. 113 Entropies of Supercooled Liquids... 114 Consequences of the Third Law.............................. 115 Thermal Evaluation of Entropy.............................. 116 Problems............................................. 117 CHAPTER VIII. PHASE EQUILIBRIA.... 119 Introduction........................................... 119 Two-Phase Equilibrium................................... 119 Vaporization Equilibria... 121 Variation of Vapor Pressure with Total Pressure at Constant Temperature.. 124 Representation of Phase Equilibria............................ 125 Components........................................... 126 Variables of State and Degrees of Freedom...................... 130 Partial (Molar) Gibbs Energy, or Chemical Potential................ 130 Conditions of Phase Equilibrium............................. 131 Phase Rule............................................ 133 Other Definitions of Gi... 135 Useful Partial (Molar) Properties............................. 136 G i and Criterion of Equilibrium... 136 Problems............................................. 136

Xll Contents CHAPTER IX. FUGACITY AND ACTIVITY................... 139 Introduction........................................... 139 Fugacity of Pure Gases.................................... 140 Alternative Equations for Fugacity............................ 141 Variation of Fugacity with Temperature... 142 Definition of Activity..................................... 143 Raoult's Law... 144 Henry's Law........................................... 145 Problems............................................. 149 CHAPTER X. SOLUTIONS.... 151 Part I Ideal Solutions................................... 151 Equilibrium Between an Ideal Solution and Its Vapor............... 152 Constant Pressure Binary Equilibrium Diagrams................. 156 Equilibria Between Pure Immiscible Solids and Ideal Liquid Solutions... 157 Relative Positions of Liquidus and Solidus Lines.................. 158 Depression of Freezing Point... 159 Elevation of the Boiling Point............................... 160 Determination of Molecular Weights... 160 Ideal Solubilities of Gases... 161 Part II Real Solutions... 162 Definition of Real Solutions................................ 162 Equilibrium Between a Real Solution and Its Vapor at Constant Temperature................................. 162 Equilibrium Between a Real Solution and Its Vapor at Constant Pressure.................................... 166 Variation of Activity and Activity Coefficients with Composition in Binary Solutions.................................... 170 Variation of Activities in Binary Solutions with Pressure and Temperature. 172 Dilute Solutions... 172 Molar, Partial Molar, and Excess Thermodynamic Properties of Solutions. 173 Problems............................................. 177 CHAPTER XI. PARTIAL (MOLAR) PROPERTIES.... 179 Introduction........................................... 179 Partial (Molar) Properties of Binary Systems..................... 180 Excess Gibbs Energy; Binary Systems......................... 182 Representation of G E..................... 183 Alternative Equations..................................... 187 Regular Solutions....................................... 189 Maximum, Minimum, and Critical Points in (11.43)................ 190 Spinodal Points......................................... 192 Theoretical Derivation of (11.40)............................. 192

Contents xiii Effect of Temperature on G E and gi........................... 195 Equations with Henrian Reference States... 199 Wagner Interaction Parameters... 200 Problems.... 201 CHAPTER XII. GIBBS ENERGY CHANGE OF REACTIONS..... 203 Introduction........................................... 203 Feasibility of Chemical Reactions.......................... 204 Equilibria in Real Gas Mixtures.............................. 209 Equilibria Involving Condensed Phases......................... 211 Determination of Standard Gibbs Energy Changes................. 212 Method I-Determination of I'l. GO from Equilibrium Constant......... 212 Method II-Thermal Data... 214 Method III-Electromotive Force (emf) Method... 214 Method IV-Spectroscopic Data and Mechanics of Molecules... 215 Thermodynamic Equations... 215 Tabulation of Thermodynamic Data........................... 216 Use of Tables.......................................... 224 Other Thermodynamic Tables and Compilations... 228 Use of Tabular Data in Experimental Work...................... 229 Complex Equilibria...................................... 238 Generalized Reactions and Their Equilibrium Constants............. 240 Problems............................................. 244 CHAPTER XIII. SOLUTIONS OF ELECTROLYTES.... 247 Introduction........................................... 247 Activity and Activity Coefficient............................. 248 Debye-Htickel Theory.................................... 250 Concentrated Electrolytes.................................. 256 Determination of Activities................................. 257 Weak Electrolytes....................................... 262 Temkin Rule........................................... 264 Problems............................................. 265 CHAPTER XIV. REVERSIBLE GALVANIC CELLS............. 267 Introduction........................................... 267 Properties of Reversible Cells............................... 268 Single Electrode Reactions................................. 268 Convention in Notation... 269 Reaction Isotherm and emf................................. 271 Standard emf of Half-cells... 272 Variation of emf with Temperature and Pressure................... 276 Ionization Constant of Water................................ 277

xiv Contents Cells with Solid Electrolytes................................ 280 Problems............................................. 282 CHAPTER XV. PHASE DIAGRAMS........................ 285 Introduction........................................... 285 Binary Phase Diagrams... 285 Erroneous Diagrams... 288 Lever Rule............................................ 290 Molar Gibbs Energy of Mixing-Composition Diagrams... 291!1G Diagrams for Other Phases... 294!1G Diagrams for Complex Systems... 298 Calculation of Phase Diagrams from Thermodynamic Data........... 299 Ternary Phase Diagrams................................... 302 Tielines.............................................. 309 Thermodynamic Consideration.............................. 309 Second Order Transitions.................................. 313 Bibliography.......................................... 314 Problems............................................. 314 Selected Binary Phase Diagrams.... 315 CHAPTER XVI. SPECIAL TOPICS... 323 Part I Surface Tension.................................. 323 Properties of Surfaces... 323 Criteria for Equilibrium................................... 324 Gibbs Adsorption Equation................................. 325 Vapor Pressure of Droplets................................. 326 Part II Gravitational Electric and Magnetic Fields.............. 327 Gravitational Field....................................... 327 Solutions............................................. 328 Centrifugal Force... 329 Electric and Magnetic Fields................................ 329 Part ill Long-Range Order.............................. 330 Ordering and Clustering................................... 331 Order-Disorder in Binary Alloys............................. 331 Long-Range Order Parameter............................... 333 Gorsky and Bragg-Williams (GBW) Approximation................ 334 Heat Capacity.......................................... 336 Problems............................................. 338 APPENDIX I. GENERAL REFERENCES.................... 339 APPENDIX II. TABLES OF THERMODYNAMIC DATA FOR EXAMPLES AND PROBLEMS IN TEXT...................... 341

Contents xv APPENDIX III. THERMODYNAMIC SIMULATOR (TSIM) FOR THERMODYNAMIC CALCULATIONS... 371 APPENDIX IV. ESTIMATION OF ACTIVITIES IN MULTICOMPONENT IONIC SOLUTIONS.................... 373 APPENDIX V. STABILITY DIAGRAMS... 381 APPENDIX VI. LIST OF SYMBOLS........................ 387 INDEX... 393

1 Group IA -,- H 1.0079 3 Li 6.941 11 Na 22.9898 19 K 39.0983 37 Rb 85.4678 55 Cs 132.905 87 Fr (223) Periodic table of the elements 2 New notation Previous IUPAC 'orm IIA ~ C A S _ ~ " " 4 Be 9.01218 12 3 4 5 6 7 8 9 10 ilia -... IV A VA VIA VilA VillA M9 2U05 IIIB IVB VB VIB VIIB,.-VIII--, 20 21 22 23 24 25 26 27 28 Ca Sc Ti V Cr Mn Fe Co Ni 40.08 44.9559 47.88 50.9415 51.996 54.9380 55.847 58.9332 58.69 38 39 40 41 42 43 44 45 46 Sr Y Zr Nb Mo Tc Ru Rh Pd 87.62 88.9059 91.224 92.9064 95.94 (98) 101.07 102.906 106.42 56 57 72 13 74 15 16 11 18 Sa La*Hf Ta W Re Os Ir Pt 137.33 138.906 'I' 178.49 180.948 183.8S 186.207 190.2 192.22 195.08 88 89! 104 a 105 a 106 a 101 a Ra Ac A U n Unp ~ Unli Uns m.025 227.028 ( (261) (262) (2631 (262) * Lanthanide series 11 12 IB lib 29 30 Cu Zn 63.546 65.39 41 48 A9 Cd 107.868 112.41 79 80 Au Hg 196.967 200.59 18 VillA 13 14 15 16 17 IIIB IVB VB VIB VIIB He ~ ilia IVA VA VIA VilA 4.00260 5 6 7 8 9 10 8 C N 0 F Ne. 10.81 12.011 14.0067 15.9994 18.9984 20.179. 13 14 15 16 11 18 AI Si P S CI Ar 26.9815 28.0855 30.9738 32.06 35.453 39.948 31 32 33 34 35 36 Ga Ge As Se Sr Kr 69.72 72.59 74.9216 78.96 79.904 83.80 49 50 51 52 53 54 In Sn Sb Te I Xe 114.82 118.71 121.15 127.60 126.905 1 J 1.29 81 82 83 84 85 86 TI Pb Bi Po At Rn 204.383 207.2 208.980 (209) (210) (222).to. Actinide series Nole: Alomic masses shown here are the 19631UPAC values (maximum of six significant figures). a SymbOls based on IUPAC systematic names. Reproduced by permission from Advanced Inorganic Chemistry, fifth edition, by F. A. Cotton and G. Wilkinson, Wiley-Interscience (1988).