THERMODYNAMICS. Second Edition

Transcription

1 THERMODYNAMICS Second Edition

2 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

3 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 ISBN ISBN (ebook) DOI / 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 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

4 To Emel Gokcen and Rama Reddy with devotion and dedication

5 PREFACE This edition of Thermodynamics is a thoroughly revised, streamlined, and corrected version of the book of the same title, first published in 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

6 CONTENTS CHAPTER I. INTRODUCTION AND DEFINITIONS.... Introduction.... Terms and Symbols Thermodynamic State of a System Boundaries of a System Temperature Work and Energy... 8 Equilibrium Objectives of Thermodynamics Problems CHAPTER II. DIFFERENTIATION, INTEGRATION, AND SPECIAL FUNCTIONS Differentials and Derivatives Second Derivatives Useful Differentials Maxima, Minima and Inflection Points L'Hopital's Theorem Homogeneous Functions Euler's Theorem on Homogeneous Functions Homogeneous Thermodynamic Functions Integrals Exact Differentials Line Integrals A Graphical Example Cross Differentials Lagrange's Method of Undetermined Multipliers Change of Independent Variables Representation of Data Determinants ix

7 x Contents Useful Series Problems CHAPTER III. THE FIRST LAW OF THERMODYNAMICS Work of Compression and Expansion Heat Reversible Processes in Closed Systems Application of the First Law to Ideal Gases Energy of Ideal Gases Heat Capacity Processes with Ideal Gases Simple Kinetic Theory of Ideal Gases Real Gases, Liquids and Solids Compressibility Factor van der Waals Equation Other Equations of State Liquids and Solids Enthalpy and Heat Capacity Heat Capacity of Solids Empirical Representation of Heat Capacity Relationship between C and ~ H -~ H ~ Enthalpy Change of Phase Transformations... : Thermochemistry Variation of /}., HI- with Temperature Bond Energies Adiabatic Flame Temperature Problems CHAPTER IV. THE SECOND LAW OF THERMODYNAMICS The Second Law of Thermodynamics Carnot Engine Carnot Theorem Kelvin Temperature Scale Carnot Engine with an Ideal Gas Refrigeration Engine Spontaneous Processes Reversible Cyclic Processes Entropy Change in Reversible Processes Entropy Change in Irreversible Processes Method of Caratheodory The Second Law of Thermodynamics Problems

8 Contents Xl CHAPTER V. ENTROPY AND RELATED FUNCTIONS Entropy Change Entropy of Mixing of Ideal Gases Entropy of Phase Change and Chemical Reactions Entropy, Randomness and Probability Thermodynamic Equations of State Difference Between C p and C v Variation of C p and C v with P and V Joule-Kelvin Expansion of Gases Problems CHAPTER VI. HELMHOLTZ AND GIBBS ENERGIES Introduction and Definitions Partial Differential Relations Isothermal Changes in A and G Criteria for Reversibility and Irreversibility Examples Problems CHAPTER VII. THE THIRD LAW OF THERMODYNAMICS Introduction The Third Law of Thermodynamics Entropy from Statistical Mechanics... '. 113 Entropies of Supercooled Liquids Consequences of the Third Law Thermal Evaluation of Entropy Problems CHAPTER VIII. PHASE EQUILIBRIA Introduction Two-Phase Equilibrium Vaporization Equilibria Variation of Vapor Pressure with Total Pressure at Constant Temperature Representation of Phase Equilibria Components Variables of State and Degrees of Freedom Partial (Molar) Gibbs Energy, or Chemical Potential Conditions of Phase Equilibrium Phase Rule Other Definitions of Gi Useful Partial (Molar) Properties G i and Criterion of Equilibrium Problems

9 Xll Contents CHAPTER IX. FUGACITY AND ACTIVITY Introduction Fugacity of Pure Gases Alternative Equations for Fugacity Variation of Fugacity with Temperature Definition of Activity Raoult's Law Henry's Law Problems CHAPTER X. SOLUTIONS Part I Ideal Solutions Equilibrium Between an Ideal Solution and Its Vapor Constant Pressure Binary Equilibrium Diagrams Equilibria Between Pure Immiscible Solids and Ideal Liquid Solutions Relative Positions of Liquidus and Solidus Lines Depression of Freezing Point Elevation of the Boiling Point Determination of Molecular Weights Ideal Solubilities of Gases Part II Real Solutions Definition of Real Solutions Equilibrium Between a Real Solution and Its Vapor at Constant Temperature Equilibrium Between a Real Solution and Its Vapor at Constant Pressure Variation of Activity and Activity Coefficients with Composition in Binary Solutions Variation of Activities in Binary Solutions with Pressure and Temperature. 172 Dilute Solutions Molar, Partial Molar, and Excess Thermodynamic Properties of Solutions. 173 Problems CHAPTER XI. PARTIAL (MOLAR) PROPERTIES Introduction Partial (Molar) Properties of Binary Systems Excess Gibbs Energy; Binary Systems Representation of G E Alternative Equations Regular Solutions Maximum, Minimum, and Critical Points in (11.43) Spinodal Points Theoretical Derivation of (11.40)

10 Contents xiii Effect of Temperature on G E and gi Equations with Henrian Reference States Wagner Interaction Parameters Problems CHAPTER XII. GIBBS ENERGY CHANGE OF REACTIONS Introduction Feasibility of Chemical Reactions Equilibria in Real Gas Mixtures Equilibria Involving Condensed Phases Determination of Standard Gibbs Energy Changes Method I-Determination of I'l. GO from Equilibrium Constant Method II-Thermal Data Method III-Electromotive Force (emf) Method Method IV-Spectroscopic Data and Mechanics of Molecules Thermodynamic Equations Tabulation of Thermodynamic Data Use of Tables Other Thermodynamic Tables and Compilations Use of Tabular Data in Experimental Work Complex Equilibria Generalized Reactions and Their Equilibrium Constants Problems CHAPTER XIII. SOLUTIONS OF ELECTROLYTES Introduction Activity and Activity Coefficient Debye-Htickel Theory Concentrated Electrolytes Determination of Activities Weak Electrolytes Temkin Rule Problems CHAPTER XIV. REVERSIBLE GALVANIC CELLS Introduction Properties of Reversible Cells Single Electrode Reactions Convention in Notation Reaction Isotherm and emf Standard emf of Half-cells Variation of emf with Temperature and Pressure Ionization Constant of Water

11 xiv Contents Cells with Solid Electrolytes Problems CHAPTER XV. PHASE DIAGRAMS Introduction Binary Phase Diagrams Erroneous Diagrams Lever Rule Molar Gibbs Energy of Mixing-Composition Diagrams !1G Diagrams for Other Phases !1G Diagrams for Complex Systems Calculation of Phase Diagrams from Thermodynamic Data Ternary Phase Diagrams Tielines Thermodynamic Consideration Second Order Transitions Bibliography Problems Selected Binary Phase Diagrams CHAPTER XVI. SPECIAL TOPICS Part I Surface Tension Properties of Surfaces Criteria for Equilibrium Gibbs Adsorption Equation Vapor Pressure of Droplets Part II Gravitational Electric and Magnetic Fields Gravitational Field Solutions Centrifugal Force Electric and Magnetic Fields Part ill Long-Range Order Ordering and Clustering Order-Disorder in Binary Alloys Long-Range Order Parameter Gorsky and Bragg-Williams (GBW) Approximation Heat Capacity Problems APPENDIX I. GENERAL REFERENCES APPENDIX II. TABLES OF THERMODYNAMIC DATA FOR EXAMPLES AND PROBLEMS IN TEXT

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

13 1 Group IA -,- H Li Na K Rb Cs Fr (223) Periodic table of the elements 2 New notation Previous IUPAC 'orm IIA ~ C A S _ ~ " " 4 Be ilia -... IV A VA VIA VilA VillA M9 2U05 IIIB IVB VB VIB VIIB,.-VIII--, Ca Sc Ti V Cr Mn Fe Co Ni Sr Y Zr Nb Mo Tc Ru Rh Pd (98) Sa La*Hf Ta W Re Os Ir Pt 'I' S ! 104 a 105 a 106 a 101 a Ra Ac A U n Unp ~ Unli Uns m ( (261) (262) (2631 (262) * Lanthanide series IB lib Cu Zn A9 Cd Au Hg VillA IIIB IVB VB VIB VIIB He ~ ilia IVA VA VIA VilA C N 0 F Ne AI Si P S CI Ar Ga Ge As Se Sr Kr In Sn Sb Te I Xe J TI Pb Bi Po At Rn (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).