INTRODUCTION to the of MATERIALS THERMODYNAMICS INTRODUCTION to the THERMODYNAMICS of MATERIALS INTRODUCTION to the THERMODYNAMICS of MATERIALS For more than thirty years, this text has been the definitive introduction to the thermodynamic principles of materials and their multitude of applications. New to this edition is a detailed discussion of acetylene combustion and a numerical explanation for the expansion of ideal gases, as well as additional worked examples covering a wide variety of applied thermodynamics concepts. FIFTH EDITION The accompanying CD has been completely updated to use Excel as a computational thermodynamics tool. Twenty-five examples related to the text are solved in step-by-step detail.
Students can conduct thermodynamic calculations, generate equation parameters from tabular data, calculate reaction parameters, and perform equilibrium calculations involving non-ideal solutions. This textbook is ideal for advanced undergraduates and first- year graduate students and as a reference for professionals in metallurgy, metallurgical engineering, ceramics, and materials science. Gaskell earned his B. in Metallurgy and Technical EDITION Chemistry from the University of Glasgow and a Ph.
from McMaster University. A professor of Materials Engineering at Purdue University since 1982, he started his teaching career at the University of Pennsylvania in 1967. Gaskell ISBN 1 -5 9 1 6 -9 0 4 3 - 9 9 781591 690436 David R. Gaskell Introduction to the Thermodynamics of Materials Fifth Edition This page intentionally left blank Introduction to the Thermodynamics of Materials Fifth Edition David R.
Gaskell School of Materials Engineering Purdue University West Lafayette, IN New York • London CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2012 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U. Government works Version Date: 2012904 International Standard Book Number-13: 978-0-203-10610-5 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the valid- ity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained.
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Visit the Taylor & Francis Web site at http://www.com and the CRC Press Web site at http://www.com For Hugh, Mac and Roydon This page intentionally left blank Contents Preface xiii 1 Introduction and Definition of Terms 1 1.2 The Concept of State 1 1.4 The Equation of State of an Ideal Gas 5 1.5 The Units of Energy and Work 8 1.6 Extensive and Intensive Properties 8 1.7 Phase Diagrams and Thermodynamic Components 9 1.8 Numerical Examples 12 2 The First Law of Thermodynamics 15 2.2 The Relationship between Heat and Work 16 2.3 Internal Energy and the First Law of Thermodynamics 17 2.4 Constant-Volume Processes 21 2.5 Constant-Pressure Processes and the Enthalpy H 21 2.7 Reversible Adiabatic Processes 25 2.8 Reversible Isothermal Pressure or Volume Changes of an Ideal Gas 27 2.10 Numerical Examples 29 Problems 34 3 The Second Law of Thermodynamics 37 3.2 Spontaneous or Natural Processes 38 3.3 Entropy and the Quantification of Irreversibility 39 3.5 An Illustration of Irreversible and Reversible Processes 41 3.6 Entropy and Reversible Heat 43 3.7 The Reversible Isothermal Compression of an Ideal Gas 46 3.8 The Reversible Adiabatic Expansion of an Ideal Gas 47 3.9 Summary Statements 48 vii viii Contents 3.10 The Properties of Heat Engines 48 3.11 The Thermodynamic Temperature Scale 51 3.12 The Second Law of Thermodynamics 53 3.14 Entropy and the Criterion for Equilibrium 57 3.15 The Combined Statement of the First and Second Laws of Thermodynamics 58 3.17 Numerical Examples 61 Problems 66 4 The Statistical Interpretation of Entropy 69 4.2 Entropy and Disorder on an Atomic Scale 70 4.3 The Concept of Microstate 71 4.4 Determination of the Most Probable Microstate 72 4.5 The Influence of Temperature 76 4.6 Thermal Equilibrium and the Boltzmann Equation 78 4.7 Heat Flow and the Production of Entropy 79 4.8 Configurational Entropy and Thermal Entropy 80 4.10 Numerical Examples 84 Problems 86 5 Auxiliary Functions 87 5.3 The Helmholtz Free Energy A 89 5.4 The Gibbs Free Energy G 94 5.5 Summary of the Equations for a Closed System 95 5.6 The Variation of the Composition and Size of the System 95 5.7 The Chemical Potential 97 5.10 The Upstairs-Downstairs-Inside-Out Formula 101 5.11 The Gibbs-Helmholtz Equation 102 5.13 Example of the Use of the Thermodynamic Relations 104 5.14 Numerical Example 105 Problems 107 6 Heat Capacity, Enthalpy, Entropy, and the Third Law of Thermodynamics 109 6.2 Theoretical Calculation of the Heat Capacity 110 6.3 The Empirical Representation of Heat Capacities 114 Contents ix 6.4 Enthalpy as a Function of Temperature and Composition 115 6.5 The Dependence of Entropy on Temperature and the Third Law of Thermodynamics 124 6.6 Experimental Verification of the Third Law 127 6.7 The Influence of Pressure on Enthalpy and Entropy 133 6.9 Numerical Examples 135 Problems 147 7 Phase Equilibrium in a One-Component System 149 7.2 The Variation of Gibbs Free Energy with Temperature at Constant Pressure 150 7.3 The Variation of Gibbs Free Energy with Pressure at Constant Temperature 157 7.4 Gibbs Free Energy as a Function of Temperature and Pressure 159 7.5 Equilibrium between the Vapor Phase and a Condensed Phase 160 7.6 Graphical Representation of Phase Equilibria in a One-Component System 162 7.7 Solid-Solid Equilibria 168 7.8 Summary 171 Numerical Examples 172 Problems 175 8 The Behavior of Gases 177 8.2 The P-V-T Relationships of Gases 177 8.3 Deviations from Ideality and Equations of State for Real Gases 180 8.4 The van der Waals Gas 182 8.5 Other Equations of State for Nonideal Gases 191 8.6 The Thermodynamic Properties of Ideal Gases and Mixtures of Ideal Gases 192 8.7 The Thermodynamic Treatment of Nonideal Gases 198 8.9 Numerical Examples 206 Problems 208 9 The Behavior of Solutions 211 9.2 Raoult’s Law and Henry’s Law 211 9.3 The Thermodynamic Activity of a Component in Solution 215 x Contents 9.4 The Gibbs-Duhem Equation 216 9.5 The Gibbs Free Energy of Formation of a Solution 218 9.6 The Properties of Raoultian Ideal Solutions 221 9.8 Application of the Gibbs-Duhem Relation to the Determination of Activity 229 9.10 A Statistical Model of Solutions 245 9.13 Numerical Examples 257 Problems 259 10 Gibbs Free Energy Composition and Phase Diagrams of Binary Systems 263 10.2 Gibbs Free Energy and Thermodynamic Activity 264 10.3 The Gibbs Free Energy of Formation of Regular Solutions 266 10.4 Criteria for Phase Stability in Regular Solutions 268 10.5 Liquid and Solid Standard States 273 10.6 Phase Diagrams, Gibbs Free Energy, and Thermodynamic Activity 283 10.7 The Phase Diagrams of Binary Systems That Exhibit Regular Solution Behavior in the Liquid and Solid States 292 10.9 Numerical Example 299 Problems 301 11 Reactions Involving Gases 305 11.2 Reaction Equilibrium in a Gas Mixture and the Equilibrium Constant 306 11.3 The Effect of Temperature on the Equilibrium Constant 311 11.4 The Effect of Pressure on the Equilibrium Constant 312 11.5 Reaction Equilibrium as a Compromise between Enthalpy and Entropy 314 11.6 Reaction Equilibrium in the System SO2(g)–SO3(g)–O2(g) 316 11.7 Equilibrium in H2O–H2 and CO2–CO Mixtures 321 11.9 Numerical Examples 324 Problems 335 Contents xi 12 Reactions Involving Pure Condensed Phases and a Gaseous Phase 337 12.2 Reaction Equilibrium in a System Containing Pure Condensed Phases and a Gas Phase 338 12.3 The Variation of the Standard Gibbs Free Energy Change with Temperature 343 12.5 The Effect of Phase Transformations 353 12.6 The Oxides of Carbon 358 12.7 Graphical Representation of Equilibria in the System Metal–Carbon–Oxygen 365 12.9 Numerical Examples 369 Problems 380 13 Reaction Equilibria in Systems Containing Components in Condensed Solution 383 13.2 The Criteria for Reaction Equilibrium in Systems Containing Components in Condensed Solution 385 13.3 Alternative Standard States 393 13.4 The Gibbs Phase Rule 399 13.5 Binary Systems Containing Compounds 417 13.6 Graphical Representation of Phase Equilibria 429 13.7 The Formation of Oxide Phases of Variable Composition 437 13.8 The Solubility of Gases in Metals 446 13.9 Solutions Containing Several Dilute Solutes 450 13.11 Numerical Examples 462 Problems 470 14 Phase Diagrams for Binary Systems in Pressure-Temperature- Composition Space 475 14.2 A Binary System Exhibiting Complete Mutual Solubility of the Components in the Solid and Liquid States 475 14.3 A Binary System Exhibiting Complete Mutual Solubility in the Solid and Liquid States and Showing Minima on the Melting, Boiling, and Sublimation Curves 480 14.4 A Binary System Containing a Eutectic Equilibrium and Having Complete Mutual Solubility in the Liquid 485 xii Contents 14.5 A Binary System Containing a Peritectic Equilibrium and Having Complete Mutual Solubility in the Liquid State 493 14.6 Phase Equilibrium in a Binary System Containing an Intermediate Phase That Melts, Sublimes, and Boils Congruently 501 14.7 Phase Equilibrium in a Binary System Containing an Intermediate Phase That Melts and Sublimes Congruently and Boils Incongruently 508 14.8 Phase Equilibrium in a Binary System with a Eutectic and One Component That Exhibits Allotropy 513 14.9 A Binary Eutectic System in Which Both Components Exhibit Allotropy 517 14.10 Phase Equilibrium at Low Pressure: The Cadmium-Zinc System 524 14.11 Phase Equilibrium at High Pressure: The Na2OAl2O32SiO2–SiO2 System 525 14.2 The Relationship between Chemical and Electrical Driving Forces 535 15.3 The Effect of Concentration on EMF 540 15.6 The Temperature Coefficient of the EMF 549 15.8 The Thermodynamics of Aqueous Solutions 552 15.9 The Gibbs Free Energy of Formation of Ions and Standard Reduction Potentials 555 15.12 Numerical Examples 576 Problems 579 Appendices A Selected Thermodynamic and Thermochemical Data 581 B Exact Differential Equations 589 C The Generation of Auxiliary Functions as Legendre Transformations 591 Nomenclature 599 Answers 603 Index 615 Preface The current edition of this text has benefited significantly from the critical comments and suggestions made by Professors William Fahrenholtz and Mark Schlesinger of the University of Missouri–Rolla and Professor Stanley Howard of the South Dakota School of Mines and Technology. Professor Fahrenholtz provided several worked examples, which have been included in the text. I am grateful for these contributions. I again express my extreme gratitude to Dr.
Arthur Morris, Professor Emeritus of the Department of Metallurgical Engineering at the University of Missouri–Rolla for providing a CD-ROM to supplement the text. The examples on this disk have been completely revised and expanded and cover a wider range of subjects than those included in the fourth edition. This CD provides a major improvement in the usefulness of this text as a learning tool. Gaskell Purdue University A word about the CD The CD contains a thermodynamic database, descriptive material, special programs, and 25 worked-out examples showing how to use Microsoft® Excel∗ for making thermodynamic calculations.
The example solutions are completely revised from the 4th Edition to make better use of Excel’s calculational tools. New examples were added to cover statistical treatment of thermodynamic data.