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Contents Preface xiii 1 Introduction and DeÞnition of Terms 1 1.1 Introduction 1 1.2 The Concept of State 1 1.3 Simple Equilibrium 4 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 13 2 The First Law of Thermodynamics 15 2.1 Introduction 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 2.6 Heat Capacity 21 2.7 Reversible Adiabatic Processes 25 2.8 Reversible Isothermal Pressure or Volume Changes of an Ideal Gas 27 2.9 Summary 28 2.10 Numerical Examples 29 Problems 34 3 The Second Law of Thermodynamics 37 3.1 Introduction 37 3.2 Spontaneous or Natural Processes 38 3.3 Entropy and the QuantiÞcation of Irreversibility 39 3.4 Reversible Processes 40 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 3.10 The Properties of Heat Engines 48 3.11 The Thermodynamic Temperature Scale 51 3.12 The Second Law of Thermodynamics 53 3.13 Maximum Work 55 3.14 Entropy and the Criterion for Equilibrium 57 3.15 The Combined Statement of the First and Second Laws of Thermodynamics 58 3.16 Summary 59 3.17 Numerical Examples 61 Problems 66 4 The Statistical Interpretation of Entropy 69 4.1 Introduction 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 Inßuence of Temperature 76 4.6 Thermal Equilibrium and the Boltzmann Equation 78 4.7 Heat Flow and the Production of Entropy 79 4.8 ConÞgurational Entropy and Thermal Entropy 80 4.9 Summary 83 4.10 Numerical Examples 84 Problems 86 5 Auxiliary Functions 87 5.1 Introduction 87 5.2 The Enthalpy H 89 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 96 5.7 The Chemical Potential 97 5.8 Thermodynamic Relations 98 5.9 Maxwell's Equations 99 5.10 The Upstairs-Downstairs-Inside-Out Formula 101 5.11 The Gibbs-Helmholtz Equation 102 5.12 Summary 103 5.13 Example of the Use of the Thermodynamic Relations 104 5.14 Numerical Examples Problems 106 6 Heat Capacity, Enthalpy, Entropy, and the Third Law of Thermodynamics 109 6.1 Introduction 109 6.2 Theoretical Calculation of the Heat Capacity 110 6.3 The Empirical Representation of Heat Capacities 115 6.4 Enthalpy as a Function of Temperature and Composition 116 6.5 The Dependence of Entropy on Temperature and the Third Law of Thermodynamics 125 6.6 Experimental VeriÞcation of the Third Law 128 6.7 The Inßuence of Pressure on Enthalpy and Entropy 134 6.8 Summary 136 6.9 Numerical Examples 137 Problems 147 7 Phase Equilibrium in a One-Component System 149 7.1 Introduction 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 8.1 Introduction 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 8.8 Summary 204 8.9 Numerical Examples 206 Problems 208 9 The Behavior of Solutions 211 9.1 Introduction 211 9.2 Raoult's Law and Henry's Law 211 9.3 The Thermodynamic Activity of a Component in Solution 215 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 9.7 Nonideal Solutions 226 9.8 Application of the Gibbs-Duhem Relation to the Determination of Activity 229 9.9 Regular Solutions 240 9.10 A Statistical Model of Solutions 245 9.11 Subregular Solutions 252 9.12 Summary 254 9.13 Numerical Examples 257 Problems 259 10 Gibbs Free Energy Composition and Phase Diagrams of Binary Systems 263 10.1 Introduction 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 10.8 Summary 298 10.9 Numerical Example 299 Problems 301 11 Reactions Involving Gases 305 11.1 Introduction 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 11.8 Summary 323 11.9 Numerical Examples 324 Problems 335 12 Reactions Involving Pure Condensed Phases and a Gaseous Phase 337 12.1 Introduction 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 12.4 Ellingham Diagrams 346 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 12.8 Summary 368 12.9 Numerical Examples 369 Problems 380 13 Reaction Equilibria in Systems Containing Components in Condensed Solution 383 13.1 Introduction 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 13.10 Summary 460 13.11 Numerical Examples 462 Problems 470 14 Phase Diagrams for Binary Systems in Pressure-Temperature -Composition Space 475 14.1 Introduction 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 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 14.12 Summary 531 15 Electrochemistry 533 15.1 Introduction 533 15.2 The Relationship between Chemical and Electrical Driving Forces 535 15.3 The Effect of Concentration on EMF 540 15.4 Formation Cells 541 15.5 Concentration Cells 544 15.6 The Temperature CoefÞcient of the EMF 549 15.7 Heat Effects 551 15.8 The Thermodynamics of Aqueous Solutions 552 15.9 The Gibbs Free Energy of Formation of Ions and Standard Reduction Potentials 555 15.10 Pourbaix Diagrams 564 15.11 Summary 574 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

Library of Congress Subject Headings for this publication:

Metallurgy.

Thermodynamics.

Materials -- Thermal properties.