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Contents Preface 3 Contents 6 Chapter 1 15 - Introductory Remarks 15 1.1 Scope and Objectives 16 1.2 Level of Course 16 1.3 Course Outline 16 1.4 Books 18 Part I 20 -Thermodynamics 20 Chapter 2 - 21 Basic Concepts and Definitions 21 2.1 Systems and Surroundings 22 2.2 State Variables and Thermodynamic Properties 22 2.3 Intensive and Extensive Variables 23 2.4 Homogeneous and Heterogeneous Systems, Phases 24 2.5 Work 24 2.6 Reversible and Quasi-Static Processes 25 2.6.1 Quasi-Static Process 26 2.6.2 Reversible process 27 2.7 29 Adiabatic and Diathermal Walls 29 2.8 Thermal Contact and Thermal Equilibrium 29 Chapter 3 - 30 The Laws of Thermodynamics 1 30 3.1 The Zeroth Law. Temperature 31 3.2 The First Law. Traditional Approach 33 3.3 Mathematical Interlude I. Exact and Inexact Differentials 35 3.4 The First Law: Axiomatic Approach 36 3.5 Some Applications of the First Law 39 3.5.1 Heat Capacity 39 3.5.2 Heat and Internal Energy 39 3.5.3 Heat and Enthalpy 40 3.6 Mathematical Interlude II; Partial Derivatives 42 3.7 Other Applications of the First Law 43 3.7.1 CP - CV 43 3.7.2 Isothermal Change, Ideal Gas 44 3.7.3 Adiabatic Change, Ideal Gas 44 3.7.4 The Joule and the Joule-Thomson Coefficients 46 Chapter 4 - 48 The Laws of Thermodynamics II 48 4.1 The Second Law. Traditional Approach 48 4.2 Engine Efficiency. Absolute Temperature 52 4.2.1 Ideal Gas 52 4.2.2 Coupled Cycles 52 4.3 Generalization. Arbitrary Cycle. 54 4.4 The Clausius Inequality 55 4.5 The. Second Law. Axiomatic Approach (Carathéodory) 57 4.6 Mathematical Interlude III. Pfaffian Differential Forms 59 4.7 Pfaffian Expressions in Two Variables 60 4.8 Pfaffian Expressions in More Than Two Dimensions 61 4.9 Carathéodory's Theorem 62 4.10. Entropy. Axiomatic Approach 62 4.11 Some Applications of the Second Law 68 4.11.1 Reversible Processes (PV work only) 68 4.11.2 Irreversible Processes 69 Chapter 5 - 71 Useful Functions: The Free Energy Functions 71 5.1 Mathematical Interlude IV: Legendre Transformations 72 5.2 Maxwell Relations 74 5.3 The Gibbs-Helmholtz Equations 74 5.4 Relation of (A and (G to Work: Criteria for Spontaneity 75 5.4.1 Expansion and Other Types of Work 75 5.4.2 Comments 77 5.5 Generalization to Open Systems and Systems of Variable Composition 79 5.5.1 Single Component System 79 5.5.2 Multicomponent Systems 79 5.6 The Chemical Potential 80 5.7 Mathematical Interlude V: Euler's Theorem 80 5.8 Thermodynamic Potentials 82 Chapter 6 - 86 The Third Law of Thermodynamics 86 6.1 Statements of the Third Law 87 Chapter 7 - 91 General Conditions for Equilibrium and Stability 91 7.1 Virtual Variations 92 7.2 Thermodynamic Potentials; Inequalities 93 7.4 Equilibrium Condition from Energy 95 7.4.1 Boundary Fully Heat Conducting, Deformable, Permeable (Normal System) 96 7.4.2 Special Cases: Boundary Semi-Heat Conducting, Semi-Deformable, or Semi- Permeable 97 7.5 Equilibrium Conditions from Other Potentials 98 7.6 General Conditions for Stability 98 7.7 Stability Conditions from E 99 7.8 Stability Conditions from Cross-Terms. 101 7.9 Stability Conditions from Other Potentials 102 7.10 Derivatives of Thermodynamic Potentials with Respect to Intensive Variables 103 Chapter 8 - 105 Application of Thermodynamics to Gases, Liquids, and Solids 105 8.1 Gases 105 8.2 Enthalpy, Entropy, Chemical Potential, Fugacity 107 8.2.1 Enthalpy 107 8.2.2 Entropy 108 8.3 Standard States of Gases 111 8. 4 Mixtures of Gases 112 8.4.1 Partial Fugacity 112 8.4.2 Free Energy, Entropy, Enthalpy, and Volume of Mixing of Gases 113 8.5 Thermodynamics of Condensed Systems 113 8.5.1 The Chemical Potential 114 8.5.2 Entropy 115 8.5.3 Enthalpy 115 Chapter 9 - 116 Phase and Chemical Equilibria 116 9.1 The Phase Rule 116 9.2 The Clapeyron Equation 118 9.3 The Clausius-Clapeyron Equation 118 9.4 The Generalized Clapeyron Equation 120 9.5 Chemical Equilibrium 121 9.6 The Equilibrium Constant 123 Chapter 10 - 125 Solutions-Non-Electrolytes 125 10.1 Activities and Standard States Conventions 125 10.1.1 Gases 125 10.1.2 Pure Liquids and Solids 126 10.1.3 Mixtures 126 10.2 Ideal and Ideally-Dilute Solutions; Raoult's and Henry's Laws 128 10.2.1 Ideal Solutions 128 10.2.2 Ideally Dilute Solutions 129 10.3 Thermodynamic Functions of Mixing 131 10.3.1 For Ideal Solutions 131 10.3.2 For Non-Ideal Solutions 131 10.4 Colligative Properties 132 10.4.1 Lowering of Solvent Vapor Pressure 133 10.4.2 Freezing Point Depression 133 10.43 Boiling Point Elevation 135 10.4.4 Osmotic Pressure 135 Chapter 11 - 138 Processes Involving Work Other than Pressure-Volume Work 138 11.1 PV-Work and One Other Type of Work 139 11.2 PV-, ( -, and fL-Work 140 Chapter 12 - 142 Phase Transitions and Critical Phenomena 142 12.1 Stable, Metastable, and Unstable Isotherms 143 12.2 The Critical Region* 146 Part II - 150 Introductory Statistical Mechanics 150 Chapter 13 - 151 Principles of Statistical Mechanics. 151 13.1 Introduction 151 13.2 Preliminary Discussion; Simple Problem 152 13.3 Time- and Ensemble-Averages 153 13.4 Number of Microstates, (D, Distributions Di 154 13.5 Mathematical Interlude VI. Combinatory Analysis 157 13.6 Fundamental Problem in Statistical Mechanics 159 13.7 Maxwell-Bolzmann,Fermi-Dirac, Bose-Einstein Statistics. "Corrected" Maxwell-Boltzmann Statistics 160 13.7.1 Maxwell-Boltzmann Statistics 160 13.7.2 Fermi-Dirac Statistics 160 13.7.3 Bose-Einstein Statistics 160 13.8 Systems of Distinguishable (Localized) and Indistinguishable (Non -Localized) Particles 162 13.9 Maximizing (D 162 13.10 Probability of a Quantum State. The Partition Function 164 13.10.1 Maxwell-Boltzmann Statistics 164 13.10.2 Corrected Maxwell-Boltzmann Statistics 165 Chapter 14 - 166 Thermodynamic Connection 166 14.1 Energy, Heat, and Work 166 14.2 Entropy 167 14.3 Identification of ( with 1/kT 168 14.4 Pressure 169 14.5 The Functions E, H, S, A, G, and ( 170 Chapter 15 - 173 Molecular Partition Function 173 15.1 Translational Partition Function 173 15.2 Vibrational Partition Function. Diatomics 174 15.3 Rotational Partition Function. Diatomics 175 15.4 Electronic Partition Function 176 15.5 Nuclear Spin States 177 15.6 The "Zero" of Energy 178 Chapter 16 - 181 Statistical Mechanical Applications 181 16.1 Population Ratios 181 16.2 Thermodynamic Functions of Gases 182 16.3 Equilibrium Constants 184 16.4 Systems of Localized Particles. The Einstein Solid 186 16.4.1 Energy 187 16.4.2 Heat Capacity 188 16.4.3 Entropy 188 Annotated Reference Bibliography 193 Appendix I 195 Homework Problem Sets 195 PROBLEM SET I 195 PROBLEM SET II 197 PROBLEM SET III 199 PROBLEMS SET IV 201 PROBLEM SET V 203 PROBLEM SET VI 204 PROBLEMS VII 205 PROBLEM SET VIII 206 PROBLEM SET IX 207 PROBLEM SET X 208 Appendix II 208 Solutions to Problems 209 SOLUTION TO SET I 209 SOLUTION TO SET II 212 SOLUTION TO SET III 214 SOLUTION TO SET IV 218 SOLUTION TO SET V 221 SOLUTION TO SET VI 223 SOLUTION TO SET VII 226 SOLUTION TO SET VIII 229 SOLUTION TO SET IX 231 SOLUTION TO SET X 234
Library of Congress Subject Headings for this publication: Thermodynamics, Statistical mechanics