CLASSICAL AND GEOMETRICAL THEORY OF CHEMICAL AND PHASE THERMODYNAMICS -- CONTENTS -- PREFACE -- PART I INDUCTIVE FOUNDATIONS OF CLASSICAL THERMODYNAMICS -- 1. Mathematical Preliminaries: Functions and Differentials -- 1.1 Physical Conception of Mathematical Functions and Differentials -- 1.2 Four Useful Identities -- 1.3 Exact and Inexact Differentials -- 1.4 Taylor Series -- 2. Thermodynamic Description of Simple Fluids -- 2.1 The Logic of Thermodynamics -- 2.2 Mechanical and Thermal Properties of Gases: Equations of State -- 2.3 Thermometry and the Temperature Concept -- 2.4 Real and Ideal Gases -- 2.4.1 Compressibility Factor and Ideal Gas Deviations -- 2.4.2 Van der Waals and Other Model Equations of State -- 2.4.3 The Virial Equation of State -- 2.5 Condensation and the Gas-Liquid Critical Point -- 2.6 Van der Waals Model of Condensation and Critical Behavior -- 2.7 The Principle of Corresponding States -- 2.8 Newtonian Dynamics in the Absence of Frictional Forces -- 2.9 Mechanical Energy and the Conservation Principle -- 2.10 Fundamental Definitions: System, Property, Macroscopic, State -- 2.10.1 System -- 2.10.2 Property -- 2.10.3 Macroscopic -- 2.10.4 State -- 2.11 The Nature of the Equilibrium Limit -- 3. General Energy Concept and the First Law -- 3.1 Historical Background of the First Law -- 3.2 Reversible and Irreversible Work -- 3.3 General Forms of Work -- 3.3.1 Pressure-Volume Work -- 3.3.2 Surface Tension Work -- 3.3.3 Elastic Work -- 3.3.4 Electrical (emf) Work -- 3.3.5 Electric Polarization Work -- 3.3.6 Magnetic Polarization Work -- 3.3.7 Overview of General Work Forms -- 3.4 Characterization and Measurement of Heat -- 3.5 General Statements of the First Law -- 3.6 Thermochemical Consequences of the First Law -- 3.6.1 Heat Capacity and the Enthalpy Function -- 3.6.2 Joule's Experiment.

3.6.3 Joule-Thomson Porous Plug Experiment -- 3.6.4 Ideal Gas Thermodynamics -- 3.6.5 Thermochemistry: Enthalpies of Chemical Reactions -- 3.6.6 Temperature Dependence of Reaction Enthalpies -- 3.6.7 Heats of Solution -- 3.6.8 Other Aspects of Enthalpy Decompositions -- 4. Engine Efficiency, Entropy, and the Second Law -- 4.1 Introduction: Heat Flow, Spontaneity, and Irreversibility -- 4.2 Heat Engines: Conversion of Heat to Work -- 4.3 Carnot's Analysis of Optimal Heat-Engine Efficiency -- 4.4 Theoretical Limits on Perpetual Motion: Kelvin's and Clausius' Principles -- 4.5 Kelvin's Temperature Scale -- 4.6 Carnot's Theorem and the Entropy of Clausius -- 4.7 Clausius' Formulation of the Second Law -- 4.8 Summary of the Inductive Basis of Thermodynamics -- PART II GIBBSIAN THERMODYNAMICS OF CHEMICAL AND PHASE EQUILIBRIA -- 5. Analytical Criteria for Thermodynamic Equilibrium -- 5.1 The Gibbs Perspective -- 5.2 Analytical Formulation of the Gibbs Criterion for a System in Equilibrium -- 5.3 Alternative Expressions of the Gibbs Criterion -- 5.4 Duality of Fundamental Equations: Entropy Maximization versus Energy Minimization -- 5.5 Other Thermodynamic Potentials: Gibbs and Helmholtz Free Energy -- 5.6 Maxwell Relations -- 5.7 Gibbs Free Energy Changes in Laboratory Conditions -- 5.8 Post-Gibbsian Developments -- 5.8.1 The Fugacity Concept -- 5.8.2 The "Third Law" of Thermodynamics: A Critical Assessment -- 6. Thermodynamics of Homogeneous Chemical Mixtures -- 6.1 Chemical Potential in Multicomponent Systems -- 6.2 Partial Molar Quantities -- 6.3 The Gibbs-Duhem Equation -- 6.4 Physical Nature of Chemical Potential in Ideal and Real Gas Mixtures -- 7. Thermodynamics of Phase Equilibria -- 7.1 The Gibbs Phase Rule -- 7.2 Single-Component Systems -- 7.2.1 The Phase Diagram of Water -- 7.2.2 Clapeyron and Clausius-Clapeyron Equations for Phase Boundaries.

7.2.3 Illustrative Phase Diagrams for Pure Substances -- 7.3 Binary Fluid Systems -- 7.3.1 Vapor-Pressure (P-x) Diagrams: Raoult and Henry Limits -- 7.3.2 The Lever Rule -- 7.3.3 Positive and Negative Deviations -- 7.3.4 Boiling-Point Diagrams: Theory of Distillation -- 7.3.5 Immiscibility and Consolute Behavior -- 7.3.6 Colligative Properties and Van't Hoff Osmotic Equation -- 7.3.7 Activity and Activity Coefficients -- 7.4 Binary Solid-Liquid Equilibria -- 7.4.1 Eutectic Behavior -- 7.4.2 Congruent Melting -- 7.4.3 Incongruent Melting and Peritectics -- 7.4.4 Alloys and Partial Miscibility -- 7.4.5 Phase Boundaries and Gibbs Free Energy of Mixing -- 7.5 Ternary and Higher Systems -- 8. Thermodynamics of Chemical Reaction Equilibria -- 8.1 Analytical Formulation of Chemical Reactions in Terms of the Advancement Coordinate -- 8.2 Criterion of Chemical Equilibrium: The Equilibrium Constant -- 8.3 General Free Energy Changes: de Donder's Affinity -- 8.4 Standard Free Energy of Formation -- 8.5 Temperature and Pressure Dependence of the Equilibrium Constant -- 8.5.1 Temperature Dependence: Van't Hoff Equation -- 8.5.2 Pressure Dependence -- 8.6 Le Chatelier's Principle -- 8.7 Thermodynamics of Electrochemical Cells -- 8.8 Ion Activities in Electrolyte Solutions -- 8.9 Concluding Synopsis of Gibbs' Theory -- PART III METRIC GEOMETRY OF EQUILIBRIUM THERMODYNAMICS -- 9. Introduction to Vector Geometry and Metric Spaces -- 9.1 Vector and Matrix Algebra -- 9.2 Dirac Notation -- 9.3 Metric Spaces -- 10. Metric Geometry of Thermodynamic Responses -- 10.1 The Space of Thermodynamic Response Vectors -- 10.2 The Metric of Thermodynamic Response Space -- 10.3 Linear Dependence, Dimensionality, and Gibbs-Duhem Equations -- 11. Geometrical Representation of Equilibrium Thermodynamics -- 11.1 Thermodynamic Vectors and Geometry.

11.2 Conjugate Variables and Conjugate Vectors -- 11.3 Metric of a Homogeneous Fluid -- 11.4 General Transformation Theory in Thermodynamic Metric Space -- 11.5 Saturation Properties Along the Vapor-Pressure Curve -- 11.6 Self-Conjugate and Normal Response Modes -- 11.7 Geometrical Characterization of Common Fluids -- 11.8 Stability Conditions and the "Third Law" for Homogeneous Phases -- 11.9 The Critical Instability Limit -- 11.10 Critical Divergence and Exponents -- 11.11 Phase Heterogeneity and Criticality -- 12. Geometrical Evaluation of Thermodynamic Derivatives -- 12.1 Thermodynamic Vectors and Derivatives -- 12.2 General Solution for Two Degrees of Freedom and Relationship to Jacobian Methods -- 12.3 General Partial Derivatives in Higher-Dimensional Systems -- 12.4 Phase-Boundary Derivatives in Multicomponent Systems -- 12.5 Stationary Points of Phase Diagrams: Gibbs-Konowalow Laws -- 12.6 Higher-Order Derivatives and State Changes -- 13. Further Aspects of Thermodynamic Geometry -- 13.1 Reversible Changes of State: Riemannian Geometry -- 13.2 Near-Equilibrium Irreversible Thermodynamics: Diffusional Geometry -- 13.3 Quantum Statistical Thermodynamic Origins of Chemical and Phase Thermodynamics -- 13.3.1 Nonequilibrium Displacement Variables of Mayer and Co-workers -- 13.3.2 Quantum Statistical Thermodynamics and the Statistical Origins of Metric Geometry -- 13.3.3 Evaluation of Molecular Partition Functions for Reactive Mixtures -- 13.3.4 Quantum Cluster Equilibrium Theory of Phase Thermodynamics -- Appendix: Units and Conversion Factors -- AUTHOR INDEX -- SUBJECT INDEX.