Classical and geometrical theory of chemical and phase thermodynamics : a non-calculus based approach

Because It Is Grounded In Math, Chemical Thermodynamics Is Often Perceived As A Difficult Subject And Many Students Are Never Fully Comfortable With It. The First Authoritative Textbook Presentation Of Equilibrium Chemical And Phase Thermodynamics In A Reformulated Geometrical Framework, Chemical And Phase Thermodynamics Shows How This Famously Difficult Subject Can Be Accurately Expressed With Only Elementary High-school Geometry Concepts. Featuring Numerous Suggestions For Research-level Extensions, This Simplified Alternative To Standard Calculus-based Thermodynamics Expositions Is Perfect For Undergraduate And Beginning Graduate Students As Well As Researchers.--jacket. Part. I. Inductive Foundations Of Classical Thermodynamics. Mathematical Preliminaries: Functions And Differentials ; Thermodynamic Description Of Simple Fluids ; General Energy Concept And The First Law ; Engine Efficiency, Entropy, And The Second Law -- Pt. Ii. Gibbsian Thermodynamics Of Chemical And Phase Equilibria ; Analytical Criteria For Thermodynamic Equilibrium ; Thermodynamics Of Homogeneous Chemical Mixtures ; Thermodynamics Of Phase Equilibria ; Thermodynamics Of Chemical Reaction Equilibria -- Pt. Iii. Metric Geometry Of Equilibrium Thermodynamics. Introduction To Vector Geometry And Metric Spaces ; Metric Geometry Of Thermodynamic Responses ; Geometrical Representation Of Equilibrium Thermodynamics ; Geometrical Evaluation Of Thermodynamic Derivatives ; Further Aspects Of Thermodynamic Geometry. Frank Weinhold. Errata Slip Inserted. Includes Bibliographical References And Index. Cover Page......Page 1 Title: CLASSICAL AND GEOMETRICAL THEORY OF CHEMICAL AND PHASE THERMODYNAMICS......Page 3 ISBN 978-0470402368......Page 4 CONTENTS......Page 6 PREFACE......Page 11 PART I INDUCTIVE FOUNDATIONS OF CLASSICAL THERMODYNAMICS......Page 13 1.1 PHYSICAL CONCEPTION OF MATHEMATICAL FUNCTIONS AND DIFFERENTIALS......Page 15 1.2 FOUR USEFUL IDENTITIES......Page 19 1.3 EXACT AND INEXACT DIFFERENTIALS......Page 22 1.4 TAYLOR SERIES......Page 27 2.1 THE LOGIC OF THERMODYNAMICS......Page 29 2.2 MECHANICAL AND THERMAL PROPERTIES OF GASES: EQUATIONS OF STATE......Page 30 2.3 THERMOMETRY AND THE TEMPERATURE CONCEPT......Page 36 2.4 REAL AND IDEAL GASES......Page 42 2.4.1 Compressibility Factor and Ideal Gas Deviations......Page 43 2.4.2 Van der Waals and Other Model Equations of State......Page 48 2.4.3 The Virial Equation of State......Page 56 2.5 CONDENSATION AND THE GAS–LIQUID CRITICAL POINT......Page 59 2.6 VAN DER WAALS MODEL OF CONDENSATION AND CRITICAL BEHAVIOR......Page 62 2.7 THE PRINCIPLE OF CORRESPONDING STATES......Page 66 2.8 NEWTONIAN DYNAMICS IN THE ABSENCE OF FRICTIONAL FORCES......Page 68 2.9 MECHANICAL ENERGY AND THE CONSERVATION PRINCIPLE......Page 70 2.10.1 System......Page 72 2.10.2 Property......Page 73 2.10.3 Macroscopic......Page 75 2.10.4 State......Page 76 2.11 THE NATURE OF THE EQUILIBRIUM LIMIT......Page 77 3.1 HISTORICAL BACKGROUND OF THE FIRST LAW......Page 79 3.2 REVERSIBLE AND IRREVERSIBLE WORK......Page 83 3.3.1 Pressure–Volume Work......Page 88 3.3.2 Surface Tension Work......Page 90 3.3.3 Elastic Work......Page 91 3.3.4 Electrical (emf) Work......Page 92 3.3.5 Electric Polarization Work......Page 93 3.3.6 Magnetic Polarization Work......Page 95 3.3.7 Overview of General Work Forms......Page 96 3.4 CHARACTERIZATION AND MEASUREMENT OF HEAT......Page 97 3.5 GENERAL STATEMENTS OF THE FIRST LAW......Page 99 3.6.1 Heat Capacity and the Enthalpy Function......Page 101 3.6.2 Joule’s Experiment......Page 103 3.6.3 Joule–Thomson Porous Plug Experiment......Page 105 3.6.4 Ideal Gas Thermodynamics......Page 107 3.6.5 Thermochemistry: Enthalpies of Chemical Reactions......Page 113 3.6.6 Temperature Dependence of Reaction Enthalpies......Page 119 3.6.7 Heats of Solution......Page 120 3.6.8 Other Aspects of Enthalpy Decompositions......Page 124 4.1 INTRODUCTION: HEAT FLOW, SPONTANEITY, AND IRREVERSIBILITY......Page 129 4.2 HEAT ENGINES: CONVERSION OF HEAT TO WORK......Page 134 4.3 CARNOT’S ANALYSIS OF OPTIMAL HEAT-ENGINE EFFICIENCY......Page 135 4.4 THEORETICAL LIMITS ON PERPETUAL MOTION: KELVIN’S AND CLAUSIUS’ PRINCIPLES......Page 140 4.5 KELVIN’S TEMPERATURE SCALE......Page 142 Paraphrase of the Three Laws of Thermodynamics......Page 143 4.6 CARNOT’S THEOREM AND THE ENTROPY OF CLAUSIUS......Page 146 4.7 CLAUSIUS’ FORMULATION OF THE SECOND LAW......Page 151 4.8 SUMMARY OF THE INDUCTIVE BASIS OF THERMODYNAMICS......Page 157 PART II GIBBSIAN THERMODYNAMICS OF CHEMICAL AND PHASE EQUILIBRIA......Page 159 5.1 THE GIBBS PERSPECTIVE......Page 161 5.2 ANALYTICAL FORMULATION OF THE GIBBS CRITERION FOR A SYSTEM IN EQUILIBRIUM......Page 164 5.3 ALTERNATIVE EXPRESSIONS OF THE GIBBS CRITERION......Page 169 5.4 DUALITY OF FUNDAMENTAL EQUATIONS: ENTROPY MAXIMIZATION VERSUS ENERGY MINIMIZATION......Page 172 5.5 OTHER THERMODYNAMIC POTENTIALS: GIBBS AND HELMHOLTZ FREE ENERGY......Page 174 5.6 MAXWELL RELATIONS......Page 176 5.7 GIBBS FREE ENERGY CHANGES IN LABORATORY CONDITIONS......Page 182 5.8 POST-GIBBSIAN DEVELOPMENTS......Page 192 5.8.1 The Fugacity Concept......Page 193 5.8.2 The "Third Law" of Thermodynamics: A Critical Assessment......Page 195 6.1 CHEMICAL POTENTIAL IN MULTICOMPONENT SYSTEMS......Page 207 6.2 PARTIAL MOLAR QUANTITIES......Page 209 6.3 THE GIBBS–DUHEM EQUATION......Page 213 6.4 PHYSICAL NATURE OF CHEMICAL POTENTIAL IN IDEAL AND REAL GAS MIXTURES......Page 216 CHAPTER 7 Thermodynamics of Phase Equilibria......Page 221 7.1 THE GIBBS PHASE RULE......Page 223 7.2 SINGLE-COMPONENT SYSTEMS......Page 228 7.2.1 The Phase Diagram of Water......Page 229 7.2.2 Clapeyron and Clausius–Clapeyron Equations for Phase Boundaries......Page 231 7.2.3 Illustrative Phase Diagrams for Pure Substances......Page 236 7.3 BINARY FLUID SYSTEMS......Page 245 7.3.1 Vapor-Pressure (P-x) Diagrams: Raoult and Henry Limits......Page 249 7.3.2 The Lever Rule......Page 253 7.3.3 Positive and Negative Deviations......Page 255 7.3.4 Boiling-Point Diagrams: Theory of Distillation......Page 259 7.3.5 Immiscibility and Consolute Behavior......Page 262 7.3.6 Colligative Properties and Van’t Hoff Osmotic Equation......Page 265 7.3.7 Activity and Activity Coefficients......Page 272 7.4 BINARY SOLID–LIQUID EQUILIBRIA......Page 275 7.4.1 Eutectic Behavior......Page 276 7.4.2 Congruent Melting......Page 277 7.4.4 Alloys and Partial Miscibility......Page 278 7.4.5 Phase Boundaries and Gibbs Free Energy of Mixing......Page 279 7.5 TERNARY AND HIGHER SYSTEMS......Page 285 8.1 ANALYTICAL FORMULATION OF CHEMICAL REACTIONS IN TERMS OF THE ADVANCEMENT COORDINATE......Page 293 8.2 CRITERION OF CHEMICAL EQUILIBRIUM: THE EQUILIBRIUM CONSTANT......Page 294 ࠀ⸀アパート 䜀䔀一䔀刀䄀䰀 䘀刀䔀䔀 䔀一䔀刀䜀夀 䌀䠀䄀一䜀䔀匀㨀 䐀䔀 䐀伀一䐀䔀删ᤀ匀 䄀䘀䘀䤀一䤀吀......Page 297 8.4 STANDARD FREE ENERGY OF FORMATION......Page 298 ࠀ⸀㔀⸀㄀ 吀攀洀瀀攀爀愀琀甀爀攀 䐀攀瀀攀渀搀攀渀挀攀㨀 嘀愀渠ᤀ琀 䠀漀昀昀 䔀焀甀愀琀椀漀......Page 300 8.5.2 Pressure Dependence......Page 301 ࠀ⸀㘀 䰀䔀 䌀䠀䄀吀䔀䰀䤀䔀删ᤀ匀 倀刀䤀一䌀䤀倀䰀......Page 302 8.7 THERMODYNAMICS OF ELECTROCHEMICAL CELLS......Page 304 8.8 ION ACTIVITIES IN ELECTROLYTE SOLUTIONS......Page 308 ࠀ⸉ CONCLUDING SYNOPSIS OF GIBBS’ THEORY......Page 317 PART III METRIC GEOMETRY OF EQUILIBRIUM THERMODYNAMICS......Page 323 CHAPTER 9 Introduction to Vector Geometry and Metric Spaces......Page 325 9.1 VECTOR AND MATRIX ALGEBRA......Page 327 9.2 DIRAC NOTATION......Page 335 9.3 METRIC SPACES......Page 340 10.1 THE SPACE OF THERMODYNAMIC RESPONSE VECTORS......Page 343 10.2 THE METRIC OF THERMODYNAMIC RESPONSE SPACE......Page 345 10.3 LINEAR DEPENDENCE, DIMENSIONALITY, AND GIBBS–DUHEM EQUATIONS......Page 349 11.1 THERMODYNAMIC VECTORS AND GEOMETRY......Page 357 11.2 CONJUGATE VARIABLES AND CONJUGATE VECTORS......Page 360 11.3 METRIC OF A HOMOGENEOUS FLUID......Page 365 11.4 GENERAL TRANSFORMATION THEORY IN THERMODYNAMIC METRIC SPACE......Page 369 11.5 SATURATION PROPERTIES ALONG THE VAPOR-PRESSURE CURVE......Page 372 11.6 SELF-CONJUGATE AND NORMAL RESPONSE MODES......Page 375 11.7 GEOMETRICAL CHARACTERIZATION OF COMMON FLUIDS......Page 378 11.8 STABILITY CONDITIONS AND THE "THIRD LAW" FOR HOMOGENEOUS PHASES......Page 388 11.9 THE CRITICAL INSTABILITY LIMIT......Page 391 11.10 CRITICAL DIVERGENCE AND EXPONENTS......Page 396 11.11 PHASE HETEROGENEITY AND CRITICALITY......Page 398 CHAPTER 12 Geometrical Evaluation of Thermodynamic Derivatives......Page 405 12.1 THERMODYNAMIC VECTORS AND DERIVATIVES......Page 406 12.2 GENERAL SOLUTION FOR TWO DEGREES OF FREEDOM AND RELATIONSHIP TO JACOBIAN METHODS......Page 413 12.3 GENERAL PARTIAL DERIVATIVES IN HIGHERDIMENSIONAL SYSTEMS......Page 417 12.4 PHASE-BOUNDARY DERIVATIVES IN MULTICOMPONENT SYSTEMS......Page 420 12.5 STATIONARY POINTS OF PHASE DIAGRAMS: GIBBS–KONOWALOW LAWS......Page 426 12.6 HIGHER-ORDER DERIVATIVES AND STATE CHANGES......Page 429 CHAPTER 13 Further Aspects of Thermodynamic Geometry......Page 433 13.1 REVERSIBLE CHANGES OF STATE: RIEMANNIAN GEOMETRY......Page 436 13.2 NEAR-EQUILIBRIUM IRREVERSIBLE THERMODYNAMICS: DIFFUSIONAL GEOMETRY......Page 441 13.3 QUANTUM STATISTICAL THERMODYNAMIC ORIGINS OF CHEMICAL AND PHASE THERMODYNAMICS......Page 451 13.3.1 Nonequilibrium Displacement Variables of Mayer and Co-workers......Page 454 13.3.2 Quantum Statistical Thermodynamics and the Statistical Origins of Metric Geometry......Page 457 13.3.3 Evaluation of Molecular Partition Functions for Reactive Mixtures......Page 464 13.3.4 Quantum Cluster Equilibrium Theory of Phase Thermodynamics......Page 467 APPENDIX: Units and Conversion Factors......Page 477 AUTHOR INDEX......Page 481 SUBJECT INDEX......Page 485 Back Page......Page 503 "Because it is grounded in math, chemical thermodynamics is often perceived as a difficult subject and many students are never fully comfortable with it. The first authoritative textbook presentation of equilibrium chemical and phase thermodynamics in a reformulated geometrical framework, Chemical and Phase Thermodynamics shows how this famously difficult subject can be accurately expressed with only elementary high-school geometry concepts. Featuring numerous suggestions for research-level extensions, this simplified alternative to standard calculus-based thermodynamics expositions is perfect for undergraduate and beginning graduate students as well as researchers." --Book Jacket Annotation Because it is grounded in math, chemical thermodynamics is often perceived as a difficult subject and many students are never fully comfortable with it. The first authoritative textbook presentation of equilibrium chemical and phase thermodynamics in a reformulated geometrical framework, Chemical and Phase Thermodynamics shows how this famously difficult subject can be accurately expressed with only elementary high-school geometry concepts. Featuring numerous suggestions for research-level extensions, this simplified alternative to standard calculus-based thermodynamics expositions is perfect for undergraduate and beginning graduate students as well as researchers