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CHEMICAL THERMODYNAMICS. With Examples for Nonequilibrium Processes
Eu, Byung Chan
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Últimas novedades química general termodinámica
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Thermodynamics is an ever evolving subject. This book aims to introduce to advanced undergraduate students and graduate students the fundamental ideas and notions of the first and second laws of thermodynamics in a manner unavailable in the usual textbooks on the subject of thermodynamics. For example, it treats the notions of unavailable work, compensated and uncompensated heats, and dissipation, which make it possible to formulate the thermodynamic laws in more broadened forms than those in the conventional treatment of equilibrium thermodynamics. It thus strives to prepare students for more advanced subjects of irreversible processes, which are encountered in our everyday scientific activities. In addition, it also aims to provide them with functional and practical knowledge of equilibrium chemical thermodynamics of reversible processes in real fluids. It discusses temperature, work and heat, thermodynamic laws, equilibrium conditions and thermodynamic stability, thermodynamics of reversible processes in gases and liquids, in surfaces, chemical equilibria, reversible processes in electrolyte solutions and dielectrics in static electric and magnetic fields. A couple of examples for irreversible processes associated with fluid flows and chemical pattern formation and wave propagations are discussed as examples for applications of broader treatments of the thermodynamic laws in the realm of irreversible phenomena. Contents: Introduction Temperature, Work, and Heat The First Law of Thermodynamics The Second Law of Thermodynamics Equilibrium Conditions and Thermodynamic Stability The Third Law of Thermodynamics Thermodynamics of Mixtures and Open Systems Heterogeneous Equilibria Thermodynamics of Real Fluids Canonical Equation of State Thermodynamics of Real Gas Mixtures Chemical Equilibria Thermodynamics of Solutions Thermodynamics of Surfaces Electrolyte Solutions Debye–Hückel Theory of Strong Electrolyte Solutions Galvanic Cells and Electromotive Forces Thermodynamics of Electric and Magnetic Fields Thermodynamics of Nonequilibrium Processes Appendices Local Form of Energy Conservation Law Various Coefficients Used in Chapter 10 Thermodynamics is an ever evolving subject. This book aims to introduce to advanced undergraduate students and graduate students the fundamental ideas and notions of the first and second laws of thermodynamics in a manner unavailable in the usual textbooks on the subject of thermodynamics. For example, it treats the notions of unavailable work, compensated and uncompensated heats, and dissipation, which make it possible to formulate the thermodynamic laws in more broadened forms than those in the conventional treatment of equilibrium thermodynamics. It thus strives to prepare students for more advanced subjects of irreversible processes, which are encountered in our everyday scientific activities. In addition, it also aims to provide them with functional and practical knowledge of equilibrium chemical thermodynamics of reversible processes in real fluids. It discusses temperature, work and heat, thermodynamic laws, equilibrium conditions and thermodynamic stability, thermodynamics of reversible processes in gases and liquids, in surfaces, chemical equilibria, reversible processes in electrolyte solutions and dielectrics in static electric and magnetic fields. A couple of examples for irreversible processes associated with fluid flows and chemical pattern formation and wave propagations are discussed as examples for applications of broader treatments of the thermodynamic laws in the realm of irreversible phenomena. Contents: Introduction Temperature, Work, and Heat The First Law of Thermodynamics The Second Law of Thermodynamics Equilibrium Conditions and Thermodynamic Stability The Third Law of Thermodynamics Thermodynamics of Mixtures and Open Systems Heterogeneous Equilibria Thermodynamics of Real Fluids Canonical Equation of State Thermodynamics of Real Gas Mixtures Chemical Equilibria Thermodynamics of Solutions Thermodynamics of Surfaces Electrolyte Solutions Debye–Hückel Theory of Strong Electrolyte Solutions Galvanic Cells and Electromotive Forces Thermodynamics of Electric and Magnetic Fields Thermodynamics of Nonequilibrium Processes Appendices Local Form of Energy Conservation Law Various Coefficients Used in Chapter 10
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CHEMICAL THERMODYNAMICS - With Examples for Nonequilibrium Processes © World Scientific Publishing Co. Pte. Ltd. http://www.worldscibooks.com/chemistry/7619.html Contents Preface vii 1. Introduction 1 2. Temperature, Work, and Heat 9 2.1 Temperature . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.1 Centigrade (Celsius) Scale . . . . . . . . . . . . . 12 2.1.2 Fahrenheit Scale . . . . . . . . . . . . . . . . . . 14 2.1.3 Absolute Temperature Scale and Ideal Gas Thermometer . . . . . . . . . . . . . . . . . 14 2.2 Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.3 Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.4 Heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.5 Reversible Processes and Reversible Work . . . . . . . . 28 3. The First Law of Thermodynamics 31 3.1 Equivalence of Heat and Energy . . . . . . . . . . . . . . 31 3.2 The First Law of Thermodynamics . . . . . . . . . . . . 33 3.3 Enthalpy . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.3.1 Differential Forms for Enthalpy . . . . . . . . . . 37 3.3.2 The Difference in Isobaric and Isochoric Heat Capacities for Ideal Gases . . . . . . . . . . . . . 39 3.4 Work and Heat of Isothermal Reversible Expansion . . . 40 3.5 Work of Adiabatic Expansion . . . . . . . . . . . . . . . 40 3.6 Heat Capacity and Heat Change . . . . . . . . . . . . . 41 ix CHEMICAL THERMODYNAMICS - With Examples for Nonequilibrium Processes © World Scientific Publishing Co. Pte. Ltd. http://www.worldscibooks.com/chemistry/7619.html x Chemical Thermodynamics 3.7 Thermochemistry . . . . . . . . . . . . . . . . . . . . . . 44 3.7.1 Heat of Reaction . . . . . . . . . . . . . . . . . . 44 3.7.2 Standard States and Heat of Formation . . . . . 45 3.7.3 Hess’s Law . . . . . . . . . . . . . . . . . . . . . 46 3.7.4 Kirchhoff’s Equation . . . . . . . . . . . . . . . . 49 3.8 Mathematical Notes . . . . . . . . . . . . . . . . . . . . . 50 3.8.1 Exact Differentials . . . . . . . . . . . . . . . . . 51 3.8.2 Chain Relations . . . . . . . . . . . . . . . . . . 52 3.8.3 Jacobians . . . . . . . . . . . . . . . . . . . . . . 54 4. The Second Law of Thermodynamics 57 4.1 Carnot Cycle . . . . . . . . . . . . . . . . . . . . . . . . 60 4.2 Carnot’s Theorem . . . . . . . . . . . . . . . . . . . . . 65 4.3 Thermodynamic Temperature . . . . . . . . . . . . . . . 70 4.4 Entropy and Calortropy . . . . . . . . . . . . . . . . . . 72 4.4.1 Clausius Inequality . . . . . . . . . . . . . . . . . 72 4.4.2 Entropy . . . . . . . . . . . . . . . . . . . . . . . 74 4.4.3 Calortropy . . . . . . . . . . . . . . . . . . . . . 76 4.4.4 Inequalities of Entropy and Calortropy . . . . . . 79 4.5 Carnot’s Theorem and Real Gases . . . . . . . . . . . . 85 4.6 Examples of Other Cycles . . . . . . . . . . . . . . . . . 88 4.6.1 Rankine Cycle . . . . . . . . . . . . . . . . . . . 88 4.6.2 Otto Cycle . . . . . . . . . . . . . . . . . . . . . 88 4.6.3 Diesel Cycle . . . . . . . . . . . . . . . . . . . . . 89 4.7 Calculation of Entropy Change . . . . . . . . . . . . . . 90 4.7.1 Phase Transition and Entropy Change . . . . . . 90 4.7.2 Entropy Changes of an Ideal Gas . . . . . . . . . 91 4.8 Free Energies . . . . . . . . . . . . . . . . . . . . . . . . 93 4.8.1 Helmholtz Free Energy . . . . . . . . . . . . . . 93 4.8.2 Gibbs Free Energy . . . . . . . . . . . . . . . . . 93 4.9 Maxwell’s Relations . . . . . . . . . . . . . . . . . . . . 93 5. Equilibrium Conditions and Thermodynamic Stability 103 5.1 Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . 103 5.2 Equilibrium Conditions . . . . . . . . . . . . . . . . . . . 106 5.3 Stability of Equilibrium . . . . . . . . . . . . . . . . . . . 112 CHEMICAL THERMODYNAMICS - With Examples for Nonequilibrium Processes © World Scientific Publishing Co. Pte. Ltd. http://www.worldscibooks.com/chemistry/7619.html Contents xi 6. The Third Law of Thermodynamics 115 7. Thermodynamics of Mixtures and Open Systems 121 7.1 Chemical Potentials . . . . . . . . . . . . . . . . . . . . . 121 7.1.1 The Gibbs Theory . . . . . . . . . . . . . . . . . 121 7.1.2 Alternative Consideration . . . . . . . . . . . . . 123 7.1.3 Fundamental Relations for Open Systems . . . . 124 7.2 Partial Molar Properties . . . . . . . . . . . . . . . . . . 125 7.3 Measurement of Partial Molar Properties . . . . . . . . . 130 7.3.1 Method of Intercepts . . . . . . . . . . . . . . . . 131 7.3.2 Direct Method . . . . . . . . . . . . . . . . . . . 132 7.3.3 Method of Apparent Molar Property . . . . . . . 133 7.3.4 Density Dependence of Mi . . . . . . . . . . . . 133 8. Heterogeneous Equilibria 135 8.1 Equilibrium Conditions for a Multiphase System . . . . . 135 8.1.1 Mechanical Equilibrium . . . . . . . . . . . . . . 137 8.1.2 Thermal Equilibrium . . . . . . . . . . . . . . . . 139 8.1.3 Material Equilibrium . . . . . . . . . . . . . . . . 140 8.2 Gibbs Phase Rule . . . . . . . . . . . . . . . . . . . . . . 143 8.3 One-Component, Two-Phase Systems . . . . . . . . . . . 144 8.3.1 Vapor Pressure and Measurement of Äh . . . . . 147 8.3.2 Ramsay–Young Rule . . . . . . . . . . . . . . . . 148 8.4 Two-Component Systems . . . . . . . . . . . . . . . . . . 151 9. Thermodynamics of Real Fluids 159 9.1 Constitutive Equations . . . . . . . . . . . . . . . . . . . 159 9.1.1 Ideal Gas Equation of State . . . . . . . . . . . . 161 9.1.2 Caloric Equation of State . . . . . . . . . . . . . 161 9.1.3 Ratio of Specific Heats and Compressibility . . . 162 9.1.4 Sound Wave Velocity and Polytropic Ratio . . . 163 9.2 Virial Equation of State . . . . . . . . . . . . . . . . . . 166 9.3 van der Waals Equation of State . . . . . . . . . . . . . . 168 9.4 Law of Corresponding States . . . . . . . . . . . . . . . . 172 9.5 Thermodynamic Functions . . . . . . . . . . . . . . . . . 173 9.5.1 Reversible Work . . . . . . . . . . . . . . . . . . 174 9.5.2 Heat Change in Isothermal Expansion . . . . . . 175 CHEMICAL THERMODYNAMICS - With Examples for Nonequilibrium Processes © World Scientific Publishing Co. Pte. Ltd. http://www.worldscibooks.com/chemistry/7619.html xii Chemical Thermodynamics 9.5.3 Standard States . . . . . . . . . . . . . . . . . . 176 9.5.4 Enthalpy . . . . . . . . . . . . . . . . . . . . . . 177 9.5.5 Internal Energy . . . . . . . . . . . . . . . . . . . 181 9.5.6 Entropy . . . . . . . . . . . . . . . . . . . . . . . 184 9.5.6.1 Real Gases . . . . . . . . . . . . . . . . 185 9.5.6.2 Substances in Condensed Phase . . . . 187 9.5.7 Gibbs Free Energy . . . . . . . . . . . . . . . . . 188 9.6 Fugacity . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 9.7 Joule–Thomson Experiment . . . . . . . . . . . . . . . . 193 9.8 Liquefaction of Gases . . . . . . . . . . . . . . . . . . . . 198 9.9 Entropy Surface . . . . . . . . . . . . . . . . . . . . . . . 200 9.9.1 Ideal Gas . . . . . . . . . . . . . . . . . . . . . . 201 9.9.2 van der Waals Gas . . . . . . . . . . . . . . . . . 202 10. Canonical Equation of State 205 10.1 Canonical Equation of State . . . . . . . . . . . . . . . . 206 10.2 Reduced Variables . . . . . . . . . . . . . . . . . . . . . . 208 10.3 Reduced Canonical Equation of State . . . . . . . . . . . 210 10.4 Models for the GvdW Parameters . . . . . . . . . . . . . 211 10.4.1 Subcritical Regime . . . . . . . . . . . . . . . . . 211 10.4.2 Supercritical Regime . . . . . . . . . . . . . . . . 213 10.5 Reduced Chemical Potential . . . . . . . . . . . . . . . . 213 10.6 Specific Heat . . . . . . . . . . . . . . . . . . . . . . . . . 215 10.7 Virial and Joule–Thomson Coefficients . . . . . . . . . . 216 10.7.1 Virial Coefficients . . . . . . . . . . . . . . . . . 217 10.7.2 Joule–Thomson Coefficient . . . . . . . . . . . . 218 10.7.3 Asymptotic Behavior of the Second Virial Coefficient . . . . . . . . . . . . . . . . . . 219 10.8 Stability Conditions of Mechanical and Material Equilibria . . . . . . . . . . . . . . . . . . . . . 219 10.8.1 Classical Definition of Critical Point . . . . . . . 219 10.8.2 Extended Definition . . . . . . . . . . . . . . . . 220 10.9 Critical Properties of Fluids . . . . . . . . . . . . . . . . 222 10.9.1 Critical Point . . . . . . . . . . . . . . . . . . . . 222 10.9.2 Critical Isotherm for Pressure . . . . . . . . . . . 223 10.9.3 Spinodal Curve . . . . . . . . . . . . . . . . . . . 225 10.9.4 Excess Chemical Potential . . . . . . . . . . . . . 227 CHEMICAL THERMODYNAMICS - With Examples for Nonequilibrium Processes © World Scientific Publishing Co. Pte. Ltd. http://www.worldscibooks.com/chemistry/7619.html Contents xiii 10.9.5 Liquid–Vapor Coexistence Curve . . . . . . . . . 231 10.9.5.1 Equilibrium Conditions . . . . . . . . . 231 10.9.5.2 Coexistence Curve . . . . . . . . . . . . 232 10.9.6 Excess Heat Capacity . . . . . . . . . . . . . . . 235 10.9.7 Isothermal Compressibility . . . . . . . . . . . . 237 10.10 Quadratic Model . . . . . . . . . . . . . . . . . . . . . . 238 10.10.1 Subcritical Regime . . . . . . . . . . . . . . . . . 238 10.10.2 Supercritical Regime . . . . . . . . . . . . . . . . 240 10.10.3 Critical Point . . . . . . . . . . . . . . . . . . . . 241 10.10.4 Critical Isotherms . . . . . . . . . . . . . . . . . 242 10.10.5 Spinodal Curve . . . . . . . . . . . . . . . . . . . 242 10.11 Concluding Remarks . . . . . . . . . . . . . . . . . . . . 243 11. Thermodynamics of Real Gas Mixtures 247 11.1 Chemical Potentials for Mixtures . . . . . . . . . . . . . 247 11.2 Entropy of Mixing . . . . . . . . . . . . . . . . . . . . . . 253 11.3 Heat of Mixing . . . . . . . . . . . . . . . . . . . . . . . 256 11.4 Activity and Activity Coefficient . . . . . . . . . . . . . . 257 11.5 Canonical Equation of State for a Mixture . . . . . . . . 260 12. Chemical Equilibria 265 12.1 A Single Reaction . . . . . . . . . . . . . . . . . . . . . . 265 12.2 Coupled Chemical Reactions . . . . . . . . . . . . . . . 268 12.3 Chemical Reactions in a Multiphase System . . . . . . . 269 12.4 Equilibrium Constant . . . . . . . . . . . . . . . . . . . . 271 12.5 van’t Hoff Equation . . . . . . . . . . . . . . . . . . . . . 273 12.6 Equilibrium Constant for Real Gases . . . . . . . . . . . 276 13. Thermodynamics of Solutions 279 13.1 Chemical Potentials of Solutions . . . . . . . . . . . . . . 279 13.2 Ideal Solutions . . . . . . . . . . . . . . . . . . . . . . . . 283 13.3 Raoult’s Law . . . . . . . . . . . . . . . . . . . . . . . . . 286 13.4 Two-Component, Two-Phase Equilibrium Reconsidered . . . . . . . . . . . . . . . . . . . . . . . . . 289 13.5 Margules Expansions . . . . . . . . . . . . . . . . . . . . 293 13.6 Regular Solutions . . . . . . . . . . . . . . . . . . . . . . 295 13.7 Real Solutions . . . . . . . . . . . . . . . . . . . . . . . . 298 CHEMICAL THERMODYNAMICS - With Examples for Nonequilibrium Processes © World Scientific Publishing Co. Pte. Ltd. http://www.worldscibooks.com/chemistry/7619.html xiv Chemical Thermodynamics 13.8 Osmotic Coefficient of Bjerrum . . . . . . . . . . . . . . 303 13.9 Determination of Activity Coefficients . . . . . . . . . . 307 13.9.1 Vapor Fugacity . . . . . . . . . . . . . . . . . . . 308 13.9.2 Freezing Point Depression . . . . . . . . . . . . . 308 13.9.3 Boiling Point Elevation . . . . . . . . . . . . . . 313 13.9.4 Osmotic Pressure . . . . . . . . . . . . . . . . . . 317 13.9.5 Solubility . . . . . . . . . . . . . . . . . . . . . . 319 14. Thermodynamics of Surfaces 323 14.1 Dividing Surface . . . . . . . . . . . . . . . . . . . . . . . 324 14.2 Gibbs Relation for Interface . . . . . . . . . . . . . . . . 325 14.3 Nearly Planar Surface and Surface Tension . . . . . . . . 331 14.4 Gibbs–Duhem Relation for Interface . . . . . . . . . . . . 334 14.5 Location of the Dividing Surface and Surface Tension . . . . . . . . . . . . . . . . . . . . . . . 335 14.6 Gibbs Phase Rule Including Interface . . . . . . . . . . . 336 14.7 Thermodynamics of Interface . . . . . . . . . . . . . . . 337 14.7.1 Invariance of Derivatives to the Position of the Dividing Surface . . . . . . . . . . . . . . 337 14.7.2 Various Thermodynamic Relations for Interface . . . . . . . . . . . . . . . . . . . . . 339 14.7.3 Liquid–Vapor Equilibrium . . . . . . . . . . . . . 340 14.7.3.1 Density Dependence of ã . . . . . . . . 340 14.7.3.2 Temperature Dependence of ã . . . . . 342 15. Electrolyte Solutions 345 15.1 Mean Activity and Mean Activity Coefficient . . . . . . 346 15.2 Isopiestic Method . . . . . . . . . . . . . . . . . . . . . . 348 15.3 Activity Coefficient from Freezing Point Measurement . . . . . . . . . . . . . . . . . . . . . . . . 351 15.4 Activity Coefficient from Osmotic Pressure Measurement . . . . . . . . . . . . . . . . . . . . . . . . 352 16. Debye–H¨uckel Theory of Strong Electrolyte Solutions 355 16.1 Ionic Atmosphere . . . . . . . . . . . . . . . . . . . . . . 356 16.2 Mean Potential and the Excess Free Energy . . . . . . . 357 CHEMICAL THERMODYNAMICS - With Examples for Nonequilibrium Processes © World Scientific Publishing Co. Pte. Ltd. http://www.worldscibooks.com/chemistry/7619.html Contents xv 17. Galvanic Cells and Electromotive Forces 363 17.1 Reversible Galvanic Cells and Reversible Electrodes . . . 363 17.2 Electrochemical Potentials . . . . . . . . . . . . . . . . . 364 17.3 Galvanic Cells Without Liquid Junction . . . . . . . . . 366 17.3.1 Cell Diagrams and the Sign Convention . . . . . 367 17.4 Fuel Cells . . . . . . . . . . . . . . . . . . . . . . . . . . 371 17.5 Donnan Membrane Equilibrium . . . . . . . . . . . . . . 376 18. Thermodynamics of Electric and Magnetic Fields 379 18.1 Dielectrics in Electrostatic Field . . . . . . . . . . . . . . 379 18.2 Field Dependence of Thermodynamic Quantities . . . . . 384 18.2.1 Electrostriction . . . . . . . . . . . . . . . . . . . 384 18.2.2 Electrocaloric Effects . . . . . . . . . . . . . . . . 385 18.3 Static Magnetic Fields . . . . . . . . . . . . . . . . . . . 387 18.3.1 Magnetostriction . . . . . . . . . . . . . . . . . . 389 18.3.2 Magnetocaloric Effects . . . . . . . . . . . . . . . 389 19. Thermodynamics of Nonequilibrium Processes 393 19.1 Extended Gibbs Relation for Calortropy . . . . . . . . . 393 19.1.1 Differential Form for Calortropy . . . . . . . . . 395 19.1.2 Variables in the Tangent Manifold . . . . . . . . 398 19.1.2.1 Nonequilibrium Effect on Temperature . . . . . . . . . . . . . 399 19.1.2.2 Nonequilibrium Effect on Pressure . . . . . . . . . . . . . . . . . 400 19.1.2.3 Nonequilibrium Effect on Chemical Potentials . . . . . . . . . . . 400 19.1.2.4 Nonequilibrium Effect on Equilibrium Constants . . . . . . . . . 402 19.2 Flow of a Non-Newtonian Liquid . . . . . . . . . . . . . 403 19.2.1 Velocity Profile of Flow in a Rectangular Channel . . . . . . . . . . . . . . . . 404 19.2.1.1 The Case of px =0 . . . . . . . . . . . 406 19.2.1.2 The Case of px =0 . . . . . . . . . . . 407 19.2.2 Non-Newtonian Viscosity . . . . . . . . . . . . . 409 19.3 Chemical Oscillations and Pattern Formation . . . . . . 412 CHEMICAL THERMODYNAMICS - With Examples for Nonequilibrium Processes © World Scientific Publishing Co. Pte. Ltd. http://www.worldscibooks.com/chemistry/7619.html xvi Chemical Thermodynamics Appendix A Local Form of Energy Conservation Law 425 Appendix B Various Coefficients Used in Chapter 10 431 B.1 Coefficients of Ð(i)(xsk, t) . . . . . . . . . . . . . . . . . . 431 B.2 Coefficients Pij . . . . . . . . . . . . . . . . . . . . . . . 432 B.3 Coefficients Ð(i) j (t) . . . . . . . . . . . . . . . . . . . . . 433 B.4 Coefficients of the Spinodal Equations . . . . . . . . . . 436 Index 441 |
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