Contents. 1 Introduction and guide for this text 1. 2 Equilibrium and entropy 6. 3 Energy and how the microscopic world works 21

Transcription

1 Preface Reference tables Table A Counting and combinatorics formulae Table B Useful integrals, expansions, and approximations Table C Extensive thermodynamic potentials Table D Intensive per-particle thermodynamic potentials for single-component systems Table E Thermodynamic calculus manipulations Table F Measurable quantities Table G Common single-component statistical-mechanical ensembles Table H Fundamental physical constants page xv i i xix xx xxi xxii 1 Introduction and guide for this text 1 2 Equilibrium and entropy What is equilibrium? Classical thermodynamics Statistical mechanics Comparison of classical thermodynamics and statistical mechanics Combinatorial approaches to counting 15 Problems 18 3 Energy and how the microscopic world works Quantum theory The classical picture Classical microstates illustrated with the ideal gas Ranges of microscopic interactions and scaling with system size From microscopic to macroscopic Simple and lattice molecular models A simple and widely relevant example: the two-state system 38 Problems 41 4 Entropy and how the macroscopic world works Microstate probabilities The principle of equal a priori probabilities Ensemble averages and time averages in isolated systems Thermal equilibrium upon energy exchange General forms for equilibrium and the principle of maximum entropy The second law and internal constraints Equivalence with the energy-minimum principle 70 in this web service

2 x 4.8 Ensemble averages and Liouville s theorem in classical systems 72 Problems 75 5 The fundamental equation Equilibrium and derivatives of the entropy Differential and integrated versions of the fundamental equations Intensive forms and state functions 85 Problems 91 6 The first law and reversibility The first law for processes in closed systems The physical interpretation of work A classic example involving work and heat Special processes and relationships to the fundamental equation Baths as idealized environments Types of processes and implications from the second law Heat engines Thermodynamics of open, steady-flow systems 107 Problems Legendre transforms and other potentials New thermodynamic potentials from baths Constant-temperature coupling to an energy bath Complete thermodynamic information and natural variables Legendre transforms: mathematical convention Legendre transforms: thermodynamic convention The Gibbs free energy Physical rationale for Legendre transforms Extremum principles with internal constraints The enthalpy and other potentials Integrated and derivative relations Multicomponent and intensive versions Summary and look ahead 142 Problems Maxwell relations and measurable properties Maxwell relations Measurable quantities General considerations for calculus manipulations 154 Problems Gases Microstates in monatomic ideal gases Thermodynamic properties of ideal gases 165 in this web service

3 xi 9.3 Ideal gas mixtures Nonideal or imperfect gases Nonideal gas mixtures 171 Problems Phase equilibrium Conditions for phase equilibrium Implications for phase diagrams Other thermodynamic behaviors at a phase transition Types of phase equilibrium Microscopic view of phase equilibrium Order parameters and general features of phase equilibrium 194 Problems Stability Metastability Common tangent line perspective on phase equilibrium Limits of metastability Generalized stability criteria 209 Problems Solutions: fundamentals Ideal solutions Ideal vapor liquid equilibrium and Raoult s law Boiling-point elevation Freezing-point depression Osmotic pressure Binary mixing with interactions Nonideal solutions in general The Gibbs Duhem relation Partial molar quantities 233 Problems Solutions: advanced and special cases Phenomenology of multicomponent vapor liquid equilibrium Models of multicomponent vapor liquid equilibrium Bubble- and dew-point calculations at constant pressure Flash calculations at constant pressure and temperature Relative volatility formulation Nonideal mixtures Constraints along mixture vapor liquid phase boundaries Phase equilibrium in polymer solutions Strong electrolyte solutions 266 Problems 274 in this web service

4 xii 14 Solids General properties of solids Solid liquid equilibrium in binary mixtures Solid liquid equilibrium in multicomponent solutions A microscopic view of perfect crystals The Einstein model of perfect crystals The Debye model of perfect crystals 296 Problems The third law Absolute entropies and absolute zero Finite entropies and heat capacities at absolute zero Entropy differences at absolute zero Attainability of absolute zero 312 Problems The canonical partition function A review of basic statistical-mechanical concepts Microscopic equilibrium in isolated systems Microscopic equilibrium at constant temperature Microstates and degrees of freedom The canonical partition function for independent molecules 332 Problems Fluctuations Distributions in the canonical ensemble The canonical distribution of energies Magnitude of energy fluctuations 350 Problems Statistical mechanics of classical systems The classical canonical partition function Microstate probabilities for continuous degrees of freedom The Maxwell Boltzmann distribution The pressure in the canonical ensemble The classical microcanonical partition function 375 Problems Other ensembles The isothermal isobaric ensemble The grand canonical ensemble Generalities and the Gibbs entropy formula 396 Problems 397 in this web service

5 xiii 20 Reaction equilibrium A review of basic reaction concepts Reaction equilibrium at the macroscopic level Reactions involving ideal gases Reactions involving ideal solutions Temperature and pressure dependence of K eq Reaction equilibrium at the microscopic level Fluctuations 414 Problems Reaction coordinates and rates Kinetics from statistical thermodynamics Macroscopic considerations for reaction rates Microscopic origins of rate coefficients General considerations for rates of rare-event molecular processes 438 Problems Molecular simulation methods Basic elements of classical simulation models Molecular-dynamics simulation methods Computing properties Simulations of bulk phases Monte Carlo simulation methods 459 Problems 464 Index 470 in this web service