Molecular Thermodynamics Transport Phenomena .Molecular Thermodynamics and Transport Phenomena ComplexitiesofScalesinSpaceandTime

  • View
    220

  • Download
    1

Embed Size (px)

Text of Molecular Thermodynamics Transport Phenomena .Molecular Thermodynamics and Transport Phenomena...

  • MolecularThermodynamics

    andTransport

    Phenomena

    Complexities of Scales in Space and Time

    http://dx.doi.org/10.1036/0071445617

  • McGraw-Hill Nanoscience and Technology Series

    KENNETH GILLEO MEMS/MOEM Packaging: Concepts, Design,Materials, and Processes

    DARREN L. HITT Microfluidics: Experimental Techniques andApplications

    JOSEPH H. KOO Polymer Nanocomposites: Processing,Characterization and Applications

    NICOLAE O. LOBONTIU Mechanical Design of Microresonators:Modeling and Applications

    OMAR MANASREH Semiconductor Heterojunctions andNanostructures

    ROBERTO PAIELLA Intersubband Transitions In Quantum StructuresMICHAEL H. PETERS Molecular Thermodynamics and Transport

    PhenomenaJENS W. TOMM AND JUAN JIMENEZ Quantum-Well High-Power

    Laser Arrays

  • MolecularThermodynamics

    andTransport

    PhenomenaComplexities of Scales in Space and Time

    Michael H. Peters, Ph.D.Virginia Commonwealth University

    McGraw-HillNew York Chicago San Francisco Lisbon London

    Madrid Mexico City Milan New Delhi San JuanSeoul Singapore Sydney Toronto

    http://dx.doi.org/10.1036/0071445617

  • Copyright 2005 by The McGraw-Hill Companies, Inc. All rights reserved. Manufactured in theUnited States of America. Except as permitted under the United States Copyright Act of 1976, no partof this publication may be reproduced or distributed in any form or by any means, or stored in a data-base or retrieval system, without the prior written permission of the publisher.

    0-07-158890-6

    The material in this eBook also appears in the print version of this title: 0-07-144561-7.

    All trademarks are trademarks of their respective owners. Rather than put a trademark symbol afterevery occurrence of a trademarked name, we use names in an editorial fashion only, and to the benefit of the trademark owner, with no intention of infringement of the trademark. Where such designations appear in this book, they have been printed with initial caps.

    McGraw-Hill eBooks are available at special quantity discounts to use as premiums and sales promotions, or for use in corporate training programs. For more information, please contact GeorgeHoare, Special Sales, at george_hoare@mcgraw-hill.com or (212) 904-4069.

    TERMS OF USE

    This is a copyrighted work and The McGraw-Hill Companies, Inc. (McGraw-Hill) and its licensorsreserve all rights in and to the work. Use of this work is subject to these terms. Except as permittedunder the Copyright Act of 1976 and the right to store and retrieve one copy of the work, you may notdecompile, disassemble, reverse engineer, reproduce, modify, create derivative works based upon,transmit, distribute, disseminate, sell, publish or sublicense the work or any part of it withoutMcGraw-Hills prior consent. You may use the work for your own noncommercial and personal use;any other use of the work is strictly prohibited. Your right to use the work may be terminated if youfail to comply with these terms.

    THE WORK IS PROVIDED AS IS. McGRAW-HILL AND ITS LICENSORS MAKE NO GUAR-ANTEES OR WARRANTIES AS TO THE ACCURACY, ADEQUACY OR COMPLETENESS OFOR RESULTS TO BE OBTAINED FROM USING THE WORK, INCLUDING ANY INFORMA-TION THAT CAN BE ACCESSED THROUGH THE WORK VIA HYPERLINK OR OTHERWISE, AND EXPRESSLY DISCLAIM ANY WARRANTY, EXPRESS OR IMPLIED,INCLUDING BUT NOT LIMITED TO IMPLIED WARRANTIES OF MERCHANTABILITY ORFITNESS FOR A PARTICULAR PURPOSE. McGraw-Hill and its licensors do not warrant or guarantee that the functions contained in the work will meet your requirements or that its operationwill be uninterrupted or error free. Neither McGraw-Hill nor its licensors shall be liable to you or anyone else for any inaccuracy, error or omission, regardless of cause, in the work or for any damagesresulting therefrom. McGraw-Hill has no responsibility for the content of any information accessedthrough the work. Under no circumstances shall McGraw-Hill and/or its licensors be liable for anyindirect, incidental, special, punitive, consequential or similar damages that result from the use of orinability to use the work, even if any of them has been advised of the possibility of such damages.This limitation of liability shall apply to any claim or cause whatsoever whether such claim or causearises in contract, tort or otherwise.

    DOI: 10.1036/0071445617

    http://dx.doi.org/10.1036/0071445617

  • In memory of Debbie and Harold

  • This page intentionally left blank

  • Contents

    Preface xiNotes on Notation xiii

    Chapter 1. Introduction to Statistical Mechanics and the ClassicalMechanics of Interacting Particles 1

    1.1 Introduction to Classical Statistical Mechanics and a Unificationof Equilibrium and Nonequilibrium Analysis 1

    1.2 Molecular Interactions in Gases, Liquids, and Solids and theNature of Intermolecular (Interatomic) Interaction Forces 41.2.1 Modeling Born repulsive and van der Waals forces 81.2.2 Models for electrostatic interactions 8

    1.3 Introduction to Classical Mechanics 181.3.1 Newtonian mechanics 19

    1.4 Lagrangian Mechanics 251.5 Hamiltons Equations of Motion 271.6 Summary 29

    Problems 30References 32Further Reading 32

    Chapter 2. Phase Space and the Liouville Equation 33

    2.1 Introduction: The Merger of Classical Mechanics andProbability Theory 33

    2.2 Derivation of the Liouville Equation 342.3 The Liouville Equation in Terms of Generalized Coordinates and

    Conjugate Momenta 402.4 Summary 48

    Problems 49References 51Further Reading 51

    vii

    For more information about this title, click here

    http://dx.doi.org/10.1036/0071445617

  • viii Contents

    Chapter 3. Reduced Density Functions and the ReducedLiouville Equation 53

    3.1 Overview: The Practical Importance of the ReducedLiouville Equation 53

    3.2 Reduced Density Functions 543.3 The Reduced Liouville Equation 573.4 The Boltzmann Transport Equation 613.5 Boltzmanns Entropy 663.6 Reduced Liouville Equation in Generalized Coordinates 703.7 Summary 73

    Problems 73References 76Further Reading 76

    Chapter 4. Equilibrium Solution to the Liouville Equation andthe Thermodynamic Properties of Matter 77

    4.1 Introduction to the Equilibrium Behavior of Matter 774.2 Solution to the Liouville Equation under Equilibrium Conditions 784.3 The Thermodynamic Functions U, P, and S 864.4 Determination of the Configurational Distribution Functions 894.5 Thermodynamic Functions for a Dilute Gas 93

    4.5.1 Hard-sphere interactions 954.5.2 Point centers of attraction or repulsion 96

    4.6 Configurational Integral Equation for Dense Gases and Liquids 984.7 Equilibrium Properties of Nonspherical Molecules 1024.8 Complex Equilibrium Systems: Multicomponent and Multiphase 1034.9 Chapter Summary and Note on the Lack of Proof of the Existence

    and Uniqueness of the Equilibrium Solution 104Problems 106References 109Further Reading 109

    Chapter 5. The General Equations of Change forNonequilibrium Systems 111

    5.1 Introduction: The Scope of Transport Phenomena 1115.2 Conservation Equation for Any Dynamical Variable 1125.3 Mass Conservation Equation (the Equation of Continuity) 1145.4 Momentum Conservation 1175.5 The Energy Balance Equation 1235.6 Entropy Conservation 1265.7 Local Equilibrium Flows 131

    Problems 136References 137Further Reading 137

  • Contents ix

    Chapter 6. Closure of the Transport Equations 139

    6.1 Introduction: Complexities of Scales in Time and Space 1396.2 Scaling of the Reduced Liouville Equation 1406.3 Regular Perturbative Expansion of the Reduced Liouville Equation

    for Dense Gases and Liquids 1476.4 Perturbation Expansion for Dilute Gases 1556.5 Chapman-Enskog Solution to the Boltzmann Transport Equation 1586.6 Property Flux Expressions for Gases 1616.7 Chapter Summary and the Closed Forms of the Transport Equations 165

    Problems 168References 168Further Reading 169

    Index 171

  • This page intentionally left blank

  • Preface

    This book is intended for upper-level undergraduates and first-yeargraduate students in science and engineering. It is basically an intro-duction to the molecular foundations of thermodynamics and transportphenomena presented in a unified manner. The mathematical and phys-ical science level sophistication are at the upper undergraduate level,and students who have been exposed to vector calculus, differentialequations, and calculus-based physics should be adequately preparedto handle the material presented. There is also sufficient advanced ma-terial in each chapter or topic for first-year graduate students in scienceor engineering.

    The basic foundations of both (equilibrium) thermodynamics andtransport phenomena lie in the descriptions and treatment of largecollections of interacting molecules and atoms. From this viewpoint,there are only minor differences in fundamentally describing the be-havior of systems at equilibrium versus nonequilibrium, and these dif-ferences are immersed in the mathematical identification of length andtime scales appropriate for any particular system. The importance ofunderstanding the complexities of length and time scales is ubiquitousthroughout science and engineering and is not unique to thermodynam-ics and transport phenomena. As such, this book will provide systematicand methodological examples of the analysis of length and time scalesand its implications for physical behavior.

    The book begins by providing the necessary background for themechanics of interacting particles in Chapter 1. Atomic and molecularinteraction forces are also presented in this introductory chapter.Chapter 2 develops the formal and general statistical representationof a collection of interacting particles through the derivation of theLi