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Overview
In this clear and concise introduction to thermodynamics and statistical mechanics the reader, who will have some previous exposure to thermodynamics, will be guided through each of the two disciplines separately initially to provide an indepth understanding of the area and thereafter the connection between the two is presented and discussed.
In addition, mathematical techniques are introduced at appropriate times, highlighting such use as: exact and inexact differentials, partial derivatives, Caratheodory's theorem, Legendre transformation, and combinatory analysis.
* Emphasis is placed equally on fundamentals and applications
* Several problems are included
Editorial Reviews
From the Publisher
"…a thorough treatment of thermodynamics at a level somewhat higher level than that in a typical undergraduate physical chemistry work." (CHOICE, February 2005)Product Details
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Meet the Author
BRUNO LINDER is Professor Emeritus of Chemistry at Florida State University. Founder of the Southeastern Theoretical Chemistry Association, he was formerly a John Simon Guggenheim Fellow at the Theoretical Physics Institute of the University of Amsterdam.
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Table of Contents
PREFACE.
1 INTRODUCTORY REMARKS.
1.1 Scope and Objectives.
1.2 Level of Course.
1.3 Course Outline.
1.4 Books.
PART I: THERMODYNAMICS.
2 BASIC CONCEPTS AND DEFINITIONS.
2.1 Systems and Surroundings.
2.2 State Variables and Thermodynamic Properties.
2.3 Intensive and Extensive Variables.
2.4 Homogeneous and Heterogeneous Systems, Phases.
2.5 Work.
2.6 Reversible and QuasiStatic Processes.
2.6.1 QuasiStatic Process.
2.6.2 Reversible Process.
2.7 Adiabatic and Diathermal Walls.
2.8 Thermal Contact and Thermal Equilibrium.
3 THE LAWS OF THERMODYNAMICS I.
3.1 The Zeroth Law—Temperature.
3.2 The First Law—Traditional Approach.
3.3 Mathematical Interlude I: Exact and Inexact Differentials.
3.4 The First Law—Axiomatic Approach.
3.5 Some Applications of the First Law.
3.5.1 Heat Capacity.
3.5.2 Heat and Internal Energy.
3.5.3 Heat and Enthalpy.
3.6 Mathematical Interlude II: Partial Derivatives.
3.6.1 Relations Between Partials of Dependent Variables.
3.6.2 Relations Between Partials with Different Subscripts.
3.7 Other Applications of the First Law.
3.7.1 C_{P} — C_{V}.
3.7.2 Isothermal Change, Ideal Gas.
3.7.3 Adiabatic Change, Ideal Gas.
3.7.4 The Joule and the JouleThomson Coefficients.
4 THE LAWS OF THERMODYNAMICS II.
4.1 The Second Law—Traditional Approach.
4.2 Engine Efficiency: Absolute Temperature.
4.2.1 Ideal Gas.
4.2.2 Coupled Cycles.
4.3 Generalization: Arbitrary Cycle.
4.4 The Clausius Inequality.
4.5 The Second Law—Axiomatic Approach (Caratheòodory).
4.6 Mathematical Interlude III: Pfaffian Differential Forms.
4.7 Pfaffian Expressions in Two Variables.
4.8 Pfaffian Expressions in More Than Two Dimensions.
4.9 Caratheòodory’s Theorem.
4.10 Entropy—Axiomatic Approach.
4.11 Entropy Changes for Nonisolated Systems.
4.12 Summary.
4.13 Some Applications of the Second Law.
4.13.1 Reversible Processes (PV Work Only).
4.13.2 Irreversible Processes.
5 USEFUL FUNCTIONS: THE FREE ENERGY FUNCTIONS.
5.1 Mathematical Interlude IV: Legendre Transformations.
5.1.1 Application of the Legendre Transformation.
5.2 Maxwell Relations.
5.3 The GibbsHelmholtz Equations.
5.4 Relation of ΔA and ΔG to Work: Criteria for Spontaneity.
5.4.1 Expansion and Other Types of Work.
5.4.2 Comments.
5.5 Generalization to Open Systems and Systems of Variable Composition.
5.5.1 Single Component System.
5.5.2 Multicomponent Systems.
5.6 The Chemical Potential.
5.7 Mathematical Interlude V: Euler’s Theorem.
5.8 Thermodynamic Potentials.
6 THE THIRD LAW OF THERMODYNAMICS.
6.1 Statements of the Third Law.
6.2 Additional Comments and Conclusions.
7 GENERAL CONDITIONS FOR EQUILIBRIUM AND STABILITY.
7.1 Virtual Variations.
7.2 Thermodynamic Potentials—Inequalities.
7.3 Equilibrium Condition From Energy.
7.3.1 Boundary Fully Heat Conducting, Deformable, Permeable (Normal System).
7.3.2 Special Cases: Boundary SemiHeat Conducting, SemiDeformable, or SemiPermeable.
7.4 Equilibrium Conditions From Other Potentials.
7.5 General Conditions for Stability.
7.6 Stability Conditions From E.
7.7 Stability Conditions From Cross Terms.
7.8 Stability Conditions From Other Potentials.
7.9 Derivatives of Thermodynamic Potentials With Respect to Intensive Variables.
8 APPLICATION OF THERMODYNAMICS TO GASES, LIQUIDS, AND SOLIDS.
8.1 Gases.
8.2 Enthalpy, Entropy, Chemical Potential, Fugacity.
8.2.1 Enthalpy.
8.2.2 Entropy.
8.2.3 Chemical Potential.
8.2.4 Fugacity.
8.3 Standard States of Gases.
8.4 Mixtures of Gases.
8.4.1 Partial Fugacity.
8.4.2 Free Energy, Entropy, Enthalpy, and Volume of Mixing of Gases.
8.5 Thermodynamics of Condensed Systems.
8.5.1 The Chemical Potential.
8.5.2 Entropy.
8.5.3 Enthalpy.
9 PHASE AND CHEMICAL EQUILIBRIA.
9.1 The Phase Rule.
9.2 The Clapeyron Equation.
9.3 The ClausiusClapeyron Equation.
9.4 The Generalized Clapeyron Equation.
9.5 Chemical Equilibrium.
9.6 The Equilibrium Constant.
10 SOLUTIONS—NONELECTROLYTES.
10.1 Activities and Standard State Conventions.
10.1.1 Gases.
10.1.2 Pure Liquids and Solids.
10.1.3 Mixtures.
10.1.3.1 Liquid–Liquid Solutions—Convention I (Con I).
10.1.3.2 Solid–Liquid Solutions—Convention II (Con II).
10.2 Ideal and Ideally Dilute Solutions; Raoult’s and Henry’s Laws.
10.2.1 Ideal Solutions.
10.2.2 Ideally Dilute Solutions.
10.3 Thermodynamic Functions of Mixing.
10.3.1 For Ideal Solutions.
10.3.2 For Nonideal Solutions.
10.4 Colligative Properties.
10.4.1 Lowering of Solvent Vapor Pressure.
10.4.2 Freezing Point Depression.
10.4.3 Boiling Point Elevation.
10.4.4 Osmotic Pressure.
11 PROCESSES INVOLVING WORK OTHER THAN PRESSUREVOLUME WORK.
11.1 PV Work and One Other Type of Work.
11.2 PV, σA, and fL Work.
12 PHASE TRANSITIONS AND CRITICAL PHENOMENA.
12.1 Stable, Metastable, and Unstable Isotherms.
12.2 The Critical Region.
PART II: INTRODUCTORY STATISTICAL MECHANICS.
13 PRINCIPLES OF STATISTICAL MECHANICS.
13.1 Introduction.
13.2 Preliminary Discussion—Simple Problem.
13.3 Time and Ensemble Averages.
13.4 Number of Microstates, Ω_{D}, Distributions D_{I}.
13.5 Mathematical Interlude VI: Combinatory Analysis.
13.6 Fundamental Problem in Statistical Mechanics.
13.7 MaxwellBoltzmann, FermiDirac, BoseEinstein Statistics ‘‘Corrected’’ MaxwellBoltzmann Statistics.
13.7.1 MaxwellBoltzmann Statistics.
13.7.2 FermiDirac Statistics.
13.7.3 BoseEinstein Statistics
13.7.4 ‘‘Corrected’’ MaxwellBoltzmann Statistics.
13.8 Systems of Distinguishable (Localized) and Indistinguishable (Nonlocalized) Particles.
13.9 Maximizing Ω_{D}
13.10 Probability of a Quantum State: The Partition Function.
13.10.1 MaxwellBoltzmann Statistics.
13.10.2 Corrected MaxwellBoltzmann Statistics.
14 THERMODYNAMIC CONNECTION.
14.1 Energy, Heat, and Work.
14.2 Entropy.
14.2.1 Entropy of Nonlocalized Systems (Gases).
14.2.2 Entropy of Localized Systems (Crystalline Solids).
14.3 Identification of β with 1/kT.
14.4 Pressure.
14.5 The Functions E, H, S, A, G, and μ.
15 MOLECULAR PARTITION FUNCTION.
15.1 Translational Partition Function.
15.2 Vibrational Partition Function: Diatomics.
15.3 Rotational Partition Function: Diatomics.
15.4 Electronic Partition Function.
15.5 Nuclear Spin States.
15.6 The ‘‘Zero’’ of Energy.
16 STATISTICAL MECHANICAL APPLICATIONS.
16.1 Population Ratios.
16.2 Thermodynamic Functions of Gases.
16.3 Equilibrium Constants.
16.4 Systems of Localized Particles: The Einstein Solid.
16.4.1 Energy.
16.4.2 Heat Capacity.
16.4.3 Entropy.
16.5 Summary.
ANNOTATED BIBLIOGRAPHY.
APPENDIX I: HOMEWORK PROBLEM SETS.
Problem Set I.
Problem Set II.
Problem Set III.
Problem Set IV.
Problem Set V.
Problem Set VI.
Problem Set VII.
Problem Set VIII.
Problem Set IX.
Problem Set X.
APPENDIX II: SOLUTIONS TO PROBLEMS.
Solution to Set I.
Solution to Set II.
Solution to Set III.
Solution to Set IV.
Solution to Set V.
Solution to Set VI.
Solution to Set VII.
Solution to Set VIII.
Solution to Set IX.
Solution to Set X.
INDEX.
First Chapter
Thermodynamics and Introductory Statistical Mechanics
By Bruno Linder
John Wiley & Sons
Copyright © 2004 John Wiley & Sons, Inc.All right reserved.
ISBN: 0471474592
Chapter One
INTRODUCTORY REMARKSThermodynamics, as developed in this course, deals with the macroscopic properties of matter or, more precisely, with processes on a macroscopic level. Mechanics (especially quantum mechanics) is concerned with molecular behavior. In principle, and in some limited cases, the molecular properties can be calculated directly from quantum mechanics. In the majority of cases, however, such properties are obtained from experimental studies such as spectral behavior or other devices, but the interpretation is based on quantum mechanics. Statistical mechanics is the branch of science that interconnects these seemingly unrelated disciplines: statistical mechanics interprets and, as far as possible, predicts the macroscopic properties in terms of the microscopic constituents.
For the purposes of the course presented in this book, thermodynamics and statistical mechanics are developed as separate disciplines. Only after the introduction of the fundamentals of statistical mechanics will the connection be made between statistical mechanics and thermodynamics. As noted, the laws of (macroscopic) thermodynamics deal with processes not structures. Therefore, no theory of matter is contained in theselaws. Traditional thermodynamics is based on common everyday experiences. For example, if two objects are brought in contact with each other, and one feels hotter than the other, the hotter object will cool while the colder one will heat up. Because thermodynamics is based on the common experience of macroscopic observations it has a generality unequaled in science. "Classical Thermodynamics," Einstein remarked, "... is the only physical theory of universal content ... which ... will never be overthrown" (Schilpp, 1949).
1.1 SCOPE AND OBJECTIVES
Class makeup varies greatly. Some students take this course as part of oneyear course, in preparation for a comprehensive or preliminary exam, required for a Master's or Ph.D. degree. Others sign up because they heard it was a "snap" course. Still others take it because they think, or their major professor thinks, that it may help them in their research. A course designed to satisfy all students' aspirations is difficult, if not impossible. A suitable compromise is one, which provides a reasonable balance between fundamentals and applications, which is the aim of this book.
1.2 LEVEL OF COURSE
Most students are likely to have had previous exposure to thermodynamics in some undergraduate course, such as physical chemistry, physics, or engineering. The present course is intended to be more advanced from the standpoints of both principles and applications. The emphasis is on the logical structure and generality of the subject. All topics of interest cannot possibly be covered in a semester course; therefore, topics that are likely to have been adequately treated in undergraduate courses are skipped.
1.3 COURSE OUTLINE
The idea is to proceed from the general to the particular. The following outline suggests itself.
Part I: Thermodynamics
A. Fundamentals
1. Basic concepts and definitions
2. The laws of thermodynamics
2.1 Traditional approach 2.2 Axiomatic approach
3. General conditions for equilibrium and stability
B. Applications
1. Thermodynamics of (Real) gases, condensed systems
2. Chemical equilibrium
2.1 Homogeneous and heterogeneous systems 2.2 Chemical reactions
3. Phase transitions and critical phenomena
4. Thermodynamics of one and twodimensional systems
4.1 Film enlarging 4.2 Rubber stretching
Part II: Introductory Statistical Mechanics
A. Fundamentals
1. Preliminary discussion 2. MaxwellBoltzmann, Corrected MaxwellBoltzmann Statistics
3. Partition Functions
4. Thermodynamic connection
B. Applications 1. Ideal gases
2. Ideal solids 3. Equilibrium constant
4. The bases of chemical thermodynamics
In addition, mathematical techniques are introduced at appropriate times, highlighting such use as:
1) Exact and inexact differentials (Section 3.3)
2) Partial Derivatives (Section 3.6)
3) Pfaffian Differential Forms (Section 4.6)
4) Legendre Transformation (Section 5.1)
5) Euler's Theorem (Section 5.7)
6) Combinatory Analysis (Section 13.5)
1.4 BOOKS
Because of the universality of the subject, books on Thermodynamics run into the thousands. Not all are textbooks, and not all are aimed at a particular discipline, such as chemistry, physics, or engineering. Most elementary chemical texts rely heavily on applications but treat the fundamentals lightly. Real systems (real gases, condensed systems, etc) are often not treated in any detail. Some books are strong on fundamentals but ignore applications. Other books are authoritative but highly opinionated, pressing for a particular point of view.
Two chemical thermodynamics books, which discuss the fundamentals in depth, are listed below.
1. J. de Heer, Phenomenological Thermodynamics, PrenticeHall, 1986.
2. J. G. Kirkwood and I. Oppenheim, Chemical Thermodynamics, McGrawHill, 1961.
Other books that may provide additional insight into various topics are listed in the Annotated Bibliography on page....
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