Statistical Thermodynamics for Pure and Applied Sciences: Statistical Thermodynamics

✍ Scribed by Frederick Richard Wayne McCourt

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 691
• Edition: 1st ed. 2021
• Category: Library

✦ Synopsis

This textbook concerns thermal properties of bulk matter and is aimed at advanced undergraduate or first-year graduate students in a range of programs in science or engineering. It provides an intermediate level presentation of statistical thermodynamics for students in the physical sciences (chemistry, nanosciences, physics) or related areas of applied science/engineering (chemical engineering, materials science, nanotechnology engineering), as they are areas in which statistical mechanical concepts play important roles. The book enables students to utilize microscopic concepts to achieve a better understanding of macroscopic phenomena and to be able to apply these concepts to the types of sub-macroscopic systems encountered in areas of nanoscience and nanotechnology.

 

 

 

✦ Table of Contents

Preface
Contents
1 Basic Background Material
1.1 Introduction
1.2 The Ideal Gas
1.2.1 Classical Ideal Gas Equation of State: Microscopic Derivation
1.2.2 Quantum Ideal Gas Equation of State
1.3 Fluctuations
1.4 Statistical Ensembles
1.4.1 Ensemble Averages
1.4.2 Variance and Standard Deviation
1.5 Problems for This Chapter
References
2 Macroscopic Thermodynamics
2.1 Basic Thermodynamic Definitions
2.2 An Introduction to Thermodynamics
2.2.1 Internal Energy, Entropy: The First Two Laws
2.3 New Thermodynamic State Functions
2.4 Expression for Heat Capacity Difference
2.5 Thermodynamic Engines
2.5.1 The Carnot Engine and Engine Cycle
The Carnot Cycle for a Classical Ideal Gas
The Carnot Cycle for a Quantum Ideal Gas
2.5.2 Reverse Carnot Engine (Refrigeration Cycle)
2.5.3 Curzon–Ahlborn Endoreversible Engine Cycle
2.5.4 The Otto and Diesel Engine Cycles
The Otto Cycle
The Diesel Cycle
2.5.5 Counterclockwise Otto Cycles
2.6 The Second Law and Stability
2.7 Extension to Multicomponent Systems
2.8 Thermodynamics of Real Gases
2.8.1 The Van der Waals Model
2.8.2 The Virial Equation of State
2.8.3 Fugacity
2.8.4 The Law of Corresponding States
2.8.5 Joule–Thomson Inversion
2.9 Problems for This Chapter
References
3 Ensembles: Systems of Particles
3.1 Microscopic Configurations
3.1.1 Illustration of the Role of the Basic Postulate
3.2 The Canonical Ensemble: Closed Systems
3.2.1 Translational States: Continuum Approximation
3.2.2 Summary of Forms for the Canonical PartitionFunction
3.2.3 Extension to N-Particle Systems
3.3 The Grand Ensemble: Open Systems
3.4 The Isothermal-Isobaric Ensemble
3.5 Problems for This Chapter
References
References
4 Mean Values and Thermodynamics
4.1 Canonical Ensemble: Closed Systems
4.1.1 Thermodynamics from the Canonical Ensemble
4.1.2 Canonical Partition Function for a Mixture
4.1.3 Microcanonical Ensemble: Isolated System
4.2 Grand Ensemble: Open Systems
4.2.1 Thermodynamics from the Grand Ensemble
4.2.2 Fluctuations in the Number of Particles
4.3 The Isothermal–Isobaric Ensemble
4.4 Interconnections Between Ensembles
4.5 Problems for this Chapter
References
5 Atomic Systems
5.1 Ground Electronic Term Atoms
5.1.1 The Canonical Partition Function
5.1.2 The Isothermal–Isobaric Partition Function
5.1.3 Translational Versus Internal State Contributions
5.2 Why Is the Chemical Potential Negative?
5.3 Electronic and Nuclear Spin States
5.3.1 Setting the Stage: Excited Electronic States
5.3.2 Excited Electronic State Contributions
5.3.3 Nuclear Spin Contributions to the Canonical Partition Function
5.3.4 The Full Canonical Atomic Partition Function
5.4 Atomic Gas Thermodynamic Functions
5.4.1 Atoms Having No Thermally Accessible Excited Electronic States
5.4.2 Influence of Excited Electronic States
5.5 Simple Harmonic Oscillator Ensembles
5.5.1 The Simple Harmonic Oscillator
5.5.2 Interlude: Degrees of Freedom
5.6 Monatomic Solids
5.7 Problems for This Chapter
References
References
6 Molecular Systems
6.1 Introduction
6.2 Diatomic Molecules
6.2.1 Setting the Stage
6.2.2 The Diatomic Vibrational Partition Function
The Simple Harmonic Oscillator Approximation
The SHO Model Partition Function: Vibrational Contribution to the Thermodynamic State Functions
Beyond the SHO Approximation: Anharmonicity Effects
6.2.3 The Diatomic Rotational Partition Function
The Rigid-Rotor Approximation
Heteronuclear Diatomic Molecules
Corrections to the Classical Expression
Centrifugal Distortion and Vibration–Rotation Interaction Corrections
Homonuclear Diatomic Molecules
Interlude: Electronic State Nuclear Interchange Symmetry
Symmetries of the Rotational Wavefunctions
Molecular Hydrogen: The Role of Nuclear Spin Symmetry
The General Homonuclear Diatomic Molecule X2
Summary for Rotational Partition Functions for Diatomic Molecules
6.2.4 Electronic Degree of Freedom
6.2.5 Overall Summary for Diatomic Molecules
6.2.6 Direct Evaluation of Internal State Contributions
6.3 Extension to the Ideal Polyatomic Gas
6.3.1 The Rigid-Rotor Simple Harmonic Oscillator Approximation
6.3.2 Summary of the RR-SHO Approximation for Polyatomic Molecules
Linear Molecule Expressions
Nonlinear Molecule Expressions
6.3.3 Beyond the RR-SHO Approximation
Vibrational Anharmonicity Corrections
Corrections to the RR-SHO Model
Linear Molecules
Nonlinear Molecules
6.4 Molecular Spectra: Nuclear Spin Effects
6.4.1 Diatomic Rotational Spectra
Heteronuclear Diatomic Molecular Spectra
Homonuclear Diatomic Molecular Spectra
6.4.2 Polyatomic Molecular Spectra
Rotational Spectra for Linear Polyatomic Molecules
Rotational Spectra for Nonlinear Molecules
6.5 Third-Law Entropy and Residual Entropy
6.6 Effect of Hindered Rotational Motions
6.6.1 Setting the Stage
6.6.2 Internal Rotation in Ethane
6.7 Problems for This Chapter
References
7 Classical Statistical Mechanics
7.1 Introduction
7.1.1 Energy Equipartition in Classical Mechanics
7.1.2 Dealing with Intermolecular Interactions
7.2 The Virial Equation of State
7.2.1 Second Virial Coefficient for Monatomic Gases
7.3 Beyond the Ideal Gas
7.4 An Approximate Description for Dense Fluids
7.5 The Liouville and Boltzmann Equations
7.5.1 The Liouville Equation
7.5.2 Interlude on Binary Collision Kinematics
7.5.3 Scattering Cross Section Concept
Inverse and Reverse Collisions
7.5.4 The Binary Collision Term and the BoltzmannEquation
7.5.5 Nonequilibrium Phenomena and the BoltzmannEquation
7.6 Problems for this Chapter
References
8 Electric and Magnetic Phenomena
8.1 Responses of Matter to Electric and Magnetic Fields
8.2 Thermodynamics of Polarizable Media
8.3 Dielectric Constant of a Polar Gas
8.3.1 Setting the Stage
8.3.2 Canonical Ensemble Description of a Dielectric Thermodynamic System
8.4 Magnetism, I. Paramagnetism
8.4.1 Thermodynamics of Magnetic Dipolar Media
8.4.2 Magnetic Susceptibility and Adiabatic Demagnetization
Interlude, Energy Transfer Between System and Surroundings
8.4.3 Thermodynamic Potentials for Magnetizable Systems
8.5 Paramagnetism in Spin Systems
8.5.1 Setting the Stage
8.5.2 Statistical Mechanics of Spin Systems
8.5.3 Multi-Electron Atoms/Ions: Setting the Stage
8.5.4 Magnetic Susceptibility for Ground Level Atoms or Ions
8.5.5 Application to Multi-Electron Atoms or Ions
8.5.6 Magnetic Susceptibilities of Sm3+ and Eu3+ Ions
8.6 Magnetism, II. Ferromagnetism
8.6.1 Setting the Stage
8.6.2 One-Dimensional Ising Chain in the Absence of an External Magnetic Field
8.6.3 One-Dimensional Ising Chain in the Presence of an External Magnetic Field
Interlude: Transfer Matrices
8.6.4 Correlation Between Spins: 1-D Ising Model
8.6.5 Some Comments on the Two-Dimensional Ising Model
8.7 Problems for This Chapter
References
References
9 Chemical Equilibrium
9.1 Setting the Stage
9.2 Derivation of the Expression for KP
9.2.1 Some Practical Matters
9.2.2 Relation Between KP(T) and Kc(T)
9.3 Four Extended Examples
9.4 Application to Chemical Kinetics
9.4.1 The ACT Model
9.4.2 From TST Expression to Experiment
9.5 Problems for This Chapter
References
10 Quantum Statistics
10.1 Setting the Stage
10.2 Two Types of Quantum Statistics
10.3 Connection to Maxwell–Boltzmann Statistics
10.4 Fermi–Dirac Statistics
10.4.1 The Ideal Fermi Gas
10.4.2 The Chemical Potential: Fermi Gas
10.4.3 Interlude: Zero-Temperature Fermi Distribution
10.4.4 Strongly Degenerate Fermi–Dirac Gas: Electrons in Metals
A. The Sommerfeld Expansion
B. Pauli Paramagnetism
10.5 Electrons in Semiconductors
10.5.1 Intrinsic Semiconductors
10.5.2 n-Type Impurity Semiconductors
10.6 Bose–Einstein Statistics
10.6.1 The Ideal Bose Gas
10.6.2 The Chemical Potential: Bose Gas
10.6.3 The Strongly Degenerate Bose–Einstein Gas: Bose–Einstein Condensation
10.6.4 The Photon Gas: Blackbody Radiation
10.7 Density Matrix and Ensemble Averages
10.8 Problems for This Chapter
References
A Aspects of Combinatorial Analysis
A.1 Some Basic Probability Concepts
B Review of Traditional Calculus
B.1 Derivatives
B.1.1 Functions of a Single Variable
B.1.2 Multivariate Functions
B.1.3 Inverse Differential Operator: Antiderivative
B.1.4 Taylor and Maclaurin Series
B.1.5 The Euler–Maclaurin Summation Formula
B.1.6 Fundamental Theorem of the Calculus
B.1.7 Regression of Series Concept
B.2 Legendre Transforms
B.3 Calculus of Variations: But Briefly
B.4 Jacobians
C Stirling Approximations
C.1 Lowest-Level Approximation to n!
C.2 Improved Stirling Approximation to n!
D Atomic and Molecular Term Symbols
D.1 Term Symbols for Multi-electron Atoms
D.2 Extended Example: The He Atom
D.3 Term Symbols for Linear Molecules
D.4 Term Symbols for Nonlinear Molecules
E Spherical/Symmetric Top Molecules
E.1 Linear Molecules: A Brief Review
E.2 Spherical Top Molecules
E.3 Symmetric Top Molecules
F Review of Solid State Concepts
F.1 The Feynman Model and Energy Bands
F.2 Generalization of the Feynman Model to Solids
F.3 Concept of Effective Mass
G Hamiltonian Mechanics
G.1 Generalized Coordinates and Momenta
G.2 Lagrangian Formulation
G.2.1 Generalized Forces
G.2.2 The Lagrange Equations
G.2.3 Constants of the Motion and Ignorable Coordinates
G.3 Hamilton's Equations
G.3.1 The Hamiltonian and Energy Conservation
G.3.2 Phase Space
G.3.3 Hamilton's Principle and Generating Functions
G.3.4 Equation of Motion for a Dynamical Variable: Poisson Brackets
Index