Equilibrium Statistical Mechanics

The International Encyclopedia of Physical Chemistry and Chemical Physics, Volume 1: Equilibrium Statistical Mechanics covers the fundamental principles and the development of theoretical aspects of equilibrium statistical mechanics. Statistical mechanical is the study of the connection between the macroscopic behavior of bulk matter and the microscopic properties of its constituent atoms and molecules.
This book contains eight chapters, and begins with a presentation of the master equation used for the calculation of the fundamental thermodynamic functions. The succeeding chapters highlight the characteristics of the partition function and its application to the analysis of perfect and imperfect gases, solids, and dense fluids. These topics are followed by discussions on the fundamentals of quantum statistics, with particular emphasis on its application in certain media. The last chapter outlines the derivation of the relations between the partition functions and the thermodynamic quantities.
This book will be of value to physical chemists, chemical physicists, mathematicians, and researchers in the allied fields of statistical mechanics.

Contenu

Chapter 1 A Master Equation and Two Partition Functions

1.1 The Scope of Statistical Mechanics

1.2 A Master Equation

1.3 The Average of a Mechanical Property

1.4 The Grand Canonical and Canonical Partition Functions

1.5 Perfect Gases

1.6 The Occupancy of a Molecular Quantum State

1.7 PF-Energy Relationship for Monatomic Perfect Gases

Chapter 2 General Characteristics of the Partition Function

2.1 Separability of the Hamiltonian

2.2 Bose-Einstein, Fermi-Dirac and Boltzmann Systems

2.3 The Classical Limit

2.4 Heat Capacity and Equipartition

2.5 Symmetry Number

2.6 Isotopes

2.7 Nuclear Spm

2.8 Coordinate Transformations

Chapter 3 Perfect Gases and the Internal Partition Function

3.1 Monatomic Molecules

3.2 Diatomic Molecules

3.3 The Oscillator Partition Function

3.4 The Linear Rotator Function

3.5 Molecular Hydrogen

3.6 Polyatomic Molecules

3.7 Polyatomic Rotator Function

3.8 Polyatomic Normal Coordinates

3.9 Polyatomic Molecule Symmetries

3.10 Perfect Gas Thermodynamic Functions

Chapter 4 Imperfect Gases

4.1 Introduction

4.2 Simple Cluster Functions

4.3 The Virial Expansion

4.4 Proof of the Virial Development

4.5 Interpretation of P|kT = Sbnzn

4.6 Evaluation of the Virial Coefficients

4.7 Condensation

4.8 Plasma and the Debye Limit

Chapter 5 Solids

5.1 Overall Survey and Electronic Excitation

5.2 Crystal Lattice Hamiltonian

5.3 Lattice Vibration Spectra

5.4 The Debye Lattice Theory

5.5 Debye Thermodynamic Functions

5.6 Thermal Expansion

5.7 Crystal Imperfections and Order-Disorder

Chapter 6 Dense Fluids

6.1 Notation and the Potential Energy

6.2 Distribution Functions

6.3 Equations for the Distribution Functions

6.4 The Potentials of Average Force

6.5 The Kirkwood Superposition Assumption

6.6 The Virial of Clausius

6.7 Calculation of Fn(z,T,[n]) from Fn(y,T,[n])

6.8 The Osmotic Pressure

6.9 The Cluster Development for Osmotic Pressure

6.10 Moments and Thermodynamic Quantities

6.11 Open and Closed System Moments

6.12 Integral Equations

6.13 Monte Carlo

Chapter 7 Quantum Statistics

7.1 Introduction

7.2 Bose-Einstein Perfect Gases

7.3 Black Body Radiation

7.4 Fermi-Dirac Perfect Gases

7.5 Density Matrix Formulation

7.6 The Momentum Representation

7.7 Matrix Transformations

7.8 The Wigner Representation

7.9 The Equilibrium Density Matrix

7.10 The Classical Limit

7.11 Perfect Bose Gas Cluster Function

Chapter 8 Derivation of the Partition Function Equations

8.1 Outline of the Derivation

8.2 The Ensemble Concept

8.3 The Microcanonical Ensemble, the Liouville Theorem

8.4 The Ergodic Hypothesis

8.5 The Quantity S = k In O

8.6 The Quantities and

8.7 The Thermodynamic Laws

8.8 The Canonical Ensembles

8.9 Methodology of the Partition Functions

8.10 The General Entropy Expression, and the Increase of Entropy

8.11 On Logic and Mathematical Rigor

Index