| |

| |

| |

Introduction to Statistical Thermodynamics | |

| |

| |

| |

Probabistic Description | |

| |

| |

| |

Macrostates and Microstates | |

| |

| |

| |

Quantum Mechanics Description of Microstates | |

| |

| |

| |

The Postulates of Statistical Mechanics | |

| |

| |

| |

The Boltzmann Energy Distribution | |

| |

| |

| |

The Canonical Partition function | |

| |

| |

| |

Some Properties of the Canonical Partition Function | |

| |

| |

| |

Relationship of the Canonical Partition Function to Thermodynamic Properties | |

| |

| |

| |

Canonical Partition Function for a Molecule with Several Independent Energy Modes | |

| |

| |

| |

Canonical Partition Function for a Collection of Noninteracting Identical Atoms | |

| |

| |

Problems | |

| |

| |

| |

The Ideal Monatomic Gas | |

| |

| |

| |

Canonical Partition Function for the Ideal Monatomic Gas | |

| |

| |

| |

Identification of b as 1/kT. | |

| |

| |

| |

General Relationships of the Canonical Partition Function to Other Thermodynamic Quantities | |

| |

| |

| |

The Thermodynamic Properties of the Ideal Monatomic Gas | |

| |

| |

| |

Energy Fluctuations in the Canonical Ensemble | |

| |

| |

| |

The Gibbs Entropy Equation | |

| |

| |

| |

Translational State Degeneracy | |

| |

| |

| |

Distinguishability, Indistinguishability and the Gibbs' Paradox | |

| |

| |

| |

A Classical Mechanics - Quantum Mechanics Comparison: The Maxwell-Boltzmann Distribution of Velocities | |

| |

| |

Problems | |

| |

| |

| |

Ideal Polyatomic Gas | |

| |

| |

| |

The Partition Function for an Ideal Diatomic Gas | |

| |

| |

| |

The Thermodynamic Properties of the Ideal Diatomic Gas | |

| |

| |

| |

The Partition Function for an Ideal Polyatomic Gas | |

| |

| |

| |

The Thermodynamic Properties of an Ideal Polyatomic Gas | |

| |

| |

| |

The Heat Capacities of Ideal Gases | |

| |

| |

| |

Normal Mode Analysis: the Vibrations of a Linear Triatomic Molecule | |

| |

| |

Problems | |

| |

| |

| |

Chemical Reactions in Ideal Gases | |

| |

| |

| |

The Non-Reacting Ideal Gas Mixture | |

| |

| |

| |

Partition Function of a Reacting Ideal Chemical Mixture | |

| |

| |

| |

Three Different Derivations of the Chemical Equilibrium Constant in an Ideal Gas Mixture | |

| |

| |

| |

Fluctuations in a Chemically Reacting System | |

| |

| |

| |

The Chemically Reacting Gas Mixture. The General Case | |

| |

| |

| |

An Example. The Ionization of Argon | |

| |

| |

Problems | |

| |

| |

| |

Other Partition Functions | |

| |

| |

| |

The Microcanonical Ensemble | |

| |

| |

| |

The Grand Canonical Ensemble | |

| |

| |

| |

The Isobaric-Isothermal Ensemble | |

| |

| |

| |

The Restricted Grand or Semi Grand Canonical Ensemble | |

| |

| |

| |

Comments on the Use of Different Ensembles | |

| |

| |

Problems | |

| |

| |

| |

Interacting Molecules in a Gas | |

| |

| |

| |

The Configuration Integral | |

| |

| |

| |

Thermodynamic Properties from the Configuration Integral | |

| |

| |

| |

The Pairwise Additivity Assumption | |

| |

| |

| |

Mayer Cluster Function and Irreducible Integrals | |

| |

| |

| |

The Virial Equation of State | |

| |

| |

| |

The Virial Equation of State for Polyatomic Molecules | |

| |

| |

| |

Thermodynamic Properties from the Virial Equation of State | |

| |

| |

| |

Derivation of Virial Coefficient Formulae from the Grand Canonical Ensemble | |

| |

| |

| |

Range of Applicability of the Virial Equation | |

| |

| |

Problems | |

| |

| |

| |

Intermolecular Potentials and the Evaluation of the Second Virial Coefficient | |

| |

| |

| |

Interaction Potentials for Spherical Molecules | |

| |

| |

| |

Interaction Potentials Between Unlike Atoms. | |

| |

| |

| |

Interaction Potentials for Nonspherical Molecules. | |

| |

| |

| |

Engineering Applications/Implications of the Virial Equation of State | |

| |

| |

Problems | |

| |

| |

| |

Monatomic Crystals | |

| |

| |

| |

The Einstein Model of a Crystal | |

| |

| |

| |

The Debye Model of a Crystal | |

| |

| |

| |

Test of the Einstein and Debye Models for a Crystal | |

| |

| |

| |

Sublimation Pressures of Crystals | |

| |

| |

| |

A Comment of the Third Law of Thermodynamics | |

| |

| |

Problems | |

| |

| |

| |

Simple Lattice Models of Fluids | |

| |

| |

| |

Introduction | |

| |

| |

| |

Development of Equations of State from Lattice Theory | |

| |

| |

| |

Activity Coefficient Models for Similar Size Molecules from Lattice Theory | |

| |

| |

| |

Flory-Huggins and Other Models for Polymer Systems | |

| |

| |

| |

The Ising Model | |

| |

| |

Problems | |

| |

| |

| |

Interacting Molecules in a Dense Fluid. Configurational Distribution Functions | |

| |

| |

| |

Reduced Spatial Probability Density Functions | |

| |

| |

| |

Thermodynamic Properties from the Pair Correlation Function | |

| |

| |

| |

The Pair Correlation Function (Radial Distribution Function) at Low Density | |

| |

| |

| |

Methods of Determination of the Pair Correlation Function at High Density | |

| |

| |

| |

Fluctuations in the Number of Particles and the Compressibility Equation | |

| |

| |

| |

Determination of the Radial Distribution Function of Fluids using Coherent X-ray or Neutron Scattering | |

| |

| |

| |

Determination of the Radial Distribution Functions of Molecular Liquids | |

| |

| |

| |

Determination of the Coordination Number from the Radial Distribution Function | |

| |

| |

| |

Determination of the Radial Distribution Function of Colloids and Proteins | |

| |

| |

Problems | |

| |

| |

| |

Integral Equation Theories for the Radial Distribution function | |

| |

| |

| |

The Potential of Mean Force | |

| |

| |

| |

The Kirkwood Superposition Approximation | |

| |

| |

| |

The Ornstein-Zernike Equation | |

| |

| |

| |

Closures for the Ornstein-Zernike Equation | |

| |

| |

| |

The Percus-Yevick Equation of State | |

| |

| |

| |

The Radial Distribution Function and Thermodynamic Properties of Mixtures | |

| |

| |

| |

The Potential of Mean Force | |

| |

| |

| |

Osmotic Pressure and the Potential of Mean Force for Protein and Colloidal Solutions | |

| |

| |

Problems | |

| |

| |

| |

Computer Simulation | |

| |

| |

| |

Introduction to Molecular Level Simulation | |

| |

| |

| |

Thermodynamic Properties from Molecular Simulation | |

| |

| |

| |

Monte Carlo Simulation | |

| |

| |

| |

Molecular Dynamics Simulation | |

| |

| |

Problems | |

| |

| |

| |

Perturbation Theory | |

| |

| |

| |

Perturbation Theory for the Square-Well Potential | |

| |

| |

| |

First Order Barker-Henderson Perturbation Theory | |

| |

| |

| |

Second Order Perturbation Theory | |

| |

| |

| |

Perturbation Theory Using Other Potentials | |

| |

| |

| |

Engineering Applications of Perturbation Theory | |

| |

| |

Problems | |

| |

| |

| |

Debye-Hï¿½ckel Theory of Electrolyte Solutions | |

| |

| |

| |

Solutions Containing Ions (and electrons) | |

| |

| |

| |

Debye-Hï¿½ckel Theory | |

| |

| |

| |

The Mean Ionic Activity Coefficient | |

| |

| |

Problems | |

| |

| |

| |

The Derivation of Thermodynamic Models from the Generalized van der Waals Partition function | |

| |

| |

| |

The Statistical Mechanical Background | |

| |

| |

| |

Application of the Generalized van der Waals Partition Function to Pure Fluids | |

| |

| |

| |

Equation of State for Mixtures from the Generalized van der Waals Partition Function | |

| |

| |

| |

Activity Coefficient Models from the Generalized van der Waals Partition Function | |

| |

| |

| |

Chain Molecules and Polymers | |

| |

| |

| |

Hydrogen-bonding and Associating Fluids | |

| |

| |

Problems | |