An Introduction to Applied Statistical Thermodynamics

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ISBN: 9780470913475 | 0470913479
Cover: Paperback
Copyright: 11/16/2010

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One of the goals of An Introduction to Applied Statistical Thermodynamics is to introduce readers to the fundamental ideas and engineering uses of statistical thermodynamics, and the equilibrium part of the statistical mechanics. This text emphasises on nano and bio technologies, molecular level descriptions and understandings offered by statistical mechanics. It provides an introduction to the simplest forms of Monte Carlo and molecular dynamics simulation (albeit only for simple spherical molecules) and user-friendly MATLAB programs for doing such simulations, and also some other calculations. The purpose of this text is to provide a readable introduction to statistical thermodynamics, show its utility and the way the results obtained lead to useful generalisations for practical application. The text also illustrates the difficulties that arise in the statistical thermodynamics of dense fluids as seen in the discussion of liquids.

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-Hückel Theory of Electrolyte Solutions
Solutions Containing Ions (and electrons)
Debye-Hückel 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
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An Introduction to Applied Statistical Thermodynamics

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