1st Edition

Statistical Thermodynamics Understanding the Properties of Macroscopic Systems

    548 Pages 83 B/W Illustrations
    by CRC Press

    548 Pages 83 B/W Illustrations
    by CRC Press

    Statistical thermodynamics and the related domains of statistical physics and quantum mechanics are very important in many fields of research, including plasmas, rarefied gas dynamics, nuclear systems, lasers, semiconductors, superconductivity, ortho- and para-hydrogen, liquid helium, and so on. Statistical Thermodynamics: Understanding the Properties of Macroscopic Systems provides a detailed overview of how to apply statistical principles to obtain the physical and thermodynamic properties of macroscopic systems.

    Intended for physics, chemistry, and other science students at the graduate level, the book starts with fundamental principles of statistical physics, before diving into thermodynamics. Going further than many advanced textbooks, it includes Bose-Einstein, Fermi-Dirac statistics, and Lattice dynamics as well as applications in polaron theory, electronic gas in a magnetic field, thermodynamics of dielectrics, and magnetic materials in a magnetic field. The book concludes with an examination of statistical thermodynamics using functional integration and Feynman path integrals, and includes a wide range of problems with solutions that explain the theory.

    Basic Principles of Statistical Physics
    Microscopic and Macroscopic Description of States
    Basic Postulates
    Gibbs Ergodic Assumption
    Gibbsian Ensembles
    Experimental Basis of Statistical Mechanics
    Definition of Expectation Values
    Ergodic Principle and Expectation Values
    Properties of Distribution Function
    Relative Fluctuation of an Additive Macroscopic Parameter
    Liouville Theorem
    Gibbs Microcanonical Ensemble
    Microcanonical Distribution in Quantum Mechanics
    Density Matrix
    Density Matrix in Energy Representation
    Entropy

    Thermodynamic Functions
    Temperature
    Adiabatic Processes
    Pressure
    Thermodynamic Identity
    Laws of Thermodynamics
    Thermodynamic Potentials, Maxwell Relations
    Heat Capacity and Equation of State
    Jacobian Method
    Joule–Thomson Process
    Maximum Work
    Condition for Equilibrium and Stability in an Isolated System
    Thermodynamic Inequalities
    Third Law of Thermodynamics
    Dependence of Thermodynamic Functions on Number of Particles
    Equilibrium in an External Force Field

    Canonical Distribution
    Gibbs Canonical Distribution
    Basic Formulas of Statistical Physics
    Maxwell Distribution
    Experimental Basis of Statistical Mechanics
    Grand Canonical Distribution
    Extremum of Canonical Distribution Function

    Ideal Gases
    Occupation Number
    Boltzmann Distribution
    Entropy of a Nonequilibrium Boltzmann Gas
    Applications of Statistical Thermodynamics to Some Systems
    Free Energy of the Ideal Boltzmann Gas
    Equipartition Theorem
    Monatomic Gas
    Vibrations of Diatomic Molecules
    Rotation of Diatomic Molecules
    Nuclear Spin Effects
    Electronic Angular Momentum Effect
    Experiment and Statistical Ideas

    Quantum Statistics of Ideal Gases
    Maxwell–Boltzmann, Bose–Einstein, and Fermi–Dirac Statistics
    Generalized Thermodynamic Potential for a Quantum Ideal Gas
    Fermi–Dirac and Bose–Einstein Distributions
    Entropy of Nonequilibrium Fermi and Bose Gases
    Thermodynamic Functions for Quantum Gases
    Properties of Weakly Degenerate Quantum Gas
    Degenerate Electronic Gas at Temperature Different from Zero
    Experimental Basis of Statistical Mechanics
    Application of Statistics to an Intrinsic Semiconductor
    Application of Statistics to Extrinsic Semiconductor
    Degenerate Bose Gas
    Equilibrium or Black Body Radiation
    Application of Statistical Thermodynamics to Electromagnetic Eigenmodes

    The Electron Gas in a Magnetic Field
    Evaluation of Diamagnetism of a Free Electron Gas; Density Matrix for a Free Electron Gas
    Evaluation of Free Energy
    Application to a Degenerate Gas
    Evaluation of Contour Integrals
    Diamagnetism of a Free Electron Gas; Oscillatory Effect

    Magnetic and Dielectric Materials
    Thermodynamics of Magnetic Materials in a Magnetic Field
    Thermodynamics of Dielectric Materials in an Electric Field
    Magnetic Effects in Materials
    Adiabatic Cooling by Demagnetization

    Lattice Dynamics
    Periodic Functions of a Reciprocal Lattice
    Reciprocal Lattice
    Vibrational Modes of a Monatomic Lattice
    Vibrational Modes of a Diatomic Linear Chain
    Vibrational Modes in a Three-Dimensional Crystal
    Normal Vibration of a Three-Dimensional Crystal

    Condensed Bodies
    Application of Statistical Thermodynamics to Phonons
    Free Energy of Condensed Bodies in the Harmonic Approximation
    Condensed Bodies at Low Temperatures
    Condensed Bodies at High Temperatures
    Debye Temperature Approximation
    Volume Coefficient of Expansion
    The Experimental Basis of Statistical Mechanics

    Applications of Statistical Thermodynamics
    Multiphase Systems
    Critical Point

    Macroscopic Quantum Effects: Superfluid Liquid Helium
    Nature of the Lambda Transition
    Properties of Liquid Helium
    Landau Theory of Liquid He II
    Superfluidity of Liquid Helium

    Nonideal Classical Gases
    Pair Interactions Approximation
    Van Der Waals Equation
    Completely Ionized Gas

    Functional Integration in Statistical Physics
    Feynman Path Integrals
    Least Action Principle
    Representation of Transition Amplitude through Functional Integration
    Transition Amplitudes Using Stationary Phase Method
    Representation of Matrix Element of Physical Operator through Functional Integral
    Property of Path Integral Due to Events Occurring in Succession
    Eigenvectors
    Transition Amplitude for Time-Independent Hamiltonian
    Eigenvectors and Energy Spectrum
    Schrödinger Equation
    Green Function for Schrödinger Equation
    Functional Integration in Quantum Statistical Mechanics
    Statistical Physics in Representation of Path Integrals
    Partition Function of Forced Harmonic Oscillator
    Feynman Variational Method
    Feynman Polaron Energy

    References

    Index

    Biography

    Lukong Cornelius Fai is with ICTP Trieste, Italy and the University of Dschang, Cameroon. Gary Wysin is with Kansas State University, USA.

    "... recommended for various levels of study: from a general course to the ground specialized course of theoretical physics. Moreover, a large number of problems based on physical situations supplied with detailed solutions determine an exceptional usefulness of this book due to the development of practical skills."
    Zentralblatt MATH 1305