Introductory Statistical Thermodynamics book cover

Introductory Statistical Thermodynamics

Introductory Statistical Thermodynamics is a text for an introductory one-semester course in statistical thermodynamics for upper-level undergraduate and graduate students in physics and engineering. The book offers a high level of detail in derivations of all equations and results. This information is necessary for students to grasp difficult concepts in physics that are needed to move on to higher level courses. The text is elementary, self contained, and mathematically well-founded, containing a number of problems with detailed solutions to help students to grasp the more difficult theoretical concepts.


Upper-level undergraduates, and graduate students of physics and engineering.

Hardbound, 408 Pages

Published: December 2010

Imprint: Academic Press

ISBN: 978-0-12-384956-4


  • "The book is intended as a text for an introductory course in statistical thermodynamics for undergraduate students of physical sciences or engineering. Parts of the material may be useful as well for a graduate course. The book is quite detailed in explicit derivations of all equations and results, followed by a number of fully solved problems/exercises that illustrate theoretical concepts discussed throughout the book. An introductory chapter contains some very basic quantum mechanical background. The second chapter contains derivations of basic notions of classical statistical mechanics, together with a discussion of general laws of macroscopic thermodynamics. The third chapter addresses various applications to physically interesting cases of ideal and non-ideal gases. In the last chapter, a discussion of basic concepts of quantum statistical physics (quantum gases) is followed by a brief discussion of relativistic phenomena."--Zentralblatt Math 1225-1

    "This book is an excellent introduction to statistical thermodynamics, which covers the fundamental physical concepts used for the macroscopic description of systems with very large number of particles in thermo-dynamic equilibrium. Also the macroscopic concepts used in this book, are shown to be connected to the appropriate microscopic theories. However, in the literature, statistical thermodynamics is frequently introduced purely from macroscopic point of view. But in general the macroscopic description is largely independent on the details of the microscopic models describing the interactions of the particle in various physical systems. So learning the connection between microscopic and macroscopic concept will definitely enhance the understanding of the subject to great extent…I recommend this book as one of the most lucidly written introductory texts on Statistical Thermodynamics."--Contemporary Physics


  • 1 Introduction
    2 Introduction and Basic Concepts
    2.1 Systems of Identical Particles
    2.2 Quantum Description of Particles
    2.3 Problems with Solutions
    3 Kinetic energy of Translational Motion
    3.1 Hamiltonian of Translational Motion
    3.2 Schrödinger Equation for Translational Motion
    3.4 Normalization of the Wave function
    3.5 Quantized Energy of Translational Motion
    3.6 Problems with Solutions
    4 Energy of Vibrations
    4.1 Hamiltonian of Vibrations
    4.2 Solution of the Schrödinger equation
    4.3 Quantized Energy of Vibrations
    4.4 Hermite Polynomials
    4.5 Normalization of the Wave Function
    4.6 Problems with Solutions
    5 Kinetic Energy of Rotations
    5.1 Hamiltonian of Rotations
    5.1.1 Kinetic Energy and Hamiltonian Operator
    5.1.2 Angular Momentum Operator
    5.2 Solution of the Schrödinger equation
    5.3 Quantized Energy of Rotations
    5.4 Legendre Polynomials
    5.5 Normalization of the Wave function
    5.6 Spin Angular Momentum
    5.7 Problems with Solutions
    6 Number of accessible states and Entropy
    6.1 Introduction and Definitions
    6.2 Calculation of the Number of accessible States
    6.2.1 Classical Number of Accessible States
    6.2.2 Number of Accessible States for Bosons
    6.2.3 Number of Accessible States for Fermions
    6.3 Problems with Solutions
    7 Equilibrium States of Systems
    7.1 Equilibrium Conditions
    7.2 Occupation Numbers of Energy Levels
    7.3 Concept of Temperature
    7.4 Problems with Solutions
    8 Thermodynamic Variables
    8.1 Free Energy and the Partition Function
    8.2 Internal Energy. Caloric State Equation
    8.3 Pressure. Thermal State Equation
    8.4 Classification of Thermodynamic Variables
    8.5 Problems with Solutions
    9 Macroscopic Thermodynamics
    9.1 Changes of States. Heat and Work
    9.2.1 Zeroth Law of Thermodynamics
    9.2.2 First Law of Thermodynamics
    9.2.3 Second Law of Thermodynamics
    9.2.4 Third Law of Thermodynamics
    9.3 Open Systems
    9.4 Thermal Properties of Systems
    9.4.1 Isobaric Expansion
    9.4.2 Isochoric Expansion
    9.4.3 Isothermal Expansion
    9.4.4 Relation between Thermal Coefficients
    9.5 Caloric Properties of Systems
    9.5.1 Specific Heat at Constant Volume cV
    9.5.2 Specific Heat at Constant Pressure cP
    9.5.3 Relation between Specific Heats
    9.6 Relations between Thermodynamic Coefficients
    9.7 Problems with Solutions
    10 Variable Number of Particles
    10.1 Chemical Potential
    10.2 Thermodynamic Potential
    10.3 Phases and Phase Equilibrium
    10.3.1 Latent Heat
    10.3.2 Clausius-Clapeyron Formula
    10.4 Problems with Solutions
    11 Ideal Monoatomic Gases
    11.1 Continuous Energy Spectrum
    11.2 Continuous Partition Function
    11.3 Partition Function of Ideal Monoatomic Gases
    11.4 Kinetic Theory of Ideal Monoatomic Gases
    11.4.1 Maxwell-Boltzmann’s Speed Distribution
    11.4.2 Most probable Speed of Gas Particles
    11.4.3 Average Speed of Gas Particles
    11.4.4 Root-Mean-Square Speed of Gas Particles
    11.4.5 Average Kinetic Energy and Internal Energy
    11.4.6 Equipartition Theorem
    11.5 Thermodynamics of Ideal Monoatomic Gases
    11.5.1 Caloric State Equation
    11.5.2 Thermal State Equation
    11.5.3 Universal and Particular Gas Constants
    11.5.4 Caloric and Thermal Coefficients
    11.6 Ideal Gases in External Potentials
    11.6.1 General Maxwell-Boltzmann distribution
    11.6.2 Harmonic and Anharmonic Oscillators
    11.6.3 Classical limit of Quantum Partition Function
    11.7 Problems with Solutions
    12 Ideal Diatomic Gases
    12.1 Rotations of Gas Particles
    12.2 Vibrations of Gas Particles
    12.3 Problems with Solutions
    13 Non-ideal Gases
    13.1 Partition Function for Non-ideal Gases
    13.2 Free Energy of Non-ideal Gases
    13.3 Free Energy of Particle Interactions
    13.4 Van der Waals Equation
    13.5 Caloric State Equation for Non-ideal Gases
    13.6 Specific Heats for Non-ideal Gases
    13.7 Problems with Solutions
    14 Quasi-static Thermodynamic Processes
    14.1 Isobaric Process
    14.2 Isochoric Process
    14.3 Isothermal Process
    14.4 Adiabatic Process
    14.5 Polytropic Process
    14.6 Cyclic Processes. Carnot Cycle
    14.7 Problems with Solutions
    15 Quantum Distribution Functions
    15.1 Entropy Maximization in Quantum Statistics
    15.1.1 The Case of Bosons
    15.1.2 The Case of Fermions
    15.2 Quantum Equilibrium Distribution
    15.3 Helmholtz Thermodynamic Potential
    15.4 Thermodynamics of Quantum Systems
    15.5 Evaluation of Integrals
    15.6 Problems with Solutions
    16 Electron Gases in Metals
    16.1 Ground State of Electron Gases in Metals
    16.2 Electron Gases in Metals at Finite Temperatures
    16.3 Chemical Potential at Finite Temperatures
    16.4 Thermodynamics of Electron Gases
    16.5 Problems with Solutions
    17 Photon Gas in Equilibrium
    17.1 Planck Distribution
    17.2 Thermodynamics of Photon Gas in Equilibrium
    17.3 Problems with Solutions
    18 Other examples of Boson Systems
    18.1 Lattice Vibrations and Phonons
    18.1.1 Vibration Modes
    18.1.2 Internal Energy of Lattice Vibrations
    18.2 Bose-Einstein Condensation
    18.3 Problems with Solutions
    19 Special Topics
    19.1 Ultrarelativistic Fermion Gas
    19.1.1 Ultrarelativistic Fermion Gas
    19.1.2 Ultrarelativistic Fermion Gas
    19.2 Thermodynamics of the Expanding Universe
    19.2.1 Internal Energy of Elementary-Particle Species
    19.2.2 Entropy per Volume Element
    19.3 Problems with Solutions
    A Physical constants


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