Introductory Statistical Thermodynamics


  • Nils Dalarsson, MSc – Engineering Physics 1982 Licentiate (Swedish degree between MSc and PhD) – Theoretical Physics 1990 PhD – Theoretical Physics 1993 MBA – Mathematical Finance 1998 MSc – Education 2012 , Royal Institute of Technology, Department of Theoretical Physics, Stockholm, Sweden
  • Mariana Dalarsson
  • Leonardo Golubovic

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


Book information

  • Published: December 2010
  • 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√ʬĬ¶I recommend this book as one of the most lucidly written introductory texts on Statistical Thermodynamics."--Contemporary Physics

Table of Contents

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√ʬĬôs 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