# Introductory Statistical Thermodynamics

## 1st Edition

**Authors:**Nils Dalarsson Mariana Dalarsson Leonardo Golubovic

**eBook ISBN:**9780123849571

**Hardcover ISBN:**9780123849564

**Imprint:**Academic Press

**Published Date:**20th December 2010

**Page Count:**408

## Description

*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.

## Key Features

- Beginning chapters place an emphasis on quantum mechanics
- Includes problems with detailed solutions and a number of detailed theoretical derivations at the end of each chapter
- Provides a high level of detail in derivations of all equations and results

## Readership

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

## Table of Contents

1 Introduction

Part I QUANTUM DESCRIPTION OF SYSTEMS

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

Part II THERMODYNAMICS OF SYSTEMS

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

Part III IDEAL AND NON-IDEAL GASES

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

Part IV QUANTUM STATISTICAL PHYSICS

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

Bibliography

Index

## Details

- No. of pages:
- 408

- Language:
- English

- Copyright:
- © Academic Press 2010

- Published:
- 20th December 2010

- Imprint:
- Academic Press

- eBook ISBN:
- 9780123849571

- Hardcover ISBN:
- 9780123849564

## About the Authors

### Nils Dalarsson

Nils Dalarsson has been with the Royal Institute of Technology, Department of Theoretical Physics in Stockholm, Sweden, since 1999. His research and teaching experience spans 32 years. Former academic and private sector affiliations include University of Virginia, Uppsala University, FSB Corporation, France Telecom Corporation, Ericsson Corporation, and ABB Corporation. He holds a PhD in Theoretical Physics, an MSc in Engineering Physics, and an MSc in Education.

### Affiliations and Expertise

Royal Institute of Technology, Department of Theoretical Physics, Stockholm, Sweden

### Mariana Dalarsson

### Leonardo Golubovic

## Reviews

*"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**