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.

• 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

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

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