Thermal Physics Tutorials with Python Simulations

✍ Scribed by Minjoon Kouh, Taejoon Kouh

• Publisher: CRC Press
• Year: 2023
• Tongue: English
• Leaves: 238
• Category: Library

✦ Synopsis

This book provides an accessible introduction to thermal physics with computational approaches that complement the traditional mathematical treatments of classical thermodynamics and statistical mechanics. It guides readers through visualizations and simulations in the Python programming language, helping them to develop their own technical computing skills (including numerical and symbolic calculations, optimizations, recursive operations, and visualizations). Python is a highly readable and practical programming language, making this book appropriate for students without extensive programming experience.

Mathematics is one of the most powerful and essential tools of a physicist, or may even be considered as the language of physics. However, in recent years, computational methods have risen to complement and supplement the traditional, mathematical approaches to physics. As the new generation of physicists is expected to be well versed in modern computational tools, this tutorial was written with the goal of introducing a few elementary skills in data visualization, modeling, and simulation with a popular (as of the 2020s) programming language, Python, within the context of classical thermodynamics and statistical physics.

This book provides step-by-step instructions for each of the programming examples, and prior experience with Python is not necessary. If you are just venturing into the world of Python, the official homepage of the Python language is a great place to visit. There are other resources on Python, many of which are free and easily accessible online. There are different ways to set up your own computing environment, so that you can follow the codes in this book. For example, you may download and install the Anaconda distribution, which contains an interactive Jupyter Notebook environment as well as key Python modules. You may also use a cloud-based Python environment like Google Colab. See Appendix for more information.

This book may serve as a thermal physics textbook for a semester-long undergraduate thermal physics course or may be used as a tutorial on scientific computing with focused examples from thermal physics. This book will also appeal to engineering students studying intermediate-level thermodynamics as well as computer science students looking to understand how to apply their computer programming skills to science.

Key features:

Major concepts in thermal physics are introduced cohesively through computational and mathematical treatments.
Computational examples in Python programming language guide students on how to simulate and visualize thermodynamic principles and processes for themselves.

✦ Table of Contents

Cover
Half Title
Series Page
Title Page
Copyright Page
Dedication
Contents
Preface
CHAPTER 1: Calculating π
1.1. ESTIMATING π WITH A POLYGON
1.2. ESTIMATING π WITH RANDOM DOTS
SECTION I: Classical Thermodynamics
CHAPTER 2: Kinetic Theory of Gas
2.1. GETTING STARTED
2.2. DERIVATION OF THE IDEAL GAS LAW
2.3. SAMPLE CALCULATION
2.4. FURTHER EXPLORATIONS
2.5. TEMPERATURE
CHAPTER 3: Velocity Distribution
3.1. PARTICLE COLLISION
3.2. ONE-DIMENSIONAL EXAMPLE
3.3. MULTIPLE SOLUTIONS
3.4. FINDING SOLUTIONS WITH CODE
3.5. DISTRIBUTION OF ENERGY
3.6. DISTRIBUTION OF ENERGY AFTER MANY, MANY COLLISION EVENTS
3.7. DISTRIBUTION OF SPEED AFTER MANY, MANY COLLISION EVENTS
3.8. NOTE ON A MORE AMBITIOUS CODING PROJECT
Chapter 4: Thermal Processes
4.1. STATE AND PROCESS
4.2. PLOTTING AND NUMERICAL INTEGRATION
4.3. PV DIAGRAM
4.4. ADIABATIC PROCESS
4.5. PROOF OF PVY = CONSTANT FOR AN ADIABAT OF IDEAL GAS
4.6. CARNOT CYCLE
SECTION II: Statistical Mechanics
Chapter 5: Premise of Statistical Mechanics
5.1. ANALOGY: WEALTH DISTRIBUTION
5.2. MATHEMATICAL NOTATIONS
5.3. LISTING PERMUTATIONS
5.4. VISUALIZATION
5.5. COUNTING EXERCISE
5.6. CODE FOR ENUMERATING ALL POSSIBILITIES (VERSION 1)
5.7. CODE FOR ENUMERATING ALL POSSIBILITIES (VERSION 2)
5.8. BOLTZMANN DISTRIBUTION
5.9. MATH: LAGRANGE MULTIPLIER METHOD
5.10. MATH: STIRLING'S APPROXIMATION
5.11. BACK TO THE BOLTZMANN DISTRIBUTION
Chapter 6: Revisiting Ideal Gas
6.1. A LITTLE BIT OF QUANTUM MECHANICS
6.2. DEGENERACY
6.3. PARTITION FUNCTION
6.4. AVERAGE ENERGY OF AN IDEAL GAS
6.5. VISUALIZING ENERGY LEVELS WITH DEGENERACY
Chapter 7: Revisiting Thermal Processes
7.1. REVIEW
7.2. THERMAL PROCESSES
7.3. CHECK
Chapter 8: Entropy, Temperature, Energy, and Other Potentials
8.1. ENTROPY
8.2. LAWS OF THERMODYNAMICS
8.3. TEMPERATURE AS A RATIO OF CHANGES IN ENERGY AND ENTROPY
8.4. IDENTIFYING B = 1/kBT
8.5. MATH: VOLUME OF A SPHERE
8.6. ENTROPY OF IDEAL GAS
8.7. ENTROPY OF IDEAL GAS, AGAIN
8.8. MOTIVATION FOR OTHER METRICS OF A THERMODYNAMIC SYSTEM
8.9. FOUR THERMODYNAMIC POTENTIALS: U,H, F,G
8.10. THERMODYNAMIC RELATIONS
SECTION III: Examples
Chapter 9: Two-State System
9.1. DYNAMIC CASE
9.2. EQUILIBRIUM POTENTIAL
9.3. ACTION POTENTIAL
9.4. DIODE
Chapter 10: Specific Heat
10.1. DEFINITION OF SPECIFIC HEAT
10.2. TWO-STATE SYSTEM
10.3. SIMPLE HARMONIC OSCILLATOR (SHO)
10.4. TEMPERATURE DEPENDENCE OF ENERGY AND SPECIFIC HEAT
10.5. EINSTEIN MODEL OF SOLID
Chapter 11: Random and Guided Walks
11.1. ONE-DIMENSIONAL RANDOM WALK
11.2. TWO-DIMENSIONAL RANDOM WALK
11.3. A TANGENT
11.4. GUIDED RANDOM WALKS
Appendix
APPENDIX A: GETTING STARTED WITH PYTHON
APPENDIX B: PYTHON PROGRAMMING BASICS
APPENDIX C: PLOTS
APPENDIX D: COLORS
APPENDIX E: ANIMATION
Epilogue
Index