Thermal Physics Tutorials with Python Simulations

Cover....1 Half Title....2 Series Page....3 Title Page....4 Copyright Page....5 Dedication....6 Contents....8 Preface....12 CHAPTER 1: Calculating π....16 1.1. ESTIMATING π WITH A POLYGON....18 1.2. ESTIMATING π WITH RANDOM DOTS....21 SECTION I: Classical Thermodynamics	....26 CHAPTER 2: Kinetic Theory of Gas....28 2.1. GETTING STARTED....29 2.2. DERIVATION OF THE IDEAL GAS LAW....36 2.3. SAMPLE CALCULATION....37 2.4. FURTHER EXPLORATIONS....38 2.5. TEMPERATURE....41 CHAPTER 3: Velocity Distribution....44 3.1. PARTICLE COLLISION....44 3.2. ONE-DIMENSIONAL EXAMPLE....45 3.3. MULTIPLE SOLUTIONS....48 3.4. FINDING SOLUTIONS WITH CODE....50 3.5. DISTRIBUTION OF ENERGY....58 3.6. DISTRIBUTION OF ENERGY AFTER MANY, MANY COLLISION EVENTS....60 3.7. DISTRIBUTION OF SPEED AFTER MANY, MANY COLLISION EVENTS....66 3.8. NOTE ON A MORE AMBITIOUS CODING PROJECT....70 Chapter 4: Thermal Processes....72 4.1. STATE AND PROCESS....72 4.2. PLOTTING AND NUMERICAL INTEGRATION....73 4.3. PV DIAGRAM....74 4.4. ADIABATIC PROCESS....75 4.5. PROOF OF PVY = CONSTANT FOR AN ADIABAT OF IDEAL GAS....76 4.6. CARNOT CYCLE....79 SECTION II: Statistical Mechanics....86 Chapter 5: Premise of Statistical Mechanics....88 5.1. ANALOGY: WEALTH DISTRIBUTION....88 5.2. MATHEMATICAL NOTATIONS....91 5.3. LISTING PERMUTATIONS....92 5.4. VISUALIZATION....93 5.5. COUNTING EXERCISE....96 5.6. CODE FOR ENUMERATING ALL POSSIBILITIES (VERSION 1)....98 5.7. CODE FOR ENUMERATING ALL POSSIBILITIES (VERSION 2)....101 5.8. BOLTZMANN DISTRIBUTION....104 5.9. MATH: LAGRANGE MULTIPLIER METHOD....105 5.10. MATH: STIRLING'S APPROXIMATION....105 5.11. BACK TO THE BOLTZMANN DISTRIBUTION....108 Chapter 6: Revisiting Ideal Gas....112 6.1. A LITTLE BIT OF QUANTUM MECHANICS....112 6.2. DEGENERACY....114 6.3. PARTITION FUNCTION....120 6.4. AVERAGE ENERGY OF AN IDEAL GAS....124 6.5. VISUALIZING ENERGY LEVELS WITH DEGENERACY....125 Chapter 7: Revisiting Thermal Processes....128 7.1. REVIEW....128 7.2. THERMAL PROCESSES....131 7.3. CHECK....137 Chapter 8: Entropy, Temperature, Energy, and Other Potentials....138 8.1. ENTROPY....138 8.2. LAWS OF THERMODYNAMICS....140 8.3. TEMPERATURE AS A RATIO OF CHANGES IN ENERGY AND ENTROPY....140 8.4. IDENTIFYING B = 1/kBT....142 8.5. MATH: VOLUME OF A SPHERE....144 8.6. ENTROPY OF IDEAL GAS....148 8.7. ENTROPY OF IDEAL GAS, AGAIN....149 8.8. MOTIVATION FOR OTHER METRICS OF A THERMODYNAMIC SYSTEM....152 8.9. FOUR THERMODYNAMIC POTENTIALS: U,H, F,G....155 8.10. THERMODYNAMIC RELATIONS....159 SECTION III: Examples....162 Chapter 9: Two-State System....164 9.1. DYNAMIC CASE....173 9.2. EQUILIBRIUM POTENTIAL....175 9.3. ACTION POTENTIAL....180 9.4. DIODE....181 Chapter 10: Specific Heat....184 10.1. DEFINITION OF SPECIFIC HEAT....184 10.2. TWO-STATE SYSTEM....185 10.3. SIMPLE HARMONIC OSCILLATOR (SHO)....187 10.4. TEMPERATURE DEPENDENCE OF ENERGY AND SPECIFIC HEAT....190 10.5. EINSTEIN MODEL OF SOLID....191 Chapter 11: Random and Guided Walks....198 11.1. ONE-DIMENSIONAL RANDOM WALK....198 11.2. TWO-DIMENSIONAL RANDOM WALK....203 11.3. A TANGENT....206 11.4. GUIDED RANDOM WALKS....210 Appendix....220 APPENDIX A: GETTING STARTED WITH PYTHON....220 APPENDIX B: PYTHON PROGRAMMING BASICS....220 APPENDIX C: PLOTS....224 APPENDIX D: COLORS....227 APPENDIX E: ANIMATION....232 Epilogue....236 Index....238