Thermal Physics Tutorials with Python Simulations

238 Pages·2023·34.961 MB·English

by  Minjoon Kouh, Taejoon Kouh

Thermal Physics Tutorial
with Python Simulations
This book provides an accessible introduction to thermal physics with computa-
tional 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.
This book may serve as a thermal physics textbook for a semester-long under-
graduate thermal physics course or may be used as a tutorial on scientific com-
puting 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.
Series in Computational Physics
Series Editors: Steven A. Gottlieb and Rubin H. Landau
Parallel Science and Engineering Applications: The Charm++
Approach
Laxmikant V. Kale, Abhinav Bhatele
Introduction to Numerical Programming:A Practical Guide for
Scientists and Engineers Using Python and C/C++
Titus A. Beu
Computational Problems for Physics: With Guided Solutions
Using Python
Rubin H. Landau, Manual José Páez
Introduction to Python for Science and Engineering
David J. Pine
Thermal Physics Tutorial with Python Solutions
Minjoon Kouh and Taejoon Kouh
For more information about this series, please visit: https://www.crcpress.com/
Series-in-Computational-Physics/book-series/CRCSERCOMPHY
Thermal Physics Tutorial
with Python Simulations
Minjoon Kouh and Taejoon Kouh
First edition published 2023
by CRC Press
6000 Broken Sound Parkway NW, Suite 300, Boca Raton, FL 33487-2742
and by CRC Press
4 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN
CRC Press is an imprint of Taylor & Francis Group, LLC
© 2023 Minjoon Kouh and Taejoon Kouh
Reasonable efforts have been made to publish reliable data and information, but the author and
publisher cannot assume responsibility for the validity of all materials or the consequences of their use.
The authors and publishers have attempted to trace the copyright holders of all material reproduced
in this publication and apologize to copyright holders if permission to publish in this form has not
been obtained. If any copyright material has not been acknowledged please write and let us know so
we may rectify in any future reprint.
Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced,
transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or
hereafter invented, including photocopying, microfilming, and recording, or in any information
storage or retrieval system, without written permission from the publishers.
For permission to photocopy or use material electronically from this work, access www.copyright.com
or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923,
978-750-8400. For works that are not available on CCC please contact mpkbookspermissions@tandf.
co.uk
Trademark notice: Product or corporate names may be trademarks or registered trademarks and are
used only for identification and explanation without intent to infringe.
ISBN: 978-1-032-25756-3 (hbk)
ISBN: 978-1-032-26343-4 (pbk)
ISBN: 978-1-003-28784-1 (ebk)
DOI: 10.1201/9781003287841
Typeset in SFRM font
by KnowledgeWorks Global Ltd.
Publisher’s note: This book has been prepared from camera-ready copy provided by the authors.
To our parents, Yong Woo and Byung Ok Kouh

Contents
Preface xi
Chapter 1(cid:4) Calculating π 1
1.1 ESTIMATING π WITH A POLYGON 3
1.2 ESTIMATING π WITH RANDOM DOTS 6
Section I Classical Thermodynamics
Chapter 2(cid:4) Kinetic Theory of Gas 13
2.1 GETTING STARTED 14
2.2 DERIVATION OF THE IDEAL GAS LAW 21
2.3 SAMPLE CALCULATION 22
2.4 FURTHER EXPLORATIONS 23
2.5 TEMPERATURE 26
Chapter 3(cid:4) Velocity Distribution 29
3.1 PARTICLE COLLISION 29
3.2 ONE-DIMENSIONAL EXAMPLE 30
3.3 MULTIPLE SOLUTIONS 33
3.4 FINDING SOLUTIONS WITH CODE 35
3.5 DISTRIBUTION OF ENERGY 43
3.6 DISTRIBUTION OF ENERGY AFTER MANY, MANY
COLLISION EVENTS 45
vii
viii (cid:4) Contents
3.7 DISTRIBUTION OF SPEED AFTER MANY, MANY
COLLISION EVENTS 51
3.8 NOTE ON A MORE AMBITIOUS CODING PROJECT 55
Chapter 4(cid:4) Thermal Processes 57
4.1 STATE AND PROCESS 57
4.2 PLOTTING AND NUMERICAL INTEGRATION 58
4.3 PV DIAGRAM 59
4.4 ADIABATIC PROCESS 60
4.5 PROOFOFPVγ =CONSTANTFORANADIABATOF
IDEAL GAS 61
4.6 CARNOT CYCLE 64
Section II Statistical Mechanics
Chapter 5(cid:4) Premise of Statistical Mechanics 73
5.1 ANALOGY: WEALTH DISTRIBUTION 73
5.2 MATHEMATICAL NOTATIONS 76
5.3 LISTING PERMUTATIONS 77
5.4 VISUALIZATION 78
5.5 COUNTING EXERCISE 81
5.6 CODE FOR ENUMERATING ALL POSSIBILITIES
(VERSION 1) 83
5.7 CODE FOR ENUMERATING ALL POSSIBILITIES
(VERSION 2) 86
5.8 BOLTZMANN DISTRIBUTION 89
5.9 MATH: LAGRANGE MULTIPLIER METHOD 90
5.10 MATH: STIRLING’S APPROXIMATION 90
5.11 BACK TO THE BOLTZMANN DISTRIBUTION 93
Contents (cid:4) ix
Chapter 6(cid:4) Revisiting Ideal Gas 97
6.1 A LITTLE BIT OF QUANTUM MECHANICS 97
6.2 DEGENERACY 99
6.3 PARTITION FUNCTION 105
6.4 AVERAGE ENERGY OF AN IDEAL GAS 109
6.5 VISUALIZING ENERGY LEVELS WITH
DEGENERACY 110
Chapter 7(cid:4) Revisiting Thermal Processes 113
7.1 REVIEW 113
7.2 THERMAL PROCESSES 116
7.3 CHECK 122
Chapter 8(cid:4) Entropy, Temperature, Energy, and Other
Potentials 123
8.1 ENTROPY 123
8.2 LAWS OF THERMODYNAMICS 125
8.3 TEMPERATURE AS A RATIO OF CHANGES IN
ENERGY AND ENTROPY 125
8.4 IDENTIFYING β = 1/k T 127
B
8.5 MATH: VOLUME OF A SPHERE 129
8.6 ENTROPY OF IDEAL GAS 133
8.7 ENTROPY OF IDEAL GAS, AGAIN 134
8.8 MOTIVATION FOR OTHER METRICS OF A
THERMODYNAMIC SYSTEM 137
8.9 FOUR THERMODYNAMIC POTENTIALS: U,H,F,G 140
8.10 THERMODYNAMIC RELATIONS 144