As Taught In:
2021/2022
Level:
undergraduate
Learning Resource Types:
=> Problem Sets
=> Readings
=> Slides
Course Overview:
This is an introductory course on Statistical Mechanics and Thermodynamics given to final year undergraduates. They were last updated in May 2016.
This course offers an introduction to probability, statistical mechanics, and thermodynamics. Numerous examples are used to illustrate a wide variety of physical phenomena such as magnetism, polyatomic gases, thermal radiation, electrons in solids, and noise in electronic devices.
This course is an elective subject in most of undergraduate energy studies minor. This institute-wide program complements the deep expertise obtained in any major with a broad understanding of the interlinked realms of science, technology, and social sciences as they relate to energy and associated environmental challenges.
Prerequisites:
Physics 104 – Introduction to Quantum Mechanics
Mathematics – Differential Equations
Textbooks:
There is no reference textbooks. However, there are recommended readings, notes selected topics, and slides. Please refer to the “Readings’ tab that you may wish to discuss.
There is no shortage of textbooks on statistical mechanics and thermodynamics aimed primarily at physicists. I have about 4 feet of them on the bookshelf above my desk. This is not because the subject has been evolving. With the exception of the realization of physical systems that are very close to non-interacting Bose gasses and exhibit Bose-Einstein condensation, the topics covered have remained essentially the same for the past 60 years. Rather, few people are completely satisfied by the way the material is presented and enterprising physicists will want to have a go at it themselves.
The following texts are the ones I believe will be the most useful references for Statistical Physics and beyond.
- Zemansky, M. W., and R. H. Dittman. Heat and Thermodynamics. McGraw-Hill Science, 1996. ISBN: 9780070170599.
A classic undergraduate textbook on thermodynamics at about the same level as Physics 107. Some learners may appreciate the lengthier discussion of thermodynamics and the numerous examples treated throughout the text.
- Baierlein, Ralph. Thermal Physics. Cambridge University Press, 1999. ISBN: 9780521590822.
This was used as a required text in Statistical Physics for the past several years.
- Blundell, Stephen, and Katherine M. Blundell. Concepts in Thermal Physics. Oxford University Press, 2009. ISBN: 9780199562091.
Similar in content and level to the Baierlein book above, but I think a bit better. Score one for Oxford.
- Kittel, Charles, and Herbert Kroemer. Thermal Physics. W. H. Freeman, 1980. ISBN: 9780716710882.
A popular undergraduate textbook at the level of Physics 107. It does not follow the development we use (I think it jumps around a lot), but the alternative discussions of individual topics may be helpful to some learners.
Topics will be:
Lec 01 : Probability Random Variable
Lec 02 : Probability Functions of a Random Variable
— Problem Sets 01
Lec 03: Probability Sums of RVs and Central Limit Theorem
Lec 04: Thermodynamic Variables and State Functions
— Problem Set 02
Lec 05: The First Law and Paths
Lec 06: Statistical Mechanics and the Micro-canonical Ensemble
— Problem Set 03
Lec 07: Entropy, Temperate and the Second Law
Lec 08: Entropy as a Thermodynamic Variable
— Problem Set 04
Lec 09: Maxwell Relations and Thermodynamic Potentials
— Problem Set 05
Lec 10: Heat Engines and Carnot Cycles
Lec 11: Derivation of the Canonical Ensemble
— Problem Set 06
Lec 12: Examples Using the Canonical Ensemble
Lec 13: Polyatomic Gases
— Problem Set 07
Lec 14: Black Body Radiation
Lec 15: Paramagnets
— Problem Set 08
Lec 16: Quantum States of Mary-particle Systems
— Problem Set 09
Lec 17: Chemical Potential and Grand Canonical Ensemble
Lec 18: Density of States and Free Fermi Gas
Lec 19: Stellar Configurations and White Dwarfs
— Problem Set 10
Lec 20: Interesting and Counter-Intuitive Examples
Lec 21: Bose-Einstein Condensation
— Problem Set 11
Sources of Reading from below:
[B] = Blundell, Stephen, and Katherine M. Blundell. Concepts in Thermal Physics. Oxford University Press, 2009. ISBN: 9780199562091.
[S] Strickler, S. J. “Electronic Partition Function Paradox.” Journal of Chemical Education 43, no. 7 (1996): 364.
[Z] = Zemansky, M. W., and R. H. Dittman. Heat and Thermodynamics. McGraw-Hill Science, 1996. ISBN: 9780070170599.
—————————–
[B] Chapter 3: Probability >> Lec 01
[Z] Chapter 1: Heat and Thermodynamics & [B] Chapter 6: Partial Derivative & Chapter 7: Exact Differentials >> Lec 04
[B] Appendix C 6: Energy & Appendix C 7: Isothermal & Adiabatic Processes >> Lec 05
[B] Appendix C 8: Volume of a Hypersphere >> Lec 06
[B] Section 4.1-4.5: Statistical Definition of Temperature >> Lec 07
[B] Chapter 16: Thermodynamic Potentials >> Lec 09
[B] Chapter 13: Heat Engines and the Second Law >> Lec 10 & 11
[B] Section 20.2: Obtaining the Functions of State, Section 21.6: Heat Capacity of a Diatomic Gas, & [S] Journal of Chemical Education p.364 >> Lec 13
[B] Section 23.1-23.7: Black Body Radiation >> Lec 14
[B] Section 22.1-22.5: Chemical Potential and Grand Canonical Ensemble >> Lec 17
[B] Section 22.1: Density of States, & Section 30.2: Fermi Gas >> Lec 18
[B] Section 36.1-36.4: Compact Stellar Objects >> Lec 19
[B] Section 30.3-30.4: Bose Gas and BEC >> Lec 21
Problem sets are due as indicated on the course section. The problem contributes 20% toward the final grade. One of the 11 problem set grades, the lowest, will be dropped at the end of the term.
Also, there will be two analysis problems during the term given during the lecture times. Each contributes 40% toward the final grade. There will be a three hour final analysis during the spring exam period. It will constitute 40% of the grade.