Course Content

Updated (almost) daily. Check here first if you need anything.

	Date	Deadlines, tests and reminders	In-class topics and materials	Textbook readings	Things to do after class
Lecture 1	Tue 11/01		Course organization and syllabus What is Thermal Physics? Binomial coefficient distribution (worksheet) Probability distribution of a large number of independent random variables: the central limit theorem Intro slides Worksheet 1: Binomial coefficients Jupyter file: the coin toss experiment Watch: The Galton Board YouTube video: another way to think about binomial coefficients	Schroeder 2.1	Read the course Syllabus. Another great YouTube video (by 3Blue1Brown) on Binomial distributions. The details relevant to us start at 5:40 if you want to skip ahead. Finally, if you are looking for a very basic intro to probability concepts, you can try this chapters 1 and 3 from this online textbook (highschool level) available from wikibooks.
Lecture 2	Thu 13/01		Finish Worksheet 1 Interactions: atoms moving between containers; energy moving between atoms Lecture notes, including slides and clicker questions with answers Worksheet 1 solution files: Jupyter code and output with some extra explanations and summary slides with answers and some more explanations. Solutions to the optional page of WS1.	We are covering this material in different order than the book. Don't worry if the details don't make sense to you yet, we will get to them. Schroeder 2.3 talks conceptualy about the same things as the lecture, but uses a different example (the Einstein solid, section 2.2) that we have not covered yet. You can read 2.3 for review of the concepts, or 2.2 and 2.3 together to get a more detailed view.	Work on the first Weekly Practice on WeBWorK (opens a new tab; you must be logged into Canvas to have this link take you to your Phys 203 WebWork).
Lecture 3	Tue 18/01	Weekly Practice 1 is due before class (9am).	Thermal equilibrium Thermodynamic limit Macrostates, microstate, multiplicity Lecture notes, including clicker questions and answers	Schroeder 2.1-2.3, for definitions mostly	Weekly Practice 1 solutions
Lecture 4	Thu 20/01		Temperature and beta Probabilities and the Boltzmann factor Partition function Lecture notes Practice with Boltzmann factors	Schroeder 6.1, 6.2 (pages 229-230 only)   :-)	Friday Jan 21 (tomorrow) is the last day to withdraw from a course without a W standing. EDIT: This deadline has moved. To withdraw from the course after Jan 21, contact Faculty of Science advising office.
Lecture 5	Tue 25/01	Weekly Practice 2 is due before class (9am).	Average energy Microscopic model of pressure Ideal gas law (derivation) Thermodynamics and functions of state Functional definition of temperature and a gas thermometer Equipartition theorem Lecture notes	Schroeder 1.1, 1.2, 6.3 Note on Schroeder's approach vs our approach: Since we were able to include the result of section 6.3 (average energy of a free, non-relativistic particle, equation (6.40)), we were able to derive the ideal gas law, rather than assume it the way the book does on page 12 Schroeder 1.3, 1.4, 1.5 (up to page 22)	Weekly Practice 2 solutions Start working on Problem Set 1
Lecture 6	Thu 27/01		*** start of material for test 2*** More on the equipartition theorem (details and clicker questions from last lecture notes) Work Ideal gas and work: worksheet 2, parts 1 and 2 *** end of material for test 1*** Worksheet 2: Compression work for ideal gas Worksheet 2 solutions, parts 1 and 2 (full solutions available with next lecture) Lecture notes	Schroeder 1.4, 1.5, 1.6
Lecture 7	Tue 01/02	Weekly Practice 3 is due before class (9am).	Heat capacity: first look, ideal gas only Finish WS2: part 3 work for an adiabatic curve How a car engine works Heat engines basic concept: efficiency Animation Worksheet 2 solutions (full) Worksheets 3 and 4: Heat engines Lecture notes	Schroeder 4.1 (up to and including equation (4.1) + figures 4.1, 4.2 and 4.3)	Weekly Practice 3 solutions
Lecture 8	Thu 03/02	Test 1: it will cover lectures 1-6, together with appropriate sections from Schroeder as listed above, worksheets 1-2 and Weekly Practice assignments 1-3. This table of constants from Schroeder will be provided with the test.	Test 1: 9am-10am (50 minutes + 10 minutes for uploads etc...). Invigilated via Zoom. Heat capacities (in general) and latent heat Heat engine example: Carnot cycle with ideal gas Lecture notes	Schroeder 4.3 (section on internal combustion engines only)	Solutions to Test 1 (problems) (Answers to the multiple choice questions can be accessed directly from the Canvas test 1 quiz).
Monday, Feb 7: Return to in-person learning.   (Current as of Jan 26, 2022) Lectures will take place in Henn 200.
Lecture 9	Tue 08/02	Weekly Practice 4 is due before class (9am). Problem Set 1 is due at 4pm.	Worksheet 3 Worksheet 4, qualitative analysis WS 4 computation (skipped) The Otto cycle efficiency: Worksheet 4 extension (skipped for now) Intensive vs extensive quantities A bit of a review: microstates, macrostates, fundamental assumption of Statistical Mechanics, the Law of Increase of Multiplicity, thermodynamic limit, beta and temperature Worksheets 3 and 4: Heat engines Lecture notes Worksheet 3 solutions Solutions to WS 4 WS4 extension, Otto cycle questions Solutions WS 4, Otto cycle questions	Schroeder 2.3 Schroeder 2.4 (page 60 only) Schroeder 2.6 (up to page 77) Schroeder 3.1 Schroeder 3.2 (section on The Macroscopic View of Entropy only) Schroeder: Extensive end Intensive Quantities, pg 163-164	Weekly Practice 4 solutions Problem Set 1 solutions
Lecture 10	Thu 10/02		Entropy and the Second law of thermodynamics Connection between entropy and heat capacities Reversible and irreversible processes, examples Pressure as a derivative of internal energy The (fundamental) thermodynamic identity Lecture notes A brief note on some calculus	Schroeder 3.4 Schroeder 2.6 (reversible and irreversible processes)
Lecture 11	Tue 15/02	Weekly Practice 5 is due before class (9am).	Entropy of the ideal gas Mixing and entropy, entropy of mixing, identical particles Lecture notes	Schroeder 2.6 (entropy of an ideal gas) Schroeder 2.4 (pg 60-62) Schroeder Fig 2.10 and the second sentence underneath Schroeder 2.6 (entropy of mixing) + Schroeder 2.5 (section of Multiplicity is covered on the Worksheet, section on Interacting gases is similar in spirit to PS1, Q3 and PS2, Q4)	Weekly Practice 5 solutions
Lecture 12	Thu 17/02		Approximations, Stirling's Approximation Multiplicity of the ideal gas The paramagnet in microcannonical ensemble (WS5, part 1) *** end of material for test 2*** Lecture notes Worksheet 5: quantum systems in microcannonical ensemble Worksheet 5, part 1, solutions Useful facts about Quantum Mechanics Optional Worksheet : Multiplicity of the ideal gas Solutions for the optional Worksheet	Schroeder 2.1 Schroeder 3.3 Schroeder 2.2
Mid-term break (Feb 21-25). Monday Feb 21 is Family Day and UBC is closed.
Lecture 13	Tue 01/03	Weekly Practice 6 is due before class (9am). Problem Set 2 is due at 4pm.	Brief review of the material so far (test 2 concept review) Worksheet 5, part 2 (Einstein solid) *** start of material for test 3*** Helmholtz free energy F: introduction Worksheet 5 solutions (both parts) Lecture notes	Schroeder 2.4 (pages 63-66: the book computes the multiplicity of the Einstein solid in the high temperature limit only, which makes the Stirling approximation harder to use; section on sharpness is similar in spirit to PS1, Q3 and PS2, Q4) Schroeder 1.6 (enthalpy) Schroeder 5.1 (up to page 155)	Weekly Practice 6 solutions Problem Set 2 solutions
Lecture 14	Thu 03/03	Test 2: it will cover lectures 6-12 (the first half of lecture 13 is a useful review), together with appropriate sections from Schroeder as listed above, worksheets 3 and 5 (Part 1) and Weekly Practice assignments 4-6 Practice material is posted on Canvas You might find the following formula sheet useful: page of formulas and data (it will be included with the test).	Test 2: 9am-10am Enthalpy H and Gibbs free energy G Free energy as available work Chemical reactions and batteries (as applications) Lecture notes (including a summary of how/when to use H, F and G to think about work and heat)		Solutions to Test 2 Friday Mar 4 (tomorrow) is the last day to withdraw from a course (with a W standing).
Lecture 15	Tue 08/03	Weekly Practice 7 is due before class starts (9am)	Thermodynamic identities Maxwell relations Free energy wants to be minimized Pressure from free energy Chemical potential and diffusive equilibrium Thermodynamic identities with change in number of particles Gibbs free energy and chemical potential Worksheet 6 : thermodynamic potentials meet calculus A simple proof showing that partial derivatives commute, needed for Maxwell relations (worksheet 6) Worksheet 6 solutions Lecture notes Worksheet 7 : thermodynamic potentials meet chemical potential and calculus Worksheet 7 solutions	Schroeder 5.1 (Thermodynamic Identities) Schroeder 5.2 Schroeder 3.5 (for chemical potential)	Weekly Practice 7 solutions If you want to know more about the mathematics of Legendre transform, check out this article.
Lecture 16	Thu 10/03		Phase transitions and phase diagrams Phase transitions and Gibbs free energy Clausius-Clapeyron relation Lecture notes	Schroeder 5.3 (pg 166-169, Clausius-Clapeyron)
Lecture 17	Tue 15/03	Weekly Practice 8 is due before class starts (9am)	Example: boiling water (worksheet 8) Vapour equation, vapour partial pressure and humidity More on phase transitions: graphite and diamond nucleation and boiling (optional) superheated and supercooled water (optional) Worksheet 8: Boiling water Worksheet 8 solutions Lecture notes More (optional) material in the lecture notes: The van der Waals equation and a model of gas-liquid phase transitions	Schroeder 5.3 (except for van der Waals model) Water behaving weirdly: Behaviour of water at its triple point: youtube video Supercooled water: youtube video Superheated water: youtube video One more phase diagram video, this time with nitrogen and its triple point: youtube video	Weekly Practice 8 solutions
Lecture 18	Thu 16/03		Heat engines: the general set-up and theory Heat engines on a T-S diagram (not in the book!) Refrigerators and the COP Real refrigerators and throttling (Joule-Thomson effect) *** end of material for test 3*** Lecture notes	Schroeder 4.1, 4.2 Schroeder 4.3 (except for steam engine) Schroeder 4.4
Lecture 19	Tue 22/03	Weekly Practice 9 is due before class starts (9am)	The steam engine (Worksheet 9) COP of a real refrigerator Back to stat mech: chapters 6 and 7 Review of cannonical approach to stat mech from the beginning of course Boltzmann factor and probabilities Partition function Spectrum, multiplicities Average energies (magic formula) Lecture notes Worksheet 9: the steam engine Worksheet 9 full solutions (the order of questions on this version is different, but the questions/answers are all there).	Schroeder 4.3 (steam engine)	Weekly Practice 9 solutions
Lecture 20	Thu 24/03	Test 3: it will cover lectures 13-18, together with appropriate sections from Schroeder as listed above, worksheets 6-8 and Weekly Practice assignments 7-9. Practice material is available on Canvas. You might find this page of formulas and data. useful (it will be included with the test).	Test 3: 9am (length: 1 hour) Partition function and (Helmholtz) free energy Average energy at fixed temperature (cannonical ensemble), example: paramagnetism Partition function of composite systems (distinguishable particles) Lecture notes Worksheet 10: Averages and composite systems Worksheet 10 solutions Another optional Worksheet: Free energy from the partition function Solutions for the optional Worksheet	Schroeder 6.1 Schroeder 6.2 (without paramagnetism or rotation of diatomic molecules sections) Schroeder 6.5 (details of the proof are optional, presented in the optional Worksheet)	Solutions to Test 3
Lecture 21	Tue 29/03	Weekly Practice 10 is due before class (9am)  Problem Set 3 is due at 4pm.	Continuous random variables and the probability density Proof of the equipartition theorem (again) Speed distribution for a particle in one dimension Speed distribution for a particle in three dimensions (Maxwell Speed Distribution) Lecture notes Worksheet 11: Speed distribution in a 3D gas Worksheet 11 solutions	Schroeder 6.2 (without rotation of diatomic molecules section) Schroeder 6.3 Schroeder 6.4	Plots of the Maxwell distribution (useful for Weekly Practice 11) Weekly Practice 10 solutions Problem Set 3 solutions
Lecture 22	Thu 31/03		Partition functions of distinguishable vs indistinguishable particles Partition function of a dilute composite system of N indistinguishable particles The partition function and thermodynamics of the ideal gas Worksheet 12: ideal gas in a cannonical ensemble Worksheet 12 solutions Lecture notes	Schroeder 6.6, 6.7 (The textbook does a fully quantum mechanical treatment of the ideal gas in equations (6.75)-(6.79), before changing the sum to an integral which in effect takes the classical limit. This technique is not required material for the course.)
Lecture 23	Tue 05/04	Weekly Practice 11 due before class starts (9am)	More on indistinguishable particles Bosons and fermions The Gibbs factor and the grand partition function The Fermi-Dirac distribution (page 1 of Worksheet 13) The Bose-Einstein distribution (page 2 of Worksheet 13) Lecture notes Worksheet 13: FD and BE distributions Worksheet 13 solutions	Schroeder 7.1, 7.2	Weekly Practice 11 solutions
Lecture 24	Thu 07/04		Density of normal modes Density of states Quantum gases (applications of FD and BE distributions): Noninteracting fermion gas at T=0 (Worksheet 14, page 1) Metals, electron bands, insulators, semiconductors Blackbody radiation (Worksheet 14, page 2) The Earth and the Sun (Worksheet 14, page 3, optional) Sample normal modes animation Lecture notes Worksheet 14: Quantum gases (we only covered pages 1 and 2) Worksheet 14 solutions Black body radiation simulation Worksheet 15: Degenerate electron gas (optional, a much extended version of page 1 of worksheet 14) Worksheet 15 solutions Another optional worksheet: Computing densities of states Solutions for the optional Worksheet above	Schroeder 7.4 Schroeder 7.3 (selected)	Quantum gases (photons and electrons) practice: (Weekly Practice 13 and the old Problem Set 5, not for credit, and the solutions), focusing on Black Body Radiation and the cold non-interacting fermion gas Tomorrow, Fri April 8, is last day of classes    Problem Set 4 is due on April 20. Solutions will be posted on April 21 (see below).
Exam period is April 12-27 inclusive, including Saturdays and Sundays. Our exam has been scheduled for April 27 at noon.
UBC will be closed Friday April 15 and Monday April 18 for Easter long weekend.
After classes end		Weekly Practice 12 is an optional, bonus WW due Tuesday April 12. The grade will be used to replace a lower scoring WW (if any). Weekly Practice 12 solutions Problem Set 4 is due on April 20 (extended deadline). Problem Set 4 solutions posted April 21. Test 2 and 3 reflection assignments are due anytime before the final exam. Final Exam info and study materials. Monday office hours will continue (Zoom, 3:30-4:30 pm). Information on additional pre-exam office hours and TA help sessions will be available on Canvas (check the Announcements).
Final Exam	Wed 27/04	Time: 12:00 (noon) Duration: 2.5 hours Location: LSK 201 Format: Similar to the Tests A formula sheet will be provided. Reviewing practice material posted on Canvas (link above) is strongly recommened.