PHYS 416 Class Info

This page contains links to information for the PHYS 416 course (Thermal and Statistical Physics).

Last time I taught a similar class (including tests with solutions).

To get an excused absence for a test, it must be official through the Office of the Dean of Students.

TEST 1 will be Thur Oct 2 and will cover Chap 1 through Chap ??. Bring your book and a nongraphing, dumb calculator (can only do logs, trig functions, exponentials, powers, roots; one or two line TI-30X and TI-36X models; if you are uncertain, ask me; similar to this rule).

TEST 2 will be Thur Nov 20 and will cover Chap ?? through Chap ??. Bring your book and a calculator.

FINAL will be ??? from ???-??? in PHYS??? The final will be comprehensive. Bring your book and a calculator.

The text book for the class is An Introduction to Thermal Physics by Daniel V. Schroeder. The tests are open textbook so you must have access to a physical copy (not electronic because you can't have open laptop during test); printout of relevant pages are OK as long as they only have info from the book.

See warning at https://physics.weber.edu/thermal/ about abridged international versions! Beware!!

We will cover most of Chaps 1-7. Course description.

Syllabus

Office hours: Wednesday 2:00-3:00, Thursday 2:00-3:00 (Contact me by email if you want to arrange a special time.)

Homework will be due by midnight on Thursdays. You must show enough work on the homework so the grader can understand what you're doing. Upload a single pdf of your homework into brightspace before 11:59 pm

Jupyter notebooks used in this class Download the notebook you want from github and then upload it to your JupyterLite environment in your browser (or into Jupyter installed on your computer). Links in the class notes are directly to particular notebooks.


Chap 1,
Chap 2, einstein_model.xls, einstein_model.xlsx, einstein_model_class.xlsx, einstein_model_1sys.ipynb, einstein_model.ipynb, max_product.ipynb, vol_multidum_sphere.ipynb, max_boltz_vs_number.ipynb, scatter_boltz.ipynb,
Chap 3, paramagnetic.ipynb,
Chap 4,

Fundamentals: k_B = ?; T_K = ? for room, sun, coldest; M of N₂?; Atm. Pressure; Size of atom/molecule; Number density of atoms/molecules in air/liquid/solid; units of concepts (for example, specific heat, latent heat, enthalpy, entropy...), Stirling's approximation

Very short answers to the homework will be posted in brightspace under the content button in brightspace. These are the steps I used to solve. There are not a lot of intermediate steps, but it might help with understanding what you did incorrectly.

HWK 1 (Due Thu Aug 28, 9 problems total):
Chap 1: 1, 4, 12, 14, 16, 17 (for part d just use the 100 and 600 K points to get a and b and see how much error is at 300 K), 21, 23, 28(see specific heat pg 28 C=4.2 J/(degC g))


Remind me to give some numbers that you can check your codes if I forget.

HWK 2 (Due Thu Sep 4, 8 problems total): (example spread sheets: einstein_model.xls, einstein_model.xlsx, einstein_model_class.xlsx) Also, for the cases where you're asked to print out spread sheets that would have ~100 rows, only print out every ~10th row so you don't need reams of paper. You can also modify einstein_model_1sys.ipynb or other codes for several problems.)
Chap 2: 1, 3, 5 (only a, f, g), 8 (get numbers for the probabilities as well as expressions), 9, 11 (for prob 2.11, do one table using the parameters in the book AND one where there are 100 and 300 paramagnets with 80 energy units. To check your code using book numbers, (10,70) gives probability 3.164E-22, (20,60) gives probability 4.585E-12, and (30,50) gives probability 1.844E-6). (Hint: this is not the Einstein model but you can still figure out the multiplicity of each subsystem.)
Prob 7) Compare the multiplicity of N harmonic oscillators and N two state paramagnets with the same number of excitations, q, above the ground state. a) Get the expressions for the number of microstates in the two cases. b) For N = 100, how many excitations q are needed for the number of microstates to differ by 10%? (For the difference, I took the difference divided by the average. You probably should just compare numerically. For N=200, the relative difference goes above 10% at q=6.) c) Repeat for N = 1000. d) Explain why the two systems have similar microstates over the range of q in parts b) & c). (Hint: Can a paramagnet have 2 excitations? How many excitations can you have before this condition becomes important?)
Prob 8) For 3 harmonic oscillators, a) compute the natural log of the number of microstates vs q in a table up to q=10. b) As a completely pointless, random, make work project, compute the reciprocal difference
diff(50) = 1/[ln(Omega(3,50))-ln(Omega(3,49))] (that is N=3 and q=50 and 49)
c) Repeat for diff(100) and diff(200). d) How is this value related to q? (Fun bonus: You might want to explore the behavior for different number of harmonic oscillators) (To test your code, for 4 oscillators for q=10 gave Omega=66 and ln(Omega) =4.190; for N=4, I got diff(50)=17.162, diff(100)=33.831, diff(200)=67.165 (a totally random, pointless observation: these numbers are close to 51.5/3, 101.5/3, and 201.5/3).

HWK 3 (Due Thu Sep 11, 8 problems total):
Chap 2: (13 &14 will count as one problem), 17, 19, 21 (also find an approximation to the large N form as a Gaussian in terms of the variable z-1/2  and plot this Gaussian with the original function [I find a large difference for N=1, modest difference for N=10 in the wings, and the rest have the Gaussian roughly indistinguishable from the original function); max_product.ipynb might be useful), 22, 24 (change part d to "What is the probability to obtain more than 500,000 heads? Repeat for 501,000 heads. Repeat for 502,000 heads." give your answers to 6 significant digits [you should find slightly less than 1/2 for 500,000 heads]), 26, 27

HWK 4 (Due Thu Sep 18, 10 problems total):
Chap 2: 28 (give the answers in scientific notation, for example 3.27E6), 29 (see Fig 2.5), 33, 36
Chap 3: 1, 3, 5, 17 variation (instead of repeating Table 3.2, make the same table [except don't do last column] for N=200)
Prob 9) Repeat prob 2.29 with N_A=30 and N_B=20 and q=500. Determine the q_A for the maximum probability macrostate.
Prob 10) System a is 100 harmonic oscillators with energy E_a = h f q_a where q_a is the number of excitations in System a. System b is 200 two state systems where E_1 = 0 and E_2 = 2 h f. The energy in System b is E_b = 2 h f N_2 where N_2 is the number of excitations in System b. The two systems are in thermal contact so they can exchange energy. a) Write out the formulas that determine the total multiplicity of each macrostate. Label the macrostate by N_2. b) What fraction of the energy is in System a when the total energy is E = h f  100? b) Repeat for E = h f 200 and E = h f 400. I expect the answer in scientific notation with specific numbers. c) Explain why in equilibrium, the average energy in system b can't be larger than N_b h f. [Hint: After setting out the condition to get the E_a, I solved for the values numerically.]