Statistical Mechanics

Spring 2016

Go to **home page for Ph12b**

**Course description: **An
introductory course in statistical mechanics.

**Class meetings**:
Tuesday and Thursday 10:30-11:55 am in **269
Lauritsen**, starting March 29, 2016.

**Feedback:** If you want to send a
comment about the course, click here.

**Instructor: **

John Preskill, preskill(at)caltech(dot)edu, 206 Annenberg.

**Recitation leaders: **

Kung-Yi Su, ksu(at)caltech(dot)edu, Wednesday
6:30pm-8:30pm in 11 Downs.

Brenden Roberts, broberts(at)caltech(dot)edu, Recitations
Monday 6:30pm-7:30pm in 11 Downs. Office hours Wednesday
2:30pm-3:30pm in 240 Lauritsen.

**Graders:
**Vijay Varma, vvarma(at)caltech(dot)edu, Assignments 1, 3, 5, 7.

Mykyta Hulko, mhulko(at)caltech(dot)edu, Assignments 2,
4, 6, 8.

**Textbook: ***Thermal
Physics (2 ^{nd}
edition)* by Charles Kittel and Herbert Kroemer

We will cover most of the first 10 chapters of Kittel and
Kroemer, plus part of Chapter 14 and some supplementary material.

**Grading:** Grades will be based
on weekly problem sets (40%), a midterm (20%), and a final exam (40%).

**Homework: **Problem sets will be
posted on this page on Thursday, and will be due in the **Physics 12c IN-box**
by the East Bridge mailboxes at 8:00 pm the following Thursday. Graded homework
will be returned to the **Physics 12c OUT****-box** in 264 Lauritsen by the following
Wednesday morning. Solution sets will be posted on this page.

**Extensions:
-- **Unexcused late homework will be accepted for half credit up until
one week after the due date; there is no credit if your assignment is more than
one week late.

-- If your homework will be late for a good reason, you may request an extension before the assignment is due by sending email to that week’s grader.

-- One extension, for up to one week, is allowed without question (your silver bullet). Please put a note at the top of your problem set indicating that you are using your silver bullet.

**Honor Code: **Discussion with
others is encouraged, but the work you hand in must be your own. In particular,
do not use homework solutions from previous years or exams and exam solutions
from previous years. Please write legibly. You may use a symbolic manipulation
tool such as *Mathematica *or *MATLAB* for doing computations on
homework or exams, though this probably won’t be necessary.

**Twitter: **I’ll attempt to
summarize each lecture in 140 characters or less. See the #Ph12c
tweets.

**Lectures
**(tentative schedule)**:**

- Mar 29. Counting states (lecture notes)
- Mar 31. Entropy and temperature (lecture notes)
- Apr 5. Boltzmann distribution and free energy (lecture notes)
- Apr 7. Ideal gas, mixing (lecture notes)
- Apr 12.
Planck distribution (lecture notes, plus supplement)
- Apr 14. Debye theory, Johnson-Nyquist noise (lecture notes, plus supplement)
- Apr 19.
Chemical potential, Gibbs distribution (lecture
notes, plus supplement)
- Apr 21. Indistinguishable particles, thermodynamics of ideal gas (lecture notes)
- April 26.
Fermi gases (lecture notes)
- April 28.
Bose-Einstein condensation (lecture
notes)
- May 3. BEC continued (lecture notes, BEC homepage, Physics World March 1997)
- May 5. Heat engines, laws of thermodynamics (lecture notes)
- May 10. Gibbs free energy (lecture notes)
- May 12. Equations of state (lecture notes)
- May 17. 1
^{st}and 2^{nd}order phase transitions (lecture notes) - May 19. Ferromagnetism (lecture notes)
- May 24. Landau theory of phase transitions and scaling
- May 26. Kinetic theory (lecture notes)
- May 31. Diffusion and viscosity (lecture notes)
- Jun 2. Maxwell’s demon (lecture notes)

**Typed
Lecture Notes: **Courtesy of
Sam Elder (2010), available here.

**Lecture
Videos: **Recorded in 2011,
available at this
YouTube Channel.

Also available here, as mkv files, which you may download and play on your own computer. The lectures this year will be somewhat different than in 2011, but the videos may be useful if you miss a lecture.

**Ombudsfolks****:**: Julia Deacon, Arjun Goswami, Stephanie Kwan, Marc Muhleisen.
Contact John Preskill to volunteer.

**Homework
assignments:**

Problem
Set 1, due Apr 7. Probability and fluctuations. Solutions.

Problem
Set 2, due Apr 14. Boltzmann distribution. Solutions

Problem
Set 3, due Apr 21. Black body radiation. Solutions

Problem
Set 4, due Apr 28. Chemical potential. Solutions

Problem
Set 5, due May 12. Quantum gases and heat engines.
Solutions

Problem
Set 6, due May 19. Phase coexistence. Solutions

Problem
Set 7, due May 26. Critical phenomena and scaling.
Solutions

Problem
Set 8, due Jun 2. Kinetic theory and diffusion. Solutions

**Exams:**

Midterm
Exam, Covers all material through Problem Set 4. Solutions

54 exams were received. The median was 83, the mean was 82, the
standard deviation was 14. 12 students scored 95 or above,
and 4 scored 100.

Final
Exam, due June 10. Covers all material in the course.
Solutions

52 exams were received. The median was 82 and the mean was 80. 11 students
scored in the 90s, and the highest score was 97.

**Grades:**

Final grades were determined using the formula Grade = 0.4(Homework) +
0.2(Midterm) + 0.4(Final).

The median final grade was 86 and the mean was 84.

The ranges for letter grades were:

A+ 95-100

A 90-94

A- 85-89

B+ 80-84

B 75-79

B- 55-74

The distribution of letter grades for the course
was:

8 A+, 14 A, 7 A-, 9 B+, 9 B, 5 B- (52 total)

I hope you enjoyed
Ph 12c and learned a lot. If you have not already
done so, please review the course by responding to the TQFR survey. Your
feedback is very helpful, especially if you have suggestions for improving the
course. In particular, I would like to know: whether you liked the book,
whether the online notes and videos were useful, whether the lectures were too
much like the book, whether the homework helped you to learn, whether the
recitations were effective, whether the exams were reasonable and the grading
was fair... Or whatever else you think is relevant.

One other thing …
A few of you mentioned in the TQFR comments that the Sam Elder notes contain
serious typographical errors. It would be helpful if someone could point out
the errors, either in an email to me, or by filling out the anonymous comment
form on this page.

Thanks, and have a great
summer.