PHYSICS 425 & 625
THERMAL AND STATISTICAL PHYSICS [Homework] [return to main page].

Daily Notes, Most Recent on Top:

Week 15: December 5

Continue discussion of ideal quantum gases, with applications to black body radiation (Bosons) and electrons in metals (Fermions). Descriptive site for blackbody radiation. Site where you can do blackbody radiation calculations. Atmospheric IR calculator.

Take home portion of exam: take home the exam and correct it to regain 1/2 credit lost. Due on Thursday 8 December 2011.

Week 14: November 28

Discussion on Tuesday (by Ben Hatchett: I'm out of town, visiting Texas A&M) about binary phase transitions, especially as applied to water. Thursday we will work on Chapter 7.

My notes on water, and a direct derivation of the Clapeyron-Clausius relationship, based on the treatment by Enrico Fermi.

POW! Properties of water notes from this site.

Here is the 3D phase diagram discussion.

Week 13: November 21

Exam on Tuesday. No class Thursday. However, homework assignment due; read and devour chapter 7.

Week 12: November 14

Metallic Hydrogen Experiment! New results at megapressure.

Diamond anvil cell description, first image from this site.

Percy Williams Bridgman (interesting person!) studied high pressure physics, won a Nobel Prize.

Homework due on Tuesday and Thursday. Exam next Tuesday, Nov 22nd, see calendar on the homework page. Continue with Chapter 6, Boltzmann statistics, and begin with the Chapter 7, quantum statistics. We will look closely at two problems, 1) harmonic and anharmonic oscillators and diatomic molecules, and Maxwell Boltzmann distribution.

Potential energy review.

Morse potential: describes the H2 bond and its breakage.

Lecture on a quantum anharmonic oscillator like the H2 example we will look at.

Classical (top) and quantum harmonic oscillator modes (figure from this reference).

A harmonic oscillator in classical mechanics (A-B) and quantum mechanics (C-H). In (A-B), a ball, attached to a spring, oscillates back and forth. (C-H) are six solutions to the Schrödinger Equation for this situation. The horizontal axis is position, the vertical axis is the real part (blue) or imaginary part (red) of the wavefunction. (C,D,E,F), but not (G,H), are stationary states (energy eigenstates), which come from solutions to the Time-Independent Schrödinger Equation. From here.

The structure of the atmosphere. Note especially the exosphere and the probability for hydrogen to escape.

Week 11: November 7

FORTRAN ON THE MAC. (you can google gnufortran for other computer operating systems).

Homework due on Thursday, see calendar on the homework page. Continue with Chapter 6, Boltzmann statistics. Review the appendix on Quantum Mechanics, especially the hydrogen atom quantum numbers and degeneracy.

Prepare for exam on Tuesday, November 22nd, chapter 3 and 6.

Recent article on interstellar spectroscopy carrying on from the discussions we have had in class.


Week 10: November 1

Homework due on Tuesday and Thursday. Chapter 6, Boltzmann statistics. Review the appendix on Quantum Mechanics, especially the hydrogen atom quantum numbers and degeneracy.

Rubber band problem: Richard Feynman discusses it.


Here is a demonstration of it using a propane torch from the distrance to heat up the rubber band. Note that you could make a rubber band thermometer.


Old relative humidity gauges used human or horse hair!


Here is a discussion of the effect:

Hair hygrometer A hygrometer in which the sensitive element is a strand or strands of human hair, the length of which is a function of the relative humidity of the air. Hair is made from keratin, a protein that is wound into a coil. The turns of the coil are held together by a type of chemical bond called a hydrogen bond. Hydrogen bonds break in the presence of water, allowing the coil to stretch and the hair to lengthen. The bonds re-form when the hair dries, which allows people to style their hair simply by wetting it, shaping it, then drying it. A hygrometer measures humidity or the amount of moisture in the air. This is done by measuring the change in length of an organic fibre (e.g. human hair) brought about by the absorption of moisture. The Hair Hygrometer works on the principle that human (and horse) hair changes its length in accordance with the relative humidity of the atmosphere and not the vapour pressure. (from

How would you model this effect using thermodynamics?

Week 9: October 24

Optional Take Home Portion of the Exam:
1. Take home your exam.
2. Write up the problems missed as if they were a homework problem (on separate sheets).
3. Turn in your original exam with your corrections on Tuesday November 1st.
4. Regain up to 1/2 credit. Example: if you have a 74, can go to a 87 upon completion of the take home portion.
5. Open book, open notes; however, work on the exam by yourself.

Homework due on Tuesday and Thursday. Chapter 3. Calculations with the microcanonical ensemble. Relations of entropy, pressure, temperature, chemical potential, volume, particle number, and energy. Example problems.

Start reading chapter 6 next.

Week 8: October 17

Homework due on Thursday. Chapter 3. Calculations with the microcanonical ensemble; example of the Einstein solid heat capacity at low and high temperature. Calculation of entropy change example using thermodynamics.

Week 7: October 10

Homework due on Tuesday, midterm on Thursday (chapters 1 and 2).
Begin reading chapters 3, 6, and 7.

Watch water boil ...
Michael Faraday on how a candle works.
"... I want you now to follow me in this point - that whenever a substance burns, as the iron filings burnt in the flame of gunpowder, without assuming the vaporous state (whether it becomes liquid or remains solid), it becomes exceedingly luminous. I have here taken three or four examples apart from the candle on purpose to illustrate this point to you, because what I have to say is applicable to all substances, whether they burn or whether they do not burn - that they are exceedingly bright if they retain their solid state, and that it is to this presence of solid particles in the candle flame that it owes its brilliancy. ... "
Video on how a candle works ...

Uncalibrated optical spectra of a candle and an incandescent lamp.

Week 6: October 3

Homework due on Tuesday and Thursday.
Retrodiscussion: Heat Transfer. Thermal conductivity of an ideal gas.
Continued development of entropy: Einstein solid, Sackur Tetrode Equation - entropy of an ideal gas.

Week 5: September 26

Homework due on Tuesday and Thursday.
Chapter 2 presentation.
Chapter 2. Multiplicity, model systems using combinatorics, entropy calculation.
Basic definitions of heat and equilibrium. Maximum entropy -> equilibrium. Equilibrium -> maximum entropy.

Here is a model system, a random walk in 1 D. (Binomial distribution).

Binomial distribution from Texas A&M Stats

Week 4: September 19

Homework due on Thursday.
Continuing with chapter 1 and beginning chapter 2.
Topics: Introduction to entropy; heat capacity; enthalpy; Mathematics of Thermodynamics.
Tutorial for combinations and permutations.

Chapter 1 presentation

Week 3: September 12

Homework due on Thursday.
Continuing with chapter 1.
Topics: First law (energy conservation); heat capacity; enthalpy;
Chapter 1 presentation

Week 2: September 5

Continuing with chapter 1.
Topics: First law (energy conservation); heat capacity; enthalpy;
explanation of pressure; example problems .
Chapter 1 presentation
New Homework assignment.

Thermal vibration of a segment of protein alpha helix.
The amplitude of the vibrations increases with temperature.

This chapter in a nutshell.

Week 1: August 29

Read chapter 1. `
Chapter 1 presentation
We take a first pass at notions surrounding temperature. What is temperature, how do we measure it?
Thermocouples for large temperature ranges, solids, liquids, gases.
Thermistors for modest temperature ranges.
Doppler spectral width of absorption and emission lines and temperature.

Notice that we have already introduced the notion of the Maxwell-Boltzmann distribution of molecular speeds in a gas.
Very nice simulation of a gas.