Thermodynamics/ Statistical Mechanics Resource Packet (comments to:

Suggestions for 'Active' Classroom Learning

You may want students verify during class time the number of ways of distributing n units of energy among N distinguishable harmonic oscillators for small values of n and N . This is a prelude to the problem of entropy, energy and temperature. (Discussion of method).

When students have some ideas about the first law of thermodynamics, and some sense of dQ = TdS, they should be ready to work out for themselves in classroom groups how to come up with the temperature of a group of N distinguishable oscillators sharing n units of energy. (more details). A number of hints may be in order, depending on how the groups are progressing. The volume is constant so p dV =0. For S to change, either n or N will have to change. The problem can perhaps be stated in terms of a fixed amount of substance, so students realize that N must be constant. If studetnts are led to focus on the need for S to change, they should come to realize than n must change. There may still be some problem with the 'reduced' energy units being used. The dimensionless 'temperature' is in fact kT/e, where e is the size of oscillator energy steps. A change of 1 unit in n will lead to a change in S, and also a change in U. Then the way should be open to find the reduced temperature as (ds/dn)^(-1), with s = ln(number of ways).

The next level of difficulty is to connect two groups of identical oscillators (N1 and N2) which can initially have different amounts of energy (n1 and n2). Students can then be confronted in class with the question of where these two groups will come to equilibrium when energy units can be exchanged among them. Student ideas ought to be jelled by classroom discussion before they tackle the solution on a spreadsheet or other means (more details)

Exercises involving the boltzmann factor

A possible interpretation of thermodynamic potentials (after a Dan Schroeder post on phys-L).

(Students might be given one or two and asked to try and come up with one of the others.)

Equipartition of energy questions

Van der Waals

Miscellaneous questions