The midterm questions are here midterm-solutions.pdf

Goals:

Question 1. What are probabilities for states, general properties, Boltzmann factor, and partition function. Used for a three level system, which is a simple extension of the two level system in the notes. The first two parts ask for basic understanding of the behavior of probabilities, but they can also be ansered via the mathematics. The third part needs the mathematics, but the work to be done is easy, since the partition function cancels.

Question 2. Did the students follow the derivations for the ideal gas? Does one know how to go from a partition function to the Helmholtz free energy? If not, they might have in their notes a formule relating entropy and a derivative of the logarithm of the partition function. Finally, given the formula for the entropy, can students use it to make a prediction?

Question 3. Using the heat capacity for a solid, do students know how it relates to the entropy. Do they know how to set up a Maxwell relation, which can be answered even if the first part of the question is not correct.

Outcome:

Question 1: About half the students did not know that the probability is the Boltzmann factor over the partition function, which surpirised me. I expected this to be the easiest problem. This needs discussion in terms of set-up, did they remember from 423, did they pick up in the first two weeks?

Question 2: This one was well done, and I expect that the note sheets students brought were very useful here. But almost all related the Helmholtz free energy to the partition function.

Question 3: Most students had the first part, although hardly anybody mentioned S=0 at T=0. Half the students had problems with Maxwell. Since we did not practice this very much at all, I am not surprised.

Results: 7 students scored in teh twenties,which in my grading is A level. 5 students scored in the range 15-19, which is B level, 3 students were 11-14 C-level and 2 students were below, D level. Rough average GPA 3.0

Total	P1	P2	P3
11	2	4	5
13	4	5	4
14	3	7	4
21	9	8	4
15	3	9	3
28	10	8	10
8	2	4	2
7	0	5	2
19	4	7	8
17	3	6	8
16	2	7	7
22	6	8	8
25	10	8	7
24	9	8	7
25	8	8	9
24	10	8	6
18	6	8	4