Phys301 - Fall 2009

Exam 3 is a take home exam. It can be downloaded here: PHYC-301-Exam-3

Instructions:

• You must submit your completed work by 5:00 PM on Wednesday 25 November 2009
• You may use your own notes, the course lecture notes, and your textbook for reference
• You must work alone.  The work you submit must be yours and yours only.

The second exam is on Monday, in class.  It has four problems, each with two parts, and you will have 90 minutes to complete the entire thing.  I recommend bringing a calculator because there is one problem in which you have to compute actual values.  You may bring a page of reference notes with you to the exam.

The exam will focus on:

• Thermodynamic Identities: you should be able to derive the thermodynamic identity for the enthalpy and the free energies, including being able to determine the natural variables of a thermodynamic quantity and using the slope rule to relate properties like temperature, pressure, etc. to partial derivatives of the thermodynamic potentials.
• Equilibria and Entropy Maximization: you should be able to find properties like the pressure, temperature and chemical potential from an entropy function.  And, you should be able to determine the equilibrium properties of two systems that are in thermal, mechanical, or diffusive contact.
• Spontaneity: you should be able to predict whether a process occurs from the appropriate type of free energy (for example, using the Gibbs energy when at constant pressure and constant temperature).

Good luck studying, and don’t hesitate to email me if you have any questions.

Exam Results

I was very happy with the outcome of the exam.  For the most part, everyone did very well. Congratulations!

A copy of the exam solutions can be downloaded here: Exam 2 Solutions

If you want to measure how you did relative to the class, here a histogram of the results:

I’ve posted a new copy of the notes from Lecture 14. The original version had a mistake in which I accidentally dropped a negative sign in the relationship between the pressure, energy and volume: P = -dU/dV. Everything is now fixed, and the “cycle rule” of partial derivatives is used to fix all the signs… exactly as we solved the problem on the board in class today.

You can download the new version from the “Lecture Schedule” page… or directly from This Link to the Corrected Notes

Exam 1 covers Lectures 1-9 (including entropy and the definition of temperature).  The exam is closed book and will take place during the normal lecture time on Friday the 18th.   You may bring a sheet of paper with anything you want written on it.

Review Session
I scheduled Room 190 from 11:00 AM - 1:00 PM for the exam review session. Room 190 is the conference room next to the main lobby. See you there.

Exam Results
A scanned copy of my solutions to the exam problems can be downloaded here: Exam-1 Solutions.  In most cases, there were only a few equivalent ways to solve the problems.  This is especially true for question 1, which concerned the first law of thermodynamics as applied to expansion and compression work for the ideal gas.  There were multiple ways to solve some of the questions in the second problem.  When you get your exam back, you will notice that I worked through all of your answers and propagated your results through the questions.  This way, if you made a mistake on part (a), I didn’t count it against you in part (b), (c), … if you did those parts correctly.  In other words, there was no double-jeopardy.

Overall, I was rather happy with the outcome. If you would like to know how you did relative to the class.  Here are some of the essential statistics:

Average: 82%
High Score: 105

And here is a histogram:

Since your overall grade in the class depends on a number of factors (homework, other exams, class participation), it does not make sense to associate a letter grade with the exam scores.  However, roughly speaking, the categories in the histogram correspond to the usual letter grades.

If you got a 95% or better, you should be extremely satisfied with your work- Excellent job.  I would consider that to be A+ work.   If you scored ≤65%, then you need to be concerned, especially if your problem set grades are not especially high.  I would suggest that you come talk to me.

Good news… problem set 3 just got a little shorter. You can skip part (1.4). Don’t forget to post questions if you have any.

I have started to get a few questions concerning problems 2 and 3. Good. I’m glad to see that everyone is working on them!

I have a couple hints:

1. Yes, I know that you cannot simply plug in a rate of 10^20 into your computer and expect it to calculate the factorial.  My suggestion is to plot the Poisson distribution for a couple examples and look for the trend.  Try plugging in r=10 and plotting the data from n=0..100.  Then try plugging in r=100 and plotting the data from n=0..1000.  Look at the plot to see where the mean is located, and pay attention to how the standard deviation is changing.  Then extrapolate your result up to a very high rate.
2. Problem 2.4 and the first half of 2.5 are worked out completely in the lecture notes from Lecture 1.  Remember: normalization means that if you add up the probabilities for all possible outcomes, then the result is 1.
3. If you have not done Gaussian integrals before (although I know you have— professors talk) there is some very helpful information in Appendix B of Schroeder (entitled “Gaussian Integrals”)

Some more questions have come up concerning Gaussian integrals.  Here are a couple more hints

1. The integral
   is given to you, but if you would like to see how to compute it (the method is based on squaring the integral and transforming to polar coordinates where the integral can be done by parts followed by taking the square root of the result) is discussed on pp. 384-5 of Schroeder.
2. To evaluate the integral for the expectation value
   
   use a u-substitution u = x - x0 (along with du = dx).  This will give you two integrals, one of which is just the constant x0 times the same Gaussian integral you solved to show that the distribution is normalized.  The other integral will be the product of an odd function with an even function, so you should be able to compute it by symmetry arguments.  Otherwise, you can do integration by parts.
3. To compute the integral for the variance, I suggest differentiating both sides of the basic Gaussian integral
   to find the solution for the second moment.  This approach is detailed on pg. 386 of Schroeder, and it is a useful technique to learn because it can be used to evaluate a lot of integrals that show up in physics.

Don’t forget that I also encourage you strongly to work in groups and discuss the problems.

If you would like to join in on the discussion, one way to do that is to submit comments to this blog post (you will need to register for the website in order to leave comments).

By popular request, problem sets will be due on Mondays instead of Fridays this semester. So, Problem Set 1 is now due this coming Monday, 31 August 2009.

We will have our first problem session today at noon in Rm 184. Since we will use the time to start working through some of the problems in Problem Set 1, it will help if you print out a copy of the first homework and bring it with you.

Welcome to the course website and blog for PHYC-301: Thermodynamics and Statistical Mechanics. This site serves as the primary online resource for the course. Information about the syllabus, lectures, problem sets, and exams can be found here.

Statistical mechanics is probably my favorite topic in all of science because of the way that it brings together concepts from many fields: physics, mathematics, chemistry, and engineering.   I’m looking forward to the semester and hope that you are too.

We’re going to get started right away.  So, don’t forget to check the site regularly to look for updates.  For example, you should come prepared to each class having looked through the notes for the day (they will be available from the “Lecture Schedule” link on the right navbar).

If you have any questions, or comments, be sure to post them on the blog (instructions for how to register are on the course info page).  My hope is that this blog will facilitate discussions and allow you to get answers to your questions as fast as possible.