Physics 75: Thermodynamics and Statistical Mechanics (Fall 2001)
Announcements
9/27/01: The final exam date has been set by the registrar:
Monday, Dec. 17, 2-5 pm in Merrill 211.
Instructor
Professor Will Loinaz
Office: 223 Merrill Science Center
Phone: (413) 542-7968
email: waloinaz@amherst.edu
Office Hours: My office hours for both Physics 16 and Physics 75 are
tentatively Monday 1-3, Thursday 10-11, Friday 4-6. Right now it's first-come,
first-served, but if I tend to be swamped with Physics 16 students all the time
I'll institute a priority system and give you top priority at some block of
hours.
Course Information
Course Description
This course covers introductory thermodynamics and statistical mechanics,
including:
- Laws of thermodynamics with applications to various physical systems
- Entropy
- Introductory kinetic theory and statistical mechanics
- Applications of Fermi-Dirac and Bose-Einstein statistics
- Applications to low temperature physics, perhaps including superconductors
and liquid helium
- Phase transitions
- Nonequilibrium phenomena, such as percolation, neural networks, chaos, ...
Schedule
MWF 10-11, Th 11:30-12:30 in 209 Merrill Science Center
Prerequisites
Physics 35 or the equivalent, or my permission.
Course requirements
- Attendance:
There are only a few of you. If you don't show up,
I'll notice. If you know in advance that you must miss class, please do
me the courtesy of informing me, if possible.
- Homework:
I'll assign and grade homework weekly. Baierlein has some
nice problems and I'll assign some from there, but I'll draw from
other sources as well. I'll distribute the homeworks and solutions in
class. I'll try to post the assignments and solutions
on the web, as well as any corrections, hints, or elaborations that
might be necessary. However, I don't
guarantee that everything I say in class will make it onto the website in
a timely manner. You are encouraged to discuss homework problems; however,
the final writeup should be your own. Tentatively I expect to make the
homework due on Friday at 11:59 pm, but that's subject to negotiation.
Hmwk 1: Baierlein 1.1, 1.2, 1.4, 1.6, 1.7, 2.1, 2.3, 2.4
Hmwk 2: Baierlein 2.8, 2.9, 4.4; Kittel & Kroemer (on reserve) 2.4
Hmwk 3: Baierlein 5.1, 5.2, 5.3, 5.5, 5.6, 5.7
- Exams:
Two mid-term exams (tentatively the evenings of
10/4 and 11/15, although this is subject to negotiation)
and a final. They'll be closed book, but I'll give you some
sort of formula sheet so it won't be a memory test.
- Journal presentations:
This part is subject to revision, depending on class size.
But, in its current form: Each of you will be scheduled to give a
presentation to the class every other week.
We'll agree on some journal article for you to read and dissect.
They'll be articles or book sections
that are accessible but not trivial (say, from
Physics Today, American Journal of Physics, or Scientific American),
and of some relevance to statistical mechanics/thermodynamics.
On the designated day (say, Thursday)
you'll give a twenty minute presentation to the class on your
paper, discussing the paper's purpose, key results, any interesting
or controversial intermediate steps, and if necessary, tying it in
to stat mech/thermo. Four days before you speak you'll tell me what
paper you'll be discussing. Two days before you speak,
you'll give me a 1-2 page
synopsis of what you'll be talking about (so that I have a preview of
your take on the material and will be prepared to offer some
constructive commentary or place the work in context).
It doesn't have to be impeccable prose, just
enough for me to understand what it is you'll be taking about and see
the steps in your logic. I'll be happy to suggest papers on a variety
of subjects, and I'll post interesting candidates on this web page.
But, if you come across particular papers of interest to you (say,
some background reading relevant to your thesis, or pertinent to
work you're doing in another course), that's fine too---just run it past me
first. Alternately, rather than dissect a paper, I have a set of
computer simulations that you could program in, experiment with, and report
on. Some of these are in Mathematica, some in C.
This worked well last year, but it may need some tuning this year
depending on the size of the class. The purpose is
(1) to help you become comfortable with giving oral presentations,
(2) giving you experience extracting information from journal articles,
and (3) expose the class to the breadth of stat mech/thermodynamics.
While it's bound to take a non-negligible amount of time, I don't want
it to become onerous, especially since the core of the course is
really the problem sets. I want you to get used to extracting information
from papers efficiently, although even when you're good at it it takes some time.
We can adjust the frequency of talks,
the difficulty of the papers assigned, and the amount of direct
assistance from me, as appropriate. I'll rely on you to keep me apprised
of how it's all going and what adjustments need to be made.
Grading
Tentatively,
- Homework: 30%
- Midterm exams: 15% each
- Final: 25%
- Presentations: 15%
Textbook
Required:
- Thermal Physics, Ralph Baierlein
Additional useful references (if the library doesn't have them, I'll try to get them):
- Thermal Physics, Kittel & Kroemer
[Used as the course text in Fall 2000. A pretty good book, but the path of
the exposition tends to wander.]
- Fundamentals of Statistical and Thermal Physics, F. Reif
[The benchmark against which other undergraduate texts are measured. A
classic, but a bit dry.]
- Six Ideas That Shaped Physics, Section T, Thomas A. Moore [I used the thermodynamics
section when I taught Physics 34 in Spring 2001. It has lots of useful
insights and problems at an elementary level,
although some students that took the course thought it too verbose.]
- Introduction to Thermal Physics, Daniel Schroeder
[A new book, interesting with quite a few useful insights. A bit below
the level we're shooting for.]
- Equilibrium Thermodynamics, Adkins
- Thermodynamics and an Introduction to Thermostatistics, 2nd Edition,
H. B. Callen
[The classic exposition of axiomatic thermodynamics.]
- Statistical Physics, Mandl
- Statistical Mechanics, a Set of Lectures, R. P. Feynman
[At a higher level than this course, but full of interesting stuff.]
- Feynman Lectures on Physics (vol. 1), R. P. Feynman
[Feynman's insights are always unique and useful.]
- A Modern Course on Statistical Physics, L. E. Reichl
[A graduate text.]
- Statistical Mechanics, Pathria
- Statistical Mechanics, Kerson Huang
- Introduction to Modern Statistical Mechanics, Chandler
- Statistical Physics, Kadanoff
- Selected articles from American Journal of Physics
Lecture Schedule
I'll try to post at least an outline of the lecture on the web, if I have
time. This is more to motivate me to write them up that it is likely to
be a useful resource for you... I'll also try to arrange some guest
lectures from people that work in statistical mechanics or related field.
Week 1: Recalling Thermodynamics
Lecture 1: Wed. 9/5/01
Administrative issues; Quick overview:
What are Stat Mech and thermodynamics?
Lecture 2: Thurs. 9/6/01
Boltzmann's big idea: irreversible behavior from statistical considerations;
Temperature, thermal equilibrium, and thermoscopes: Zeroth law of
thermodynamics; Calibrating thermoscopes: the constant volume gas
thermometer.
Lecture 3: Fri. 9/7/01
Ideal gases: microscopic model, with results. First Law of thermodynamics,
and consequences for an ideal gas (heat, work, gas processes).
Macrostates, Microstates, and Multiplicity: an introduction to statistical
mechanics. Question: Why does heat flow from hot to cold? Microstates
vs. macrostates. Multiplicity. Fundamental assumption of statistical
mechanics. Some examples to practice counting: Binary state model;
Einstein model (harmonic oscillators); monatomic ideal gas. What happens
when systems get large.
Lecture 4: Sat. 9/8/01
Second Law of thermodynamics and connection to multiplicity;
entropy defined; irreversibility in general;
Week 2
Lecture : Thurs. 9/13/01
Catherine Deibel: The hyperfine structure of NaK
Mike Niemack: Closed drift thrusters
Week 3
Lecture : Thurs. 9/20/01
Matt Hummon:
Summer work on the search for violations of local Lorentz invariance--
the joys of lasers and the Pound-Drever locking technique
Rebecca Erwin: Generating functions in physics
Week 4
Lecture : Thurs. 9/27/01
Catherine Deibel: An introduction to global warming
Mike Niemack: Boltzmann's H-theorem (part 1?)
Week 5
Lecture : Thurs. 10/4/01
Matt Hummon: What if entropy were dimensionless?
Rebecca Erwin: area of a d-dimensional hypersphere AND The fraction of
all-different combinations: justifying the semi-classical partition function
Week 6
Lecture : Thurs. 10/11/01
Catherine Deibel: Entropy, information and computation
Mike Niemack: Detailed balance in the context of phonon-induced
transitions in Mn12 acetate
Week 7
Lecture : Thurs. 10/18/01
Matt Hummon: Thermodynamics of high temperature, Mie-Gruneisen solids
Rebecca Erwin: Introduction to Brownian motion
Week 8
Lecture : Thurs. 10/25/01 CLASS CANCELLED -- TO BE RESCHEDULED
AT A LATER TIME
Week 9
Lecture : Thurs. 11/1/01
Catherine Deibel: Understanding the chemical potential
Mike Niemack: Stars and statistical physics (part 1)
Week 10
Week 11
Lecture : Thurs. 11/15/01
Week 12
Lecture : Thurs. 11/29/01
Week 13
Week 14
Website
I'll keep scheduling information on this site primarily. I'm not yet
used to
Courseinfo, but as I get used to it I may post more stuff on there.
Useful Links
I'll post interesting or useful links pertinent to the course
here as they I come across them. If you come across any others, please
let me know. Most of the articles from American Journal of Physics
are appropriate for class presentations. The ones from the Los Alamos archive
are typically professional preprints and are sometimes quite long and/or
heavy going.
Presentation Schedule:
I'll post the schedule below. If you can't talk on your designated day,
please give a a little advanced warning so that we can reschedule.
When you tell me what you'd like to speak on, I'll post it below
(and a link to the paper, if possible).
Those that aren't speaking should read the
papers that the speakers will be presenting; it will make it easier for you
to digest the talk, to take an interest in the presentation, and
to contribute meaningfully to the discussion.
Those that are presenting, I encourage you to discuss your paper with me,
your classmates, other faculty, anyone else that might be interest.
Again, you can choose your own paper (run it past me first) or I can
suggest one for you. If it turns out that a paper you're interested in
requires material beyond what we've covered in the course so far, I can
give you a preview.
Other Interesting talks in the Five-College area:
Interesting and useful papers
Entropy:
Thermodynamics
A fresh look at the second law of thermodynamics,
(Physics Today, Vol. 53, No. 4, April 2000, pp. 32-37)
A simple model of irreversibility,
(American Journal of Physics, Vol. 54, No. 8, pp. 704-708)
Irreversibility, entropy production, and thermal efficiency,
(American Journal of Physics, Vol. 43, No. 11, pp. 973-980)
Is mixing a thermodynamic process?
(American Journal of Physics, Vol. 55, No. 8, pp. 725-733)
Another look at the quantum mechanical entropy of mixing,
Dennis Dieks and Vincent van Dijk,
(American Journal of Physics, Vol. 56, No. 5, pp. 430-434)
Multisystem temperature equilibration and the second law, Harvey Leff,
(American Journal of Physics, Vol. 45, No. 3, pp. 252-254)
All about work,
A. John Mallinckrodt and Harvey S. Leff
(American Journal of Physics, Vol. 60, No. 4, pp. 356-365)
Maxwell's demon, power, and time,
Harvey S. Leff
(American Journal of Physics, Vol. 58, No. 2, pp. 135-142)
Available work from a finite source and sink: How effective is a Maxwell's demon?
Harvey S. Leff
(American Journal of Physics, Vol. 55, No. 8, pp. 701-705)
Thermal efficiency at maximum work output: New results for old heat engines,
Harvey S. Leff
(American Journal of Physics, Vol. 55, No. 7, pp. 602-610)
Heat engines and the performance of external work
Harvey Leff,
(American Journal of Physics, Vol. 46, No. 3, pp. 218-224)
Thermodynamic insights from a one-particle gas, Harvey Leff,
(American Journal of Physics, Vol. 63, No. 10, pp. 895-905)
Thermodynamics of Crawford's energy equipartition journeys, Harvey Leff,
(American Journal of Physics, Vol. 62, No. 2, pp. 120-129)
Entropy of measurement and erasure: Szilard's membrane model revisited
Harvey Leff,
(American Journal of Physics, Vol. 62, No. 11, pp. 994-1000)
The operation of Maxwell's demon in a low entropy system,
A. F. Rex,
(American Journal of Physics, Vol. 58, No. 2, pp. 135-142)
The Gibbs paradox and quantum gases, P. T. Landsberg and D. Tranah,
(American Journal of Physics, Volume 55, Issue 4 pp. 359-362)
The fraction of "all different" combinations: Justifying the semiclassical partition function, Ralph Baierlein,
(American Journal of Physics, Vol. 65, No. 4, pp. 314-316)
Applications of Thermodynamics
Thermodynamics properties of an anharmonic fermionic oscillator
(American Journal of Physics, Vol. 60, No. 12, pp. 1122-1126)
Ratchet and Pawl,
(Feynman Lectures in Physics, vol. 1, Chap. 46)
The magic of helium-3 in two, or nearly two, dimensions,
(Physics Today, Vol. 51, No. 6, June 1998, pp. 30-36)
Negative pressures and cavitation in Liquid Helium,
(Physics Today, Vol. 53, No. 2, February 2000, pp. 29-34)
Quantum calorimetry
(Physics Today, Vol. 52, No. 8, August 1999, pp. 32-37)
"Temperatures Scales below 1 Kelvin", R.J Soulen, Jr. and W.E. Fogle,
1997, vol. 50, no. 8, p. 36.
Probability and Random Walks
Random walks and diffusion
(American Journal of Physics, Vol. 48, No. 1, pp. 49-56)
A theorem for physicists in the theory of random variables, D. Gillespie
(American Journal of Physics, Vol. 51, No. 6, pp. 520-532)
Asymmetry and convergence of the central limit theorem: An approach for
physicists, P. Pury
(American Journal of Physics, Vol. 58, No. 1, pp. 62-66)
Random multiplicative processes: An elementary tutorial, S. Redner
(American Journal of Physics, Vol. 58, No. 3, pp. 267-273)
Random walks: a pedestrian approach to polymers, critical phenomena, and
field theory
(American Journal of Physics, Vol. 59, No. 7, July 1991, pp. 633-645)
The mathematics of Brownian motion and Johnston noise
(American Journal of Physics, Vol. 64, No. 3, pp. 225-240)
Multi-variate Langevin and Fokker-Planck equations
(American Journal of Physics, Vol. 64, No. 10, pp. 1246-1256)
Statistical estimation of pi using random vectors
(American Journal of Physics, Vol. 67, No. 4, pp. 298-303, April 1999)
Monte Carlo estimations of e
(American Journal of Physics, Vol. 66, No. 2, pp. 138-140, February 1998)
Statistical Mechanics
Applications of Mellin transforms to the statistical mechanics of ideal quantum gases,
(American Journal of Physics, Vol. 49, No. 6, pp. 570-578)
Statistical mechanical distributions for small numbers of systems,
(American Journal of Physics, Vol. 62, No. 6, pp. 515-518)
An invertibility paradox
, P.-M. Binder, J. M. Pedraza, and S. Garzon
(American Journal of Physics, Vol. 67, No. 12, pp. 1091-1093)
Fermion-boson transmutation and comparison of statistical ensembles
in one dimension (American Journal of Physics, Vol. 64, No. 9, pp. 1168-
1176, September 1996)
Ideal quantum gases in two dimensions
(American Journal of Physics, Vol. 63, No. 4, pp. 369-375, April 1995)
Connection between nonlinear resonance and statistical behavior
(American Journal of Physics, Vol. 50, No. 4, pp. 363-373)
A method for evaluating two-spin correlations of a one-dimensional
Ising model
(American Journal of Physics, Vol. 56, No. 2, pp. 169-171)
"Chaotic Dynamics and the Origin of Statistical Laws", G.M. Zaslavsky,
1999,vol. 52, no. 8. pt. 1, p. 39.
Bose Einstein Condensation
Experimental studies of Bose-Einstein condensation
(Physics Today, Vol. 52, No. 12, December 1999, pp. 30-36)
The theory of Bose-Einstein condensation in dilute gases
(Physics Today, Vol. 52, No. 12, December 1999, pp. 37-42)
Other Applications of Statistical Mechanics
Genetic algorithms: A general search procedure
(American Journal of Physics, Vol. 62, No. 6, June 1994, pp. 549-552)
Introduction to the Ising Model (you can do a treatment using a chapter
from one of the textbooks that covers it: e.g. Schroeder, Baierlein,
Huang (more difficult), Chandler, etc.)
Non-Equilibrium Statistical Mechanics
Nonequilibrium patterns in granular mixing and segregation,
(Physics Today, Vol. 53, No. 3, March 2000, pp. 25-30)
Black holes
Black hole thermodynamics in an undergraduate thermodynamics course
(American Journal of Physics, Vol. 48, No. 12, pp. 1066-1070)
Black hole evaporation and Hawking radiation
[I don't have a single good source for this at an
introductory level. There are a few short sources which could be put together
to give a talk, though: Space, Time and Gravity, Chap. 10, by R. Wald;
Simple model for emission of particles by black holes, Am. J. Phys 46(6), June 1978,
p. 678; Comment on "Simple model for the emission of particles by black holes",
Am. J. Phys. 47(6), June 1979, p. 553; Another simple model for energy emission by
black holes, Am. J. Phys 48(9), Sept. 1980, p.725-727; Black Holes, White
Dwarfs, and Neutrons Stars, by Shapiro, et. al., sec. 12.8. All of these are
short, a few pages at most, and none are complicated. But, they're not very
satisfying, either. I'll keep looking for better references at the introductory
level.
Update: J. Traschen, a professor at UMass, has written a paper on
black hole evaporation:
An Introduction to Black Hole Evaporation
. This requires some quantum field theory, so you're not in a position to
read it end-to-end. But, with my help and some extra reading you could make
considerable headway. Along the way you'll see that even the idea of
`particle' is not such a clear-cut feature of quantum field theory in curved
space.
]
Renormalization group
Teaching the renormalization group (Am. J. Phys. 46(6), June 1978, p. 652-656)
Critical phenomena and Phase Transitions
Textbooks and Monographs: There are quite a few books on interesting
stat-mech-related subjects that are at a level that's accessible to you.
You could read a chapter or two and discuss. However, these are rarely
self-contained, and it's difficult to get both a picture of what's interesting
about the subject and some quantitative information by just reading a chapter.
You'd probably want to choose a book of interest and then plan two or three
related talks on subsequent chapters. You should check with me before
pursuing these, though, since the substance, length, and difficulty of chapters
can vary considerably within a text.
Introduction to Percolation Theory, Stauffer and Aharony
Maxwell's Demon: Entropy, Information, Computing, Leff and Rex
Feynman Lectures on Computation, especially Chap. 5: Thermodynamics
of Computation, Feynman
Fractal Concepts in Surface Growth, Barabasi and Stanley
Monte Carlo Methods in Statistical Physics, Newman and Barkema
Basic Stochastic Processes, Brzezniak and Zastawniak
Statistical Mechanics, Feynman
Path Integrals in Quamtum Mechanics, Feynman
The Mathematics of Financial Derivatives, Mott, et. al.
An Introduction to Econophysics, Mategna and Stanley
The Mathematical Theory of Communication, Shannon
Stochastic Processes in Chemistry and Physics, van Kampen
Exactly Solved Models in Statistical Mechanics, Baxter
Superfluidity and Superconductivity, Tilley & Tilley
Feynman Diagrams and the Many-Body Problem, Mattuck
Some longer research papers from the Los Alamos Archive (you can download a PDF
version of the paper by clicking on Other Formats). These are too long
to do as talks, although you could do a piece of one of them if one catches your eye.
Not all of them will be accessible to you, but you can see what people do for
research in these subfields.