PHYS 711 - Statisical Mechanics - Fall 2008

This table describes what we covered, what is planned for the lectures, and where you can read more about the material.
The content of future lectures is subject to change depending on how things go. The third column gives suggested reading
where the page numbers are given and the book codes are as follows:
G = Greiner, Neise, and Stöcker, Thermodynamics and Statistical Mechanics, Springer, 1995.
F = Fermi, Thermodynamics, Dover, 1956.
H = Huang, Statistical Mechanics (second edition), Wiley,1987.
M = McQuarrie, Statistical Mechanics, University Science Books, 2000.
P = Pathria, Statistical Mechanics (second edition), Elsevier, 1996.

8/26
Done
 Intro to thermodynamics; state quantities, 0th law and temperature; kinetic theory of the ideal gas; Maxwell-Boltzman distribution. Also some discussion of integrals, including the Gamma function.
 G 1-15; classnotes (math)
9/2
done
 Equations of state for real gases; reversible & irreversible processes. Exact and inexact differentials. 1st law; specific heat; the Carnot cycle; absolute temperature scale.
 G 16-32; 33-40
classnotes (math)
F Ch. 3; H 9-14
9/9
done
 Entropy; 2nd law; Euler theorem & Gibbs-Duhem relation; Gibbs phase rule; thermodynamic manipulations
 G 41-42; 58-61; 62-64; 
F Ch. 4; H 9-19
9/16
done
 Legendre transformation; thermodynamic potentials. Microscopic interpretation of entropy; microstates. G 80-83; Ch. 4.
G 43-51.
9/23
done
 Volume of an N-sphere; Stirling's formula; statistical definition of entropy; microstates & entropy of the classical ideal gas. G 123-131.
9/30
done
 Pseudo-qantum-mechanical ideal gas. Ensemble point of view & phase space density; ergodic hypothesis; Liouville theorem; entropy as an ensemble average.
 G 135-139, 142-146, 149-150.
10/7
done
 Microcanonical ensemble by various methods, including the method of most likely arrangement. Canonical ensemble.
 G 147-149; 161-162; see also "bean counting" notes.
10/14
 Columbus day recess
10/21
done
 Establishing that the Lagrange multiplier beta=1/(KT); link to thermodynamics; most likely energy of the canonical ensemble, expressing phase space density in terms of the density of states; stdev of the distribution of energies.
 G 162-4; 186-187; 191-194.
10/28
done		 Foundation of the Gibbs correction; ideal gas in canonical ensemble; systems of non-interacting particles; observables as ensemble averages; derivation of MB distribution.  G 164-168; 170-172; 179; 177-179; 172.
11/4
done
 Virial & equipartition theorem; system of non-interacting distinguishable quantum-mechanical harmonic oscillators
 G 194-200; 208-212
11/11
done
 Finish QM harmonic oscillators; paramagnetism (classical and QM)  G 212-223
11/18
done		 Brief discussion of the quantum treatment of gases with internal degrees of freedom; additional comments regarding the equipartition theorem; the grand (or macro) canonical ensemble; symmetric/antisymmetric wave functions and quantum statistics.
 notes & G chapter 9.
11/25
Done
 When a classical treatment is valid; grand (or macro) canonical partition functions for Fermi-Dirac, Bose-Einstein, and Maxwell-Boltzmann statistics; most likely occupancy numbers; classical and quantum limits of mean occupancy functions.  M Chapter 4; G p. 310-313 (example 12.2); P 127-137.
12/2
 
12/9 Exam day