Physics 406, Fall 2003: Statistical and Thermal Physics

Room: 1068 East Hall (Psych Department)
Time: MWF 9-10am

Instructor: Mark Newman
Office: 277 West Hall
Office hours: Thursdays 1:30-3:30pm
Email: mejn@umich.edu

Description: This course provides an introduction to the fundamentals of thermal physics including classical thermodynamics (the three laws, temperature, internal energy, entropy, and applications) and statistical mechanics (microscopic entropy, classical and quantum thermal distributions, ideal gases, Fermi and Bose gases, thermal radiation, electrons in metals, Bose-Einstein condensation, superfluidity).

There is no required textbook for this course, but there is a required coursepack:

Course pack: A required course pack for this course is available from Ulrich's Bookstore on S. University. Ask for Physics 406, Prof. Newman, Bin #1097. Price is $11.86. The course pack consists of seven chapters from the book Equilibrium Thermodynamics, 3rd edition, C. J. Adkins (Cambridge University Press, Cambridge, 1984). ISBN 0-5212-7456-7. This book is not required, but if you want more detail on the thermodynamics part of the course you may wish to look at it. A copy is on reserve at Science Library Reserves in the Science Library.

Supplementary texts (not required): The second half of the course is based on the first of these three books. The others are included for interest.

Course work: There will be weekly problem sets handed out Fridays and due in a week later in class. The problem sets will also be available for download from this web site no later than the Friday morning on which they are handed out. The first problem set will be handed out on Friday, September 12. There will be one mid-term and a final. The mid-term will take place on Wednesday, October 22 from 9am to 10am. The final will take place on Wednesday, December 17 from 10:30am to 12:30pm. Grade for the course will be 40% on the problem sets, 25% on the mid-term, and 35% on the final. The exams will be closed-book.

Problem sets:

Syllabus:

Click here for a printable version.

  1. Course pack (Adkins) 1.5 and 2.1-2.6: Introduction to classical thermodynamics. Intensive and extensive thermodynamic variables, conjugate pairs. The zeroth law of thermodynamics, the derivation and definition of temperature.
  2. Course pack (Adkins) 1.9: Mathematical preliminaries, partial derivatives, the chain rule, the reciprocal and reciprocity theorems.
  3. Course pack (Adkins) 3.1-3.7 (excluding 3.5.3): The first law of thermodynamics, conservation of energy, heat and work, work done by pressure, surface tension, in a magnetic field. Heat capacity and enthalpy.
  4. Course pack (Adkins) 4.1-4.3, 4.5, 4.6, 4.8: The second law, Clausius' statement, heat engines, the Carnot engine, irreversibility of heat flow. Carnot's Theorem, the definition of thermodynamic temperature, refrigerators and heat pumps.
  5. Course pack (Adkins) 5.1-5.6.1: Clausius' Theorem, derivation of entropy, law of increase of entropy. Entropy form of the first law, degradation of energy, heat capacities, free energy, Maxwell relations, free expansion of a gas.
  6. Course pack (Adkins) 7.1-7.3: Thermodynamic potential functions, internal energy, enthalpy, Helmholtz and Gibbs free energies. Lagrange transforms. Maxwell relations.
  7. Course pack (Adkins) 8.1-8.4, 8.6: Applications of thermodynamics. Calculation of heat capacities, ratios, differences. Adiabatic expansion of the perfect gas. Elastic rods, springs, and filaments. Surface tension. Magnetic cooling.
  8. Kittel and Kroemer, Ch. 1: Counting quantum states, simple binary models, spin models, binary alloys. Spin excess, multiplicity, width of the distribution, multiplicity as a function of energy.
  9. Kittel and Kroemer, Ch. 2: Fundamental assumption of the microcanonical ensemble, many-systems view, the ergodic hypothesis. Systems in equilibrium, the derivation of temperature and entropy, Boltzmann's constant. Properties of entropy, the law of increase of entropy (again), maximization of entropy at equilibrium.
  10. Kittel and Kroemer, Ch. 3, part 1: Derivation of the Boltzmann distribution and the partition function. Entropy of the Boltzmann distribution, Shannon's formula for the entropy, Helmholtz free energy. Minimization of the free energy.
  11. Kittel and Kroemer, Ch. 3, part 2: A particle in a box, many particles in a box, the perfect gas. Entropy of a perfect gas, the Gibbs correction, derivation of the equation of state. Sterling's approximation, the Sackur-Tetrode equation, entropy of mixing.
  12. Kittel and Kroemer, Ch. 4: The Planck distribution, black-body radiation and the Stefan-Boltzmann law. Color of thermal radiation. Phonon spectra, the Debye theory of the phonon specific heat.
  13. Kittel and Kroemer, Ch. 5: Gases with varying numbers of particles, chemical potential, generalization of the first law, chemical potential of the perfect gas, barometric pressure. The Gibbs distribution, the grand partition function, the grand potential.
  14. Kittel and Kroemer, Ch. 6: Quantum gases 1, the Fermi-Dirac distribution, the Bose-Einstein distribution, the classical limit, chemical potential, energy, pressure, and the ideal gas again.
  15. Kittel and Kroemer, Ch. 7: Quantum gases 2, the quantum limit. Fermi gases, electron gases, electronic heat capacity, astrophysical examples. Bose gases, Bose-Einstein condensation, liquid helium, superfluidity.
  16. Advanced topics (time permitting): Phase transitions, ferromagnetism, Landau theory; semiconductors, donors and acceptors, p-n junctions; spin models, Ising model, percolation; computer simulation methods, Monte Carlo methods; information theory.

Some notes on information theory can be found here. The summary sheet of equations for the final exam can be found here.

Mark Newman