Physics 406, Winter 2007: Statistical and Thermal Physics

Room: 4404 Randall Lab
Time: MWF 9-10am

Instructor: Mark Newman
Office: 322 West Hall
Office hours: Tuesdays 1:30-3:30pm

Grader: Manavendra Mahato
Office: 3484F Randall Lab
Office hours: Tuesdays 9:30-11:30am

Problem session leader: Tom Babinec
Problem session time: Monday 7-9pm
Location: 337 West Hall

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).

Course pack (required): There is no required textbook for this course, but there is a required course pack. The course pack is available from Dollar Bill Copying on Church St. Ask for Physics 406, Prof. Newman, Bin 6140. The cost is $26 plus tax (quite a lot for a course pack, but a lot less than buying a book). The course pack consists of seven chapters from the book Equilibrium Thermodynamics, 3rd edition, C. J. Adkins (Cambridge University Press, Cambridge, 1984) and seven chapters from Thermal Physics, 2nd edition, C. Kittel and H. Kroemer (Freeman, New York, 1980). Copies of the entire books are on reserve at Science Library Reserves in the Science Library, should you wish to consult them. This should not however be necessary to do well in the course: everything you should need is in the course pack.

Supplementary texts (not required): Two other books that cover the same material from different viewpoints are:

Course work: There will be weekly problem sets handed out Wednesdays 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 morning on which they are handed out. The first problem set will be handed out on Wednesday, January 10. There will be two mid-terms and a final. The final will take place on Wednesday, April 25 from 10:30am to 12:30pm in 4404 Randall (the usual classroom). Grade for the course will be 40% on the problem sets, 25% on the two mid-terms combined, and 35% on the final. The exams will be open-book, meaning you may bring the course pack to them – you cannot use your own written notes or solution sets to coursework.

Problem sets:


Summary sheet of equations for the final exam


Click here for a printable version.

  1. 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. Adkins 1.9: Mathematical preliminaries, partial derivatives, the chain rule, the reciprocal and reciprocity theorems.
  3. 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. 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. 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, free expansion of a gas.
  6. Adkins 7.1-7.3: Thermodynamic potential functions, internal energy, enthalpy, Helmholtz and Gibbs free energies. Lagrange transforms. Maxwell relations.
  7. 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, Gibbs-Shannon 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.

Mark Newman