Physics 406, Fall 2002: Statistical and Thermal Physics

Instructor: Mark Newman
Office: 277 West Hall
Office hours: Thursdays 2-4pm
Email: mejn@umich.edu

Grader: Wei Yi
Office: 1476 Randall Lab
Office hours: Wednesdays 1-3pm
Email: wyiz@umich.edu

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

Textbook (required): Thermal Physics, 2nd edition, C. Kittel and H. Kroemer (Freeman, New York, 1980). ISBN 0-7167-1088-9.

Course pack (required): A required course pack for this course is available from Ulrich's Bookstore on S. University. Ask for Physics 406, Prof. Newman, Bin #1087. Price is $9.10. The course pack consists of four 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 Shapiro Library.

Supplementary texts (not required):

• Statistical Physics, 2nd edition, Franz Mandl (John Wiley, New York, 1988). ISBN 0-471-91533-5.
• Fundamentals of Statistical and Thermal Physics, Frederick Reif (McGraw-Hill, Boston, 1965). ISBN 07-051800-9.

Grading: There will be weekly problem sets handed out Friday and due a week later. The first problem set will be handed out on Friday 13th September. There will be one mid-term and a final. Grade will be 50% on the problem sets, 20% on the mid-term, and 30% on the final.

Problem sets:

• Homework 1 - First Law of Thermodynamics
• Homework 2 - Second Law of Thermodynamics
• Homework 3 - Maxwell relations, multiplicity, and microcanonical entropy
• Homework 4 - More entropy, Sterling's approximation, the Planck distribution function
• Homework 5 - Integral approximations and the perfect gas
• Homework 6 - Thermal radiation
• Homework 7 - Phonon specific heat and chemical potential
• Homework 8 - Quantum gases in the classical limit
• Homework 9 - Fermi gases
• Homework 10 - Bose gases, phase transitions
• Homework 11 - The maximum entropy principle, Monte Carlo simulation

Syllabus:

1. First handout: Introduction to statistical physics, percolation, random walks, entropy.
2. 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.
3. Course pack (Adkins) 1.9: Mathematical preliminaries, partial derivatives, the chain rule, the reciprocal and reciprocity theorems.
4. 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.
5. 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.
6. 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.
7. 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.
8. 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.
9. 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.
10. 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.
11. 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.
12. 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.
13. 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.
14. 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.
15. 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 Lagrange multipliers are here.