Physics 406, Fall 2002: Statistical and Thermal Physics
Room: 331 Dennison
Time: MWF 9-10am
Instructor: Mark Newman
Office: 277 West Hall
Office hours: Thursdays 2-4pm
Grader: Wei Yi
Office: 1476 Randall Lab
Office hours: Wednesdays 1-3pm
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
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):
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.
- 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
- Homework 8 - Quantum gases in the classical
- Homework 9 - Fermi gases
- Homework 10 - Bose gases, phase transitions
- Homework 11 - The maximum entropy
principle, Monte Carlo simulation
Click here for a printable version.
- First handout: Introduction to
statistical physics, percolation, random walks, entropy.
- 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
- Course pack (Adkins) 1.9: Mathematical preliminaries, partial
derivatives, the chain rule, the reciprocal and reciprocity theorems.
- 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
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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,
- 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.