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
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
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.
- Thermal Physics,
2nd edition, C. Kittel and H. Kroemer (Freeman, New York, 1980). ISBN
0-7167-1088-9. A copy is on reserve at Science Library Reserves
in the Science Library.
Physics, 2nd edition, Franz Mandl (John Wiley, New York, 1988). ISBN
- Fundamentals of
Statistical and Thermal Physics, Frederick Reif (McGraw-Hill, Boston,
1965). ISBN 07-051800-9.
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.
- Homework 1 - First and Second Laws of
- Homework 2 - The Second Law and Entropy
- Homework 3 - Maxwell relations and the
counting of states
- Homework 4 - Temperature, entropy, and the
- Homework 5 - The Boltzmann distribution and
the ideal gas
- Homework 6 - Thermal radiation
- Homework 7 - Entropy of mixing, phonon
specific heat, the grand ensemble
- Homework 8 - The grand ensemble and
- Homework 9 - Fermi and Bose gases in the
- Homework 10 - Phase transitions,
mean-field theory, and Laudau theory
- Homework 11 - Information theory and
Monte Carlo simulation
Click here for a printable version.
- 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.
- Course pack (Adkins) 7.1-7.3: Thermodynamic potential functions,
internal energy, enthalpy, Helmholtz and Gibbs free energies. Lagrange
transforms. Maxwell relations.
- 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.
- 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 information theory can be found here.
The summary sheet of equations for the final exam can be found here.