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.
Summary sheet of equations for the final exam
Click here for a printable version.
- 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
- Adkins 1.9: Mathematical preliminaries, partial
derivatives, the chain rule, the reciprocal and reciprocity theorems.
- 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
- 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.
- 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.
- Adkins 7.1-7.3: Thermodynamic potential functions,
internal energy, enthalpy, Helmholtz and Gibbs free energies. Lagrange
transforms. Maxwell relations.
- 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, Gibbs-Shannon 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.