303 2007 Lecture summaries and lecture notes.
These are the lecture notes for Physics 303 - Statistical Physics
taught in Fall 2007. This course was taught from mandl - a book I
particularly liked as a student. However, Mandl is not so suitable for
a Stat. Phys. Course which must of necessity include a reasonable
amount of thermo as well.
How to read these lecture notes:
Each page has 4 panels, representing a chunk of blackboard about 3 feet
wide. The sequence of panels on a page is TL, TR, BL, BR. A 55
minute lecture is usually ten
panels, 2.5 pages.
Note on errata: I'd
be grateful, if you find a mistake, if you let me know so I can
note it here.
Acknowledgements: Thanks to
Kay Warner and John Daise for scanning these notes.
09/03/2007 Micro vs. Macro: the ideas of statistical physics.
From Newtonian mechanics to thermodynamics. The laws of thermodynamics.
2 09/05/2007 Thermal concepts: temperature, heat, pressure. Speciﬁc
heat. Thermometers. The ideal gas. Thermal expansion.
3 09/07/2007 The First Law. Thermodynamic Processes.
4 09/10/2007 Thermodynamic processes. Reversible and Irreversible
processes. Quasistatic processes. Isothermal compression of a gas.
5 09/12/2007 Irreversible work and hysteresis. Cycles. Speciﬁc
heats of an ideal gas. Adiabatic processes in an ideal gas - adiabats.
6 09/14/2007 Kinetic theory of the ideal gas. Equipartition. Real
gases and van der Waals equation.
7 09/17/2007 Extensive and intensive qtys. Equilibrium, entropy and
8 09/19/2007 S = k ln Ω. Equilibrium of an Isolated system.
9 09/21/2007 Application: The Schottky defect. Equilibrium of a
system in a heat bath.
10 09/24/2007 System in a heat bath. Probabilities in physics -
problems of interpretation. Deﬁnition of macroscopic energy as mean
11 09/26/2007 Mean energy - statistical and thermodynamic deﬁnition
of energy. Fluctuations. Mean square deviation - variance. Relation to
12 09/28/2007 Deﬁnition of Pressure. Density of states. Deﬁnition
of entropy for a system in a heat bath. Canonical Ensemble.
13 10/01/2007 Ensembles - the microcanonical and canonical
ensembles. The Helmholtz free energy and the zero-fluctuation limit.
14 10/03/2007Magnetic work. The paramagnetic solid in a heat bath.
Magnetization and heat capacity.
15 10/05/2007 High and low field limits. The Curie law. Entropy and
order in Magnetic systems.
16 10/08/2007 Entropy and order in Magnetic systems. Negative
17 10/10/2007 Ferromagnetism and the Curie-Weiss Law
18 10/12/2007 The Second Law for inﬁnitesimal changes.
19 10/22/2007 The second law for inﬁnitesimal changes. The
fundamental thermodynamic relation.
20 10/24/2007 Reversible changes. Entropy of ideal gas. Clausius
inequality. Simple applications: heating water, temperature
21 10/26/2007 Maximum work. Thermodynamic potentials.
22 10/29/2007 Maxwell relations. The third law and its
consequences. Maxwell relations for magnetic systems.
23 10/31/2007 The Clausius and Kelvin statements of the second law.
Heat engines and refrigerators.
24 11/02/2007 Adiabatic cooling.
25 11/05/2007 Basic properties of the heat capacity of solids. The
Equipartition Theorem. Dulong-Petit law and the third law of
26 11/07/2007 The Einstein theory. Low and high temperature limits
of the Einstein theory. Comparison of the Einstein theory with
27 11/09/2007 Debye’s theory. Mode counting and the density
28 11/12/2007 Mode counting and the density of states
29 11/14/2007 Debye theory. Mean energy and Heat Capacity
30 11/16/2007 Phase Equilibria. The Chemical Potential. The
equilibrium condition and phase diagrams
31 11/19/2007 The critical point. Geometric interpretation of
thermodynamic potentials. Isotherms for a gas in equilibrium with its
32 11/26/2007 Perfect gases: the partition function for a quantal
gas. The occupation number representation. The classical limit as the
low-occupation number limit. Restrictions on occupation numbers. Bosons
33 11/28/2007 Statistics and symmetry. Statistic and spin. Bosons
example: a perfect gas of photons. Partition function for photons.
Black body radiation. Plancks law
34 11/30/2007 Comparison of Planck’s law and Debye theory:
Photons and Phonons. Properties and thermodynamics of Black Body
35 12/03/2007 Systems with variable particle numbers. The Gibbs
distribution. The Grand Partition Function and Gibbs Grand Potential.
Mean occupation numbers for Bosons and Fermions.
36 12/05/2007 Fermi-Dirac Statistics. Behavior of mean occupation
number for fermions at zero and non-zero temperature. Density of states
for electrons. Energy distribution of electrons. Definition of the
Fermi energy. Free electron theory of metals - absence of
lattic-electron interaction at zero temperature in a perfect lattice.
37 12/07/2007 Absence of electron-electron scattering in free
electrons at zero temperature. Electronic heat capacity of metals -
failure of classical theory. Electronic heat capacity - quantum theory.
38 12/03/2007 Variation of chemical potential with temperature for
fermions and bosons. Temperature dependence of ground state occupation
for bosons. Bose-Einstein Condensation.
39 12/05/2007 Bose Einstein Condensation in liquid helium,
superconductors and cold atoms
40 12/07/2007 Summary lecture.