Thermodynamics and Statistical Physics
Our motivation for studying thermal physics is to gain insight into thermodynamic
quantities used to describe "many particle" systems: entropy, temperature,
chemical potential, free energy, etc. These quantities allow us to connect
our models for microscopic nature to observations
Thermal Physics, Charles Kittel and Herbert Kroemer, 2nd ed.
After a preliminary treatment of classical thermodynamics, based on reading in several chapters of a traditional introductory physics text, we will cover material in chapters 1 through 7 of the text Thermal Physics,
with some omissions. Almost all of the problems we do help to clarify, sometimes
to extend, the material discussed in these chapters. So, the problem work is very important.
An Outline of the Topics
- States of a Model System
- Probability and counting states -- the fundamental assumption; enumeration
of states in a model spin system; the multiplicity function; counting states
in two small systems able to exchange energy; relative probability in small
systems; multiplicity of a large system of spins; the Stirling approximation;
a small system and a large system in mutual contact.
- Entropy and Temperature
- Ensemble averages and probability; two large spin systems in thermal contact;
the most probable configuration and thermal equilibrium; definitions of entropy
and temperature; the increase of entropy on the approach to thermal equilibrium;
the law of increase of entropy; the laws of thermodynamics; the multiplicity
function for N quantum harmonic oscillators.
- Boltzmann Distribution and Helmholtz Free Energy
- The Boltzmann factor and the partition function, Z; U, the thermal average
energy — a first application of Z; reversible changes; pressure, work, and
heat — the thermodynamic identity; the Helmholtz free energy, F; Z for an
ideal gas — one particle, N particles; energy, equation of state, entropy
for an ideal gas.
- Thermal Radiation and Planck Distribution
- Electromagnetic cavity modes; Z for a mode; the Planck distribution function;
U of photons in a cavity; spectral density — the Planck radiation law;
the flux of radiant energy from a black body radiator.
- Chemical Potential, μ, and Gibbs Distribution
- Thermal equilibrium with particle exchange between systems; two equivalent
definitions of ?: from entropy and from F; internal and external μ —
two examples; the thermodynamic identity generalized; the Gibbs factor and
the Gibbs sum; occupying orbitals: two applications.
- Ideal Gas
- Fermions and the Fermi-Dirac distribution function; Bosons and the Bose-Einstein
distribution function; the ideal gas: the classical regime; μ, F, p, entropy,
heat capacity; reversible and irreversible expansions.
- Fermi and Bose Gases
- Ground state of a three dimensional Fermi gas; density of states; a model
of white dwarf stars; nonrelativistic and relativistic degenerate Fermi gases;
how white dwarfs can collapse; μ for bosons near absolute zero and the
Bose-Einstein condensate; orbital occupancy versus temperature — the
Einstein condensation temperature. Recent methods of producing the Bose-Einstein
condensate (see http://www.colorado.edu/physics/2000/bec/).
Examples of phenomena requiring principles of thermal physics for their
- Electronic properties of materials: conductor, semiconductor, insulator, superconductor.
- Refrigerator, heat pump, internal combustion engine, steam engine.
- Heat transfer (buildings, stars, power generators).
- Melting, freezing of substances, phase transitions. Ideal gas law.
- Heat capacities of metals, dielectrics, fluids.
- Magnetic properties of materials -- ferromagnetic, paramagnetic, diamagnetic.
- Blackbody radiation (stars, people, tungsten lamps).
- Laser physics (gas, solid state).
- Stellar structure.
- Stability of galaxies, globular clusters, etc.
- Chemical (and biochemical) reaction rates.
Physics at Hamilton