# 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 of nature.

### Text

Thermal Physics, Charles Kittel and Herbert Kroemer, 2nd ed.

An important feature of the course is that you will do a significant amount of presentation. This course is in seminar format and you will do a lot of the exposition and talking. One of my jobs is to encourage you to participate orally in our class meetings.

### Syllabus

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, written and oral, is really 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.
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 explanation:

• 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.
• Superfluidity.
• 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.