Thermal and Statistical Physics

Now that we've derived absolutely everything about the ideal gas from scratch, it's time to do something useful with it! We'd like to eventually learn how to use this stuff to build engines and refrigerators. Today we discuss the basic processes (reversible expansions) that are the building blocks of engines and refrigerators. We also cover Bose condensation at the end of class, and learn why their statistics makes bosons sticky. Lecture Audio

Review of Fermions and Bosons. Review of Fermi Gas. All about the Bose gas, and its ditsrubution function. In the classical limit, the Fermi-Dirac distribution function and the Bose-Einstein distribution function approach the same form, and we recover ideal gas physics. We derive many properties about the ideal gas, and extend it to the case of internal degrees of freedom. More detail about the equipartition theorem, and how as temperature is raised, the heat capacity jumps up every time a new degree of freedom becomes excited. Example: Diatomic molecule. (Visual aids: many diatomic molecule models made from balls and springs.) Example: Experimental verification of the ideal gas law through the Sackur-Tetrode equation for entropy. Lecture Audio

Why no two pieces of matter may occupy the same space at the same time. Fermions are antisocial; bosons are social. Bosonic examples: lasers and superfluid helium. All about Fermions. Fermions obey the Pauli exclusion principle, and each state may have either 0 or 1 fermions in it, and no more. Class Discussions: more about aluminum, what about positrons, why gecko feet are sticky. Simulation Demo: Fermi distrubution function at various temperatures. Lecture Audio

When the system and reservoir can trade particles, you can't use the Boltzmann factor and the partition function anymore. Instead, use the Gibbs factor, and the grand partition function (or Gibbs sum). We introduce these new things, and then apply them to semiconductors, aluminum soft drink cans, and blood. Lecture Audio

Introducing a new thermodynamically conjugate pair of variables: number of particles and chemical potential. Internal and external chemical potential. Voltmeters measure the total chemical potential. Great class brainstorm on internal voltages in your life. How to get a theory named after yourself. Spins in a magnetic field. Why atmospheric pressure falls off with height, hiking in high altitude, and how to solve that deuterated Kool-Aid problem we talked about in Lecture 6. Lead-Acid batteries and your car. Lecture Audio

Deriving Planck's law of blackbody radiation. How to use it to tell the temperature of a star. Discussions about stars -- absorption lines and redshifts, and how to get the temperature correct anyway. Student demo of astronomy course software -- very cool. Counting photons is like counting phonons. (Phonons are quantized vibrational modes in solids.) Visual aid: model of a squishy crystal to demonstrate phonons. Debye law of heat capacity due to phonons in solids. Lecture Audio

Deriving the ideal gas law. Equipartition Theorem. Entropy of Mixing. Hot things glow -- or how night vision goggles work (Planck blackbody radiation). Analyzing star spectra. Class discussions: Mixing 2 colors of Kool-Aid, and how to make heavy Kool-Aid out of deuterated water. Why deuterated water can extend the snow skiing season, but is unfortunately toxic. Lecture Audio

Helmholtz Free Energy is the right energy to use when temperature and volume are used as control variables. Free Energy and the Partition Function. Maxwell Relations -- you can derive them all. Legendre Transforms. Ideal Gas. Quantum Concentration. Why some slow processes are still irreversible, as with toast and frogs. Lecture Audio

Boltzmann Factor, Partition Function and how to calculate everything else from it. Live near lakes because they have a high heat capacity. Energy and Heat Capacity of a two state system, Definition of a reversible process, Definition of pressure, The Thermodynamic Identity, Thermodynamically Conjugate variables. Digressions: Is toasting bread a reversible process? Do microwaves get water hotter than other heating methods? Lecture 4 Audio

Fundamental assumption of statistical mechanics: all accessible states are equally likely. Ensemble averages are weighted averages. Two systems in thermal contact. How to define entropy and temperature. How to take partial derivatives. The laws of thermodynamics. Lecture 3 Audio

Why is the most probable configuration important? Multiplicity Function is a gaussian in the two-state system. Weighted averages. Introduction to partition function. Lecture 2 Audio

Lightning fast review of quantum mechanics. Stationary quantum states, accessible states, fundamental assumptions of statistical mechanics. How to get from the microscopic quantum level to the macroscopic behavior you observe. We visualized atomic orbitals using Atom in a Box by Dean Dauger. Lecture 1 Audio --- Lecture Audio --- Lecture Audio