Lecture 4: Partition Function and Thermodynamic Identity

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

Lecture 5: Free Energy and Maxwell Relations

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

Lecture 6: Ideal Gas Law, Planck Blackbody Radiation

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

Lecture 2: Multiplicity Function

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

Final Review 2

This is a final review for the last 1/4 of the course. This is a very short lecture, because we had a field trip to go see the prestigious Bagwell Lecture given by Purdue's very own Prof. Albert Overhauser of the world-famous Overhauser Effect. Lecture Audio

Final Review 1

This is a final review for the first 3/4 of the course. Lecture Audio

Lecture 24: Fluctuation-Dissipation Theorem

We finish two more examples of the Fluctuation-Dissipation Theorem. This is a theorem that pops up everywhere! It means that the very same microscopic processes responsible for establishing thermal equilibrium are the same microscopic processes that cause resistance in metals, drag in fluids, and other types of dissipation. We discuss thermal noise in resistors (also known as Johnson noise or Nyquist noise), and demonstrate the fluctuation-dissipation theorem in this system. We also derive the magnetic susceptibility of a collection of free spins in a magnetic field. It turns out (due to the fluctuation dissipation theorem, of course) that the higher the amount of thermal fluctuations in the system at thermal equilibrium, the easier it is to magnetize the system. Lecture Audio

Lecture23: Brownian Motion and Diffusion

Brownian motion was discovered by a botanist named Brown, when he looked at water under a microscope, and observed pollen grains "jiggling" about in it. Einstein eventually explained it as due to the random collisions the pollen grain experienced from the water molecules. We compare the pollen grain to a drunk person walking home, and calculate how far the pollen grain can get by this type of diffusion. We also introduce the fluctuation-dissipation theorem, a far-reaching principle in advanced statistical mechanics that says that the microscopic thermal fluctuations in a system are the same microscopic processes that are responsible for things like drag, viscosity, and electrical resistance. (Why is that so cool? Because it means you can predict nonequilibrium properties -- those in the presence of an applied field like voltage -- to equilibrium properties like thermal fluctuations.) We also derive Fick's law of diffusion -- particles diffuse away from high concentrations. Go figure...

Lecture 22: Nucleation in First Order (Abrupt) Phase Transitions

Supercooling Demonstration (thanks to special guest Prof. Ken Ritchie): Put filtered water in a plastic bottle in your freezer for, say, 4 hours. Now, carefully remove it from the freezer, and shake the bottle vigorously. We did this, and saw ice crystals begin to slowly form in the water, because the liquid water was supercooled, and the ice phase was technically more stable. (Some crystals even resembled snowflakes, and grew larger as they floated to the top.) You may have to experiment with how long you leave the bottle in the freezer. Too short a time, and nothing happens. If you freeze the bottle longer, a vigorous shake will turn the whole bottle white as crystals form everywhere. Too long, and it will all freeze in the freezer. Do try this at home! Today we discuss nucleation in first order (abrupt) phase transitions. The ice crystals in our supercooled bottle of water formed through nucleation -- tiny ice crystals grew larger over time. The arctic cod is a supercooled fish, ...

Lecture 21: Alloys, Mixing, and Phase Separation

Oil and water -- they don't mix. Or do they? Due to the entropy of mixing, any tiny amount of impurity is highly favored entropically. This means that in general, you can get a small amount of a substance to mix into another. But take that too far, and they no longer mix, but "phase separate" into 2 different concentrations. We discuss this from the following perspectives: energy, entropy, and free energy. Examples: binary alloy with interactions, and a mixture of He3 (fermions) and He4 (bosons). Class discussion: Can you get oil and water to mix if you heat them in a pressure cooker? Lecture Audio