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
This is a final review for the first 3/4 of the course. Lecture Audio
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 m...
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 s...
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 ...
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)...
Now that we know what order parameters are (see last lecture), we'll use the order parameter of a phase to construct the Landau free energy. The Landau free energy depends on the order parameter, and retains all the symmetries of the physical system. It's amazing how much you can get from symmetry, and we're able to see how it is that a ferromagnet can have what's called a continuous phase transition. That is, starting from zero temperature with a saturated magnetization, upon raising the temper...
We finish the van der Waals equation of state, and use it to illustrate the liquid-gas phase transition. It turns out that at low pressure, the van der Waals equation of state has a wiggle where (dp/pV)>0. Since this would cause an explosion, the system instead undergoes phase separation so that part of the container has liquid, and part has gas in it. More is different: We discuss the failure of reductionism. Reductionism is the idea that you will learn everything about an object by breaking...
We derive the shape of the phase boundary for solid to gas transitions (sublimation), examples being dry ice (CO2) or ice at low pressure. We derive the van der Waals equation of state, which is an improvement on the ideal gas equation pV=nRT. The ideal gas equation is based on two assumptions: 1. Particles occupy zero volume, and 2. Particles do not interact. Allowing for particles to have a finite size, and also allowing for the fact that at close range, gas particles feel van der Waals attrac...
We finish discussing chemical reactions, including how fast they progress, and what a catalyst can do for you. Then we begin a new topic: phases of matter and phase transitions between them. You've heard of solid, liquid, and gas, but did you know about the other phases of matter? Other phases include liquid crystals (of which there are many types). Also, electrons inside of a solid have their own phase transitions. For example, metals carry current when the electrons inside flow -- that's a liq...
We define the Gibbs Free Energy, which is the right energy function to use when you can control temperature, pressure, and particle number. This means chemists like it, because chemical reactions in a lab often take place under these conditions. We use this to derive the Law of Mass Action, which shows that the relative concentration of reactants depends only on temperature, and apply this to dissociation of the Hydrogen molecule, water, and hydrochloric acid. We also return to last lecture's di...
How refrigerators work. Why you can't cool your apartment by leaving the refrigerator door open. How heat and work depend on which path is taken. How to do completely meaningless work, the kind that's turned entirely into heat. We prove why the free energy is a useful concept: it tells you the maximum amount of work you can expect to extract from a system. The free energy is about the useful energy. We show that chemical potentials drive chemical work. How to levitate Tosanumi the sumo wrestler ...
We're having a midterm exam Wednesday, and today is a review of everything in chapters 1-7 in the text, Kittel and Kroemer's Thermal Physics. Topics include: Fundamental assumption of statistical mechanics, Laws of Thermodynamics, Probabilities and the Partition Function, Entropy and Temperature, Heat Capacity and Energy, Thermodynamic Identity, Helmholtz free energy, Free energy and the partition function, Maxwell Relations, Planck Distribution Function and blackbody radiation, Chemical potenti...
Storytime with Thursday Next (Jasper Fforde), and her Uncle Mycroft's entropy-detecting entroposcope. Why are large-scale systems capable of producing irreversible processes (like glass breaking, or red and blue Kool-aid mixing), even though the microscopic processes are reversible? We finish the electronic heat capacity of metals, first with an easy estimate to see that C~T, then with the full calculation. Using ideal gas processes (isothermal expansion, isentropic expansion), we build a Carnot...
More about Bose condensates. They're really weird -- at the lowest temperature, all bosons flock to the lowest available state, producing a "Bose condensate". Due to quantum mechanics, this is a remarkably stable state of matter, and is very hard to disturb. In fact, because the chemical potential becomes negative, it costs negative energy to add a new particle to the condensate. (Yes, bosons are "sticky" due to their statistics.) We also show why Bose condensates give rise to superfluidity (and...
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 d...
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 ...
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 Audio
