Thermal and Statistical Physics – Détails, épisodes et analyse

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 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 discussion of how superconductors repel magnetic fields. Demo: We use liquid nitrogen to cool the high temperature superconductor YBCO
below its superconducting transition temperature, so that it is in the superconducting state, and able to levitate magnets. Class discussions: How not to use a refrigerator to cool your apartment; High temperature superconductors and a small part of what's known about them.

Lecture Audio

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 with superconductors and magnets, and how much work the superconductor does in the process.
Class discussions: The heat death of the universe. (Don't worry -- the sun will die out far before that.) More about high temperature superconductors, and possible applications.

Lecture Audio

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 potential, Grand partition function, Density of States, Fermions and Bosons, Ideal Gas, Ideal Gas Processes, and a few equations to memorize for the exam.

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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 engine and discuss its efficiency. You can't beat Sadi Carnot. Class Exercise: calculate the work done in one cycle. Class discussions: the chemical potential has a slight temperature dependence in three dimensions, but not in two. Why you should never hook lead pipes to aluminum pipes in your house. A little bit about melting. Can you convert heat entirely into work, or work entirely into heat?

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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 superconductivity if the bosons are charged.) Class demonstration: The Wave (Just like the one in a baseball stadium.) The point is that many-body excitations often have very different character from the constituents. That is, "The Wave" in a crowd is an excitation of the crowd that doesn't look anything like the constituents (individual persons). Class discussions: What are superfluids and superconductors good for? What about the cuprate high temperature superconductors? Since they're ceramics, can you ever make them into wires? Are there higher temperature superconductors? How would room temperature superconductors make your life better?

We also discuss the heat capacity of metals at the end of class. Some of the electrons in a metal are free to flow, and are in a fluid phase of matter that allows us to use the Fermi ideal gas to describe some of their behavior.

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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.


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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.

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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