Thermal and Statistical Physics

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Lecture 18: Van Der Waals and Geckos Nov 02, 2005

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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 attractions, we get the new improved van der Waals equation of state for a gas made of sticky but hard molecules. Van der Waals attractions work because at close range, atoms and molecules notice each other's dipole moments. The dipole moments are due to the fact that at any given instant, the electron cloud is not quite centered on the nucleus of the atom (although it will be centered on average). This instantaneous dipole moment causes atoms in the vicinity to arrange their instantaneous dipoles so as to lower their energy, which causes attraction.
It turns out that geckos can cling to walls and ceilings because of van der Waals attractions. Gecko feet have tiny hairs that split many times to make many very fine tips, giving the hairs a very large total surface area. The fine hairs are able to form many contacts with any surface, and the surface-to-hair contact is adhesive due to van der Waals forces. One gecko foot can support the weight of an entire human.
Video: Sticky gecko feet, and their van der Waals adhesive properties.
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Lecture 17: Introduction to Phase Transitions Oct 31, 2005

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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 liquid phase of electrons. Refrigerator magnets are in a different electronic phase -- there, electrons execute tiny current loops around individual atoms, forming nanosize magnets. When they all align, the phase is called a "ferromagnet", and can be used to post notes to your refrigerator. We also discuss how you can go from liquid to gas and never encounter a phase transition! This is because liquid and gas aren't all that different to begin with. Class discussions: liquid crystal screens, melting snow, and what you really see when water boils.

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Lecture 16: Gibbs Free Energy and Chemical Reactions Oct 26, 2005

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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.
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Lecture 15: Refrigerators and Path Dependence of Work Oct 24, 2005

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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

Midterm Exam Oct 21, 2005

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We had an exam Wednesday covering chapters 1-7. In the mean time, the podcasting story (which partly featured our class) was in the Chicago Tribune today.

Midterm Review Oct 17, 2005

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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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Lecture 14: Engines Oct 12, 2005

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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?
Lecture Audio

Lecture 13: Bose Condensates Oct 05, 2005

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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.

Lecture Audio

Lecture 12: Reversible and Irreversible Expansions Oct 03, 2005

Show notes

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

Lecture 11: Bose Gas and Ideal Gas Sep 28, 2005

Show notes

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

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