27 episodes
Thermal and Statistical Physics Prof. Carlson
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- Education
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4.9 • 10 Ratings
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Thermal and Statistical Physics Purdue University Phys 416
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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
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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
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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! Shown in class: Nice movies on the web about colloid particles in milk executing Brownian motion. There's a great applet on Brownian motion to play with here. Lecture Audio
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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, living in water too salty to freeze even though it's at -1.9 degrees Celsius! The reason the fish doesn't freeze solid is due to antifreeze glycoproteins, which inhibit the growth of nucleated ice crystals. We calculate the energy barriers to nucleation at the liquid-gas transiton, and find that a nucleated liquid bubble in the gas phase must be large enough before it will turn the whole substance liquid. If it's too small, the bubble is unstable and converts back into gas. We also discuss: Slushy ice -- where is that on our phase diagram? Surface tension and faceting in crystals. Plant-eating bacteria which secrete enzymes that encourage ice nucleation on plants. And quite a bit about how snowflakes form. Much of today is from Jim Sethna's statistical mechanics book, and the part about snowflakes and ice formation is from research at my alma mater, Caltech, as presented at www.snowcrystals.com. Lecture Audio
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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
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"Energies add and the total is conserved; probabilities multiply and the product is unchanged." - Edward Teller
I joined the class late, what I knew about equilibrium statistical physics is contained in this quote from Teller’s book: “Conversations On the Dark Secrets of Physics”
Teller was one of the great physicists of the 20th century, a man of his political circumstances and times. I personally did not agree with most of his politics, with one exception, not knowing very much about anything I agreed with his concern that most people are badly educated and taught only those few skills necessary to make some money and be fitted into “the economy” to serve.
Teller clearly believes that some appreciation of complicated science can be taught to people without a lot of math. In Teller’s book you need only a little understanding of Calculus. Teller is having a conversation with his daughter Wendy and does his best to explain Physics. Wendy’s job is to ask questions and challenge her father to do better.
If you like listening to Professor Carlson’s class she presents in a conversational style and does a good job explaining physics. I do not have the book that goes along with her course, I have “Thermal Physics” by Schroeder and an old paperback by Nash.
Nash begins by stating:
"Plus ça change, plus c'est la même chose. "
I have been thinking about this statement for thirty four years but always part time and away from chasing dollars which occupies most of my clear head time.
How to teach
An excellent bridge between statistics and chemistry. Will require, or motivate you to learn, calculus.
For those interested in teaching per se, listen for the interactions; the pacing and organization of questions to students, and, especially, the timing, thoughtfulness, and tone of answers to student questions.
The explications of the equations begin with motivating physical questions, but also with relations to previously learned math "technology" or similar laws. Even the individual variables are given re-introductions as needed, like minor characters in a long novel.
This explanatory structure reminds me of really well-documented code. It applies a rudimentary narrative arc to terse facts. The tone, however, is consistently one of delight in discovery and respect for the cleverness, of, respectively, nature and science.
You'll need calculus, including Taylor expansions and harmonic oscillators, as well as Kittel and Kroehmer's "Thermal Physics", 2nd ed., to actually master the subject, but, if you're homework-phobic, you can enjoy the lectures without the stress.
When out in public, just remember to smile and nod.