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I'm teaching a conceptual introduction to physics for American 13-15 year old students this summer.

One of the main ideas I want to hit on is the relationship between energy conservation, equilibrium, and dissipative forces. (e.g. When a box sliding over the floor comes to rest, its kinetic energy mostly goes into heating the floor. We expect this because there there are many degrees of freedom in the floor, while the bulk motion of the box is at most six degrees of freedom.)

I'm looking for experiments and demonstrations of this effect. We can look at examples of turning mechanical work into heat (rub your hands together, hammer a nail, start a fire with friction), but this doesn't quite get across the idea of what thermal energy is. We might be able to observe Brownian motion, but since molecules are too small to see this has limited intuitive appeal for this age range.

Ideally, I'd like to find systems where you can actually see the "microscopic" degrees of freedom alongside the "macroscopic" degrees of freedom. This could be actual physics demonstrations, or artificial scenarios in the form of games the students play out on a field (perhaps following certain rules about the field's layout as individual decision makers, but inevitably creating a certain distribution of students in different "zones" on the field) or simulations on a computer.

All suggestions welcome, and if I implement it in the course next month, I'll report back on how it went.

(Mods, could you please mark this community wiki?)

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We don't do CW questions anymore. Questions which would have been wikified in the past are now usually closed as "not constructive," although I'm going to hold off on this one to see what the community thinks. –  David Z Jun 18 '12 at 21:51

3 Answers 3

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The obvious example would be diffusion. For example, you could show a simulation of a gas, consisting of rigid 2d circles, some of which are one colour and some of which are another. Start of with all of one colour on the left and all of the other colour on the right, and watch as they gradually become mixed. You can explain that the system could go from the mixed state to the unmixed one, but it's very unlikely.

Since a rigid ball simulation is probably a bit ambitious to implement in one month, you could instead use a lattice gas. That is, you have a grid whose squares can be one of two colours, and at each time step you randomly swap two adjacent squares. You could get the students to implement this easily enough, if you have two colours of counter for them to move around, although the system would have to be pretty small in this case, otherwise it would take too long to see the diffusion effect.

The disadvantage of diffusion as an example is that the relationship to energy conservation isn't so clear. It is there - the point is that you'd have to do work to separate two mixed gases - but it may not be so easy to explain this. When you move from rigid balls to a lattice gas, the concept of energy more-or-less disappears from the model. But on the other hand, it makes the connection between irreversibility and entropy-as-disorder very clear. (Perhaps a little too clear - in my opinion the idea that entropy = disorder isn't quite correct. But still it's a good example to introduce the concept of entropy.)

Edit: Here's a crazier, more expensive idea that may or may not work, but if it does then it'll be a really fun way to visualise microscopic degrees of freedom.

First, buy, build or hire an air-hockey table. Next you'll need (I guess) around 20-30 wooden, metal or plastic disks. They should be fairly small but big enough to float effectively on the table's surface. (This means they should be bigger than the spacing between the holes on the table, and if they're circular it'll help a lot.) Also they shouldn't be too light, because they'll need some inertia. Carefully place these on the table so that they're evenly spread out and not moving. Then place a much larger object (such as an air-hockey paddle) on the table and give it a good whack to set it in motion. What should happen is that it comes (more or less) to a stop by transferring its kinetic energy to the smaller disks. Depending on how well you can get the objects to float on the table's surface, they should keep moving for long enough to make it clear that this is what's happening.

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Thanks! Good idea. I might even be able to do this with something like an Othello board and having them do it by hand. –  Mark Eichenlaub Jun 18 '12 at 8:46

You may demonstrate numerical friction by applying a Runge-Kutta method (or even the Euler method if RK is too advanced) to a conservative system (such as Sun - Jupiter - Saturn) and notice the dissipative effect of stochastic perturbances (aka discretization errors): Ultimately, the planets will fall into the sun, though this takes many revolutions. However, the decrease of the total energy of the system can be obseved much earlier.

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And it tells the students to be careful in simulations ! It might be priceless a few years down the road ... –  Frédéric Grosshans Jun 18 '12 at 13:20
    
I wouldn't have thought of that, thank you. –  Mark Eichenlaub Jun 18 '12 at 20:36

For the simulation part, I've played some time ago with the phun 2D physics engine, where you can simulate molecules like rigid circles. You should be able to simulate the box on a floor scenario you discussed above quite quickly.

If you don't have the time to make your own, you can also find some nice demonstrations on Youtube, like

Edit: If you want something more physical, you can look at/try to reproduce this golf ball atmosphere or this granular gas, which includes nice phase transitions.

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Excellent references, thanks! –  Mark Eichenlaub Jun 18 '12 at 20:36

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