## Perpetual Motion Machines

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### What they are

My high school chemistry teacher told us there are three laws of thermodynamics: you can't get something for nothing, you can't win, and you have to lose. The first law says you can't produce matter or energy from nothing; they are conserved. The second says the amount of entropy in the universe can only increase. The third notes that friction exists, so entropy does increase. (Note from 20 years later: that's not what the third law says at all.)

Perpetual motion machines are machines that are supposed to disobey one of the laws of thermodynamics. Usually it's the second law that people want to break, reversing the flow of entropy. Entropy is the amount of disorder in the universe. (Some claim to violate the first law, they create energy from nothing. I don't consider those here.)

### Why you can't design perpetual motion machines

The second law of thermodynamics isn't actually an axiom. It can be deduced from the other laws of physics. It's an application of the pigeonhole principle.

1. The known laws of nature are reversible, that is, given a current state the previous state is uniquely determined.
2. Which implies that if you start with n possible states, after any amount of time you'll still have n possible states.
3. For every state that looks like something other than heat, there are a zillion states that look like heat.
4. Therefore any process will map at most one in a zillion heat states to something that looks like work. And only at the expense of mapping an equal number of work states to heat states. Almost all of the time heat stays heat. You can't map all the heat states to work states, they just won't fit.

I saw a published proof of the second law once that was based on quantum mechanics. Instead of arguing about n states, it represented the set of possible states as a volume in 6-dimensional space (3 for space, 3 for velocity), and showed that the volume stayed constant over time. (Um, it seems to me like that published proof covers the continuous space, while my outline of a proof was more quantum, but what do I know.)

This still allows perpetual motion machines to be built -- just not designed. If you succeed in building one you're guaranteed to be unable to explain it using the known laws of physics.

#### recycling works

But wait. Anyone using a perpetual motion machine would want to do something with the work after it's been extracted from heat. If you consider such a system as a whole, work maps to heat maps to work. The number of possible states does not decrease.

This suggests it is possible to make a machine that continually does useful work without requiring outside energy. The key is to always know what state you are in, and to make sure useful states always map to useful states. An example of such a machine is a quantum computer.

#### maximum universal entropy

The universe is a closed system, and entropy keeps increasing, so it will eventually reach maximum entropy and stay there, right? Wrong. It's a continuously expanding system, and the maximum entropy possible keeps increasing as the volume of the universe increases. The delta between current universal entropy and maximum universal entropy just keeps getting larger. Wheee!

### How to figure out why a particular design won't work

Usually a perpetual motion machine can be used to light a lightbulb. Put it in a closed system that continuously lights a lightbulb. The machine has to convert the heat and light generated into electricity to continue running the lightbulb.

Usually there is a second machine that looks just like the first machine running in reverse. Usually you get it by stopping all the particles and sending them in reverse. And usually this second machine should be a perpetual motion machine for the same reasons as the first machine.

This second machine is a perpetual motion machine, but for a very strange reason. The lightbulb continuously absorbs heat and light, converting it into electricity. And (here's the important part), the machine keeps converting electricity into heat and light. Is that what is supposed to happen? No? Well, figure out how it is happening and you've figured out why the original perpetual motion machine won't work.

### Some perpetual motion machine designs

Why won't these work? (I'm including the solutions. Tell me if you don't want to see the solutions. I think the solutions are more interesting than the designs themselves.)

• Catalyzing an endothermic chemical reation. Suppose you have a reaction AB+heat <-> A+B which favors A+B. Such reactions do exist -- for example salt dissolving in water. Find a catalyst for this reaction. It reduces entropy, so the catalyst favors AB+heat. When AB+heat is released out into solution, it decays back into A+B, absorbing heat. You've got heat released at the catalyst and absorbed in the rest of the solution. Run a thermocouple. (March 2008. My previous solution for why this won't work was wrong. I said it would stop because the catalyst wouldn't produce heat, but I said the catalyst was favoring A+B->AB+heat, so the catalyst is releasing heat. Also, catalyzed reactions exist that both absorb and release heat, google "endothermic catalyst". Those catalyzed reactions that absorb energy need to be supplied with energy, for example by radiant heat or by some other reaction, or they'll stop.)
• Boiling point. Fill a piston with a high-pressure gas at boiling point. Allow it to expand adiabatically to low pressure. The temperature of the gas can't drop (it's at its boiling point), so it condenses into a liquid or solid. Which takes up much less volume. Compress the piston again (pretty easy; only the noncondensed gas needs to be compressed now). Allow the gas to heat up again and vaporize. Repeat. This converts ambient heat into useful work. (Solution - boiling point varies with pressure. The gradient of the pressure / temperature curve for the boiling point is the one that disallows this perpetual motion machine. A "Sterling Engine" is a real engine that works on a similar principle.)
• The two metal plates. Have two metal plates next to each other in vacuum in a magnetic field, with an insulated wire (running through a lightbulb) between them, both plates are sitting on a great big insulator. Electrons naturally jump off both plates, but because of the magnetic field, electrons from one plate fall on the other, and ones from the other fall on the insulator. So you have a potential difference which lights the lightbulb. (Solution - think of the system as a whole. The insulator eventually wraps around, so plate A gets as many electrons jumping from plate B as plate B gets jumping from plate A.)
• The great red spot of Jupiter. A natural result of the Coriolis effect on bodies of gas or liquid is that vortices in one direction tend to split into smaller vortices, but vortices in the other direction tend to merge into larger vortices. Spin a system. Starting with microscopic vortices in both directions (heat), watch macroscopic motions emerge. If the system is big enough, you get a stable biggest vortex, for example the great red spot of Jupiter. Set up windmills. (Solution - Jupiter's little vorticies come from heat differentials due to sunlight and internal fusion. Without an extra energy source you don't get little vorticies to start with.)
• The elliptical mirror. Make a mirror which is a whole ellipse. Consider a photon passing through one of the focii. Because it is an ellipse, it will be reflected through the other focus. Then through the first again, and so on. After about 5 passes, no matter what direction the photon started in, it is now travelling along the major axis. Cut a tiny hole in the mirror at the major axis, a big hole around the minor axis, and let the mirror align light for you which you can use as a quasi laser beam. (Solution - this only works for the light that goes exactly through the focii. Car headlights work on a similar principle.)
• Apply a magnetic field. Take any object, any object at all. Put it in a magnetic field. The electrons and nucleii of some of the atoms will align themselves with the field, flipping their spin (see torque on a circuit). This reduces entropy in the atoms. Spin is conserved, so the object as a whole (or the magnet) will start spinning. The random atomic spins have been extracted into a macro motion. (Solution - the spin extracted this way is small compared to the energy released by applying a magnetic field.)
• Light and Weight. Consider a hollow barbell. Put a heavy generator in one end. Coat the inside of the other end with mirrors, and put a lightbulb in there run by the generator. Put the barbell in space and run the generator. The generator has mass, it is heavy, so it attracts the light. The light has no mass so it does not attract the generator. But the light does have momentum, and it bounces off the barbell on the side nearest the generator. The barbell as a whole accelerates in the direction of the generator. Momentum is not conserved. (Solution - gravity is a function of relativistic mass, not rest mass. Relativistic mass is mrest/sqrt(1-v2/c2). For light, with zero rest mass, recall e=mc2. The m in that formula is relativistic mass.)
Sorry, I can't review any more perpetual motion machines. It proved to be too great a time sink. At the moment I don't even have time to implement the things I know would work and be useful.

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