What is Feynman's Definition of Perpetual Motion?

[kgreen]

Could somebody please explain this excerpt to me from Feynman's Lectures on Physics on perpetual motion? I don't completely understand his definition of perpetual motion. Thanks!

"We must be careful to define perpetual motion...If, when we have lifted and lowered a lot of weights and restored the machine to the original condition, we find that the net result is to have lifted a weight, then we have a perpetual motion machine because we can use that lifted weight to run something else."

 

[LeonhardEuler]

More context would be useful; If you could give a source for this or fill in more of what comes after, it would probably give a better idea of what he's saying.

But I'm pretty sure I know what he's referring to. There is a certain kind of "perpetual motion machine" that is not actually declared impossible by the laws of thermodynamics. This would be a perpetual motion machine that involves a cyclical reversible process. If you haven't studied thermodynamics and don't know what reversible means in that context, basically you can think of it as removing all effects that increase overall entropy. In a certain sense, these are processes that would not look right if played backwards. Two object in friction with one another approach the same speed; played backwards they would start diverging in speed. Two miscible fluids mix together; played backwards they would separate. Two objects in thermal contact at different temperature approach the same temperature; played backwards one heats up and the other cools down. These are irreversible processes.

On the other hand, there are reversible processes. A planet orbiting the sun played backwards looks like a planet orbiting the sun in the other direction, which does not violate the laws of physics. This is a reversible process. Other processes are nearly reversible like a pendulum swinging, or a weight on a spring bouncing up and down. A machine which perfectly eliminates all irreversible processes would be a perpetual motion machine allowed by the laws of thermodynamics. However, even an orbiting planet is not perfectly free from irreversibilities since the space they occupy is not a perfect vacuum, so there is some drag. Also, according to general relativity, there are gravity waves generated by this process that carry some energy away, though these have never been measured. While this type of perpetual motion machine is not prohibited by the laws of thermodynamics, there is no guarantee that one is possible either.

In contrast to this, there are two types of perpetual motion machine prohibited by the laws of thermodynamics, sometimes called a perpetual motion machine of the first kind (PMM1) and a perpetual motion machine of the second kind (PMM2), so called because they violate the 1st and 2nd laws of thermodynamics, respectively. Both of these PMM's have irreversibilities in them. These irreversibilities sap energy from the machines. In the PMM1, this is overcome by creating energy. This violates the first law of thermodynamics. In the PMM2, the irreversibilities are overcome by somehow destroying entropy. This can be done by converting heat directly into work with no cold sink to absorb some waste heat, or by causing heat to flow up a temperature gradient with no energy input in the form of work, for instance. This violates the second law of thermodynamics.

This brings me to what Feynman was saying. Suppose you make a machine that works in cycles. You perform one cycle and the machine is restored to the original state. You find that the effect you have had on the world outside the machine is to have lifted a weight. There are three ways of doing this we can entertain. The fist is that there was some input of work (essentially, a form of energy that isn't heat) into the machine. This is uncontroversially possible, as in an electric motor, or internal combustion engine where chemical energy is used. The second case is that there was no input of energy at all into the machine, and nothing else changed in the environment except the weight being lifted. The energy of the raised weight can now be used for something else, such as pumping energy back into a machine that is losing energy from irreversibilities. This means you have the potential for a PMM1. In the final case, energy is input in the form of heat, and no waste heat flows to a cold sink. This violates the second law of thermodynamics. You can build a perpetual motion machine from this in the following way: You have a pinwheel that is rotating underwater. Because of drag, the pinwheel is slowed down and some of it's kinetic energy is turned into heat. You run the previous machine to take in this heat and turn it into mechanical energy of a weight being lifted. You then couple the weight to the pinwheel in such a way that the falling of the weight powers the pinwheel, and repeat the process ad infinitum. You have just built a PMM2.

To know which of these scenarios Feynman was talking about, we would need to see more of what he said.

 

[Some text.]

Could somebody please explain this excerpt to me from Feynman's Lectures on Physics on perpetual motion? I don't completely understand his definition of perpetual motion. Thanks!

"We must be careful to define perpetual motion...If, when we have lifted and lowered a lot of weights and restored the machine to the original condition, we find that the net result is to have lifted a weight, then we have a perpetual motion machine because we can use that lifted weight to run something else."

'Lifted weight'... There is energy available after the machine has come to rest..?
Other than a machine that can run forever, but cannot share this energy?
just my thoughts.

 

[Phrak]

Could somebody please explain this excerpt to me from Feynman's Lectures on Physics on perpetual motion? I don't completely understand his definition of perpetual motion. Thanks!

"We must be careful to define perpetual motion...If, when we have lifted and lowered a lot of weights and restored the machine to the original condition, we find that the net result is to have lifted a weight, then we have a perpetual motion machine because we can use that lifted weight to run something else."

What he means is that if you have some theoretical mechanical gizmo, run it through its motions, and the end result is the gizmo is back to it's original state but for the difference that some weight has been lifted, then you better go back and re-examine your calculations, because you screwed up somewhere.

 

[dkotschessaa]

The context is Feynman's Lecture's on Physics, #4, conservation of energy, for those looking for context. I found a PDF of that particular lecture http://www.physics.rutgers.edu/ugrad/278/feynman_energy.pdf".

There's at least one more sentence to that paragraph that I want to add.

That is, provided the machine which lifted the weight is brought back to its exact original condition, and furthermore that it is completely self-contained—that it has not received the
energy to lift that weight from some external source...

In the first, simple example, the lever has three units on one side and one on the other end of the fulcrum. Obviously it won't move unless you push it. So you haven't used the energy of the smaller weight to lift the bigger weight. You've used your own energy.

It's kind of a proof by contradiction. It helps if we re-order the words as sometimes Feynman's stream-of-consciousness teaching puts things in an order that is not always as intuitively understood by us as by him.

If, when we have lifted and lowered a lot of weights and restored the machine to the original condition, we find that the net result is to have lifted a weight

So, the machine, left on it's own, has managed to lift a weight.

then we have a perpetual motion machine because we can use that lifted weight to run something else

We would have extra energy - the weight that was lifted now has the potential energy to lift other weights.

In an extremely simplified example of a lever, imagine the 1 unit weight on one side lifts the 3 unit weight on the other side. If the 1 unit weight manages to lift the 3 unit weight without any help, then you'd have perpetual motion, since the 3 unit weight could now lower the 1 unit weight and it would just keep going. You can see how absurd this is and how obvious, though it becomes less obvious in the more complicated machines he describes later.

He also refers to energy loss, since energy will always escape from your machine one way or another, often in the form of heat. Even if it's a .0000001% energy loss, your machine cannot run forever.

-DaveKA