Greetings, all,
A non-engineer friend asked me a question recently, and I was a bit surprised and embarrassed that I couldn't answer it. So, I thought maybe some bright mind or helpful soul here in the group could help me out.
Imagine a pneumatic cylinder with thick, rigid walls. The ports at both ends of the cylinder are open, and the piston is at the mid-point of its range of travel. If we plug the port at one end of the cylinder, then the air in that end is trapped and can't escape.
We'll leave the port at the other end of the cylinder open, and lift the cylinder up out of the atmosphere and into space. We're not orbiting the cylinder, just lifting it straight up, as with an elevator, or a rocket on a perfectly vertical path. As the cylinder gains altitude, the air at the open end is exhausted. To simplify things, let's imagine that the cylinder is perfectly insulated, so that we don't have to deal with heating or cooling of the air that remains in the closed end of the cyclinder.
Let's assume that we've arranged some kind of locking mechanism, so that the piston can't move until we decide to release it. When the cyclinder has been lifted completely out of the atmosphere, we have vacuum on one side of the piston, and air on the other side (at roughly
15 PSI). This pressure differential represents stored energy, which could be used to do work if the lock were released and the piston were allowed to move.Now, here's the question: How do we account for the source of that energy? Obviously, we did work on the cyclinder while lifting it; but that can be accounted for by increased gravitational potential. We could get all that lifting energy back (less friction and efficiency, of course), just by letting the cyclinder fall back to Earth. But the energy stored in the pressurized air is something else. We don't exhaust the captured air, so we're not lifting a different mass than we'll lower, later on. We just let that air expand within the cylinder so that the piston will move, and will do some work while in space. Later, as we let the cylinder fall back into the atmosphere, the piston will return to its original position as air enters the still open end of the cylinder, and the pressure will again be equalized.
Or, we could lock the piston in place after letting the cylinder do its work in space, and then lower it into the atmosphere with the piston held at the open end. In that case, when we got back on the ground, we'd have one atmosphere of pressure at the open end of the cyclinder, and less than one atmosphere at the closed end. This would represent another pressure differential (in the opposite direction), which could be used to do even more work after the cyclinder was returned to Earth.
So, we've done work out in space as the trapped air expanded; and we've done even more work back on Earth, as the piston returned to its original position. We've captured and used some energy; which means there MUST be an equivalent loss or reduction of energy elsewhere in the environment. But I can't figure out where it is, or how to account for it.
This is only a hypothetical problem, of course - more of a brain teaser than a real challenge. But it's been bugging the heck out of me.
Any hints?
KG __ I'm sick of spam. The 2 in my address doesn't belong there.