Indubitably wrote:I appreciate that you're taking the time to explain where I'm going wrong, because that's how my ideas improve, but there is obviously some sort of disconnect, because all I'm seeing here is a reiteration of the basic reasoning behind my argument, only with a contradicting conclusion.
What I'm saying is that I actually want compression, because it should give me a a kind of infinitely variable transmission effect, and what your argument appears to imply is that compression, in and of itself, has some sort of immutable energy negating effect that would annihilate some large portion of the energy in the system even if I actually could isolate it perfectly from the environment. Perhaps there is something I'm missing in your comments about heat transfer within the system? As I understand it, this isn't really and issue, because while the pump must work harder (or rather, longer, since my plan is to move a coninuously smaller volume of air as the differential increases) and consume more power as the differential increases, it similarly requires less power as more heat migrates from the the hot side to expand gas on the cold side. I suppose I could see how for any one momentary snapshot of the system that power might seem to just sort of disappear, but hysteresis should correct for this in the long run.
The idea is rather like using a giant rubber band as a belt in a belt drive, only the belt has some sort of pinching system that forces it to contract only in one direction, so that any energy stored in stretching it must eventually contribute to forward motion of the system somewhere. At the moment when the belt is stretched it is longer but has not contributed to forward motion, so energy appears to be lost, but in fact merely hides itself in tension. What you seem to be saying is that the belt will contract without ever releasing the tension, yet the tension will be gone none the less, as would be the case with the closed check valve pressure system that never lost heat but still lost energy without doing work. If I think of the belt as just getting longer and longer without ever contracting if left in a stretched state for too long, but periodically snipping off the excess as I go, I can get something like the compression system loosing heat to the environment, but presumably the belt is reinforced with insulation that increases the amount of time it can be stretched so that I will see only negligible permanent stretching.
What specifically am I missing here? I mean, I'm really not trying to bust your balls, but if there is some fundamental flaw in my reasoning, I need to know where it is, so I can correct my understanding. You don't seem to be saying that it is simply impossible to effectively insulate the system, yet your argument does seem to assume that heat has left the system through something other than kinetic energy transferred to the wheel, and I'm just not seeing where it went.
OK, some basic physics.
When you compress a gas (or a mixture of gasses, like air) then it gets hot. Gasses have a limited capacity to store heat, set by a constant called their specific heat, which means that the temperature rise can be very high - in simple terms if you compress it a lot it gets very hot. Heat is a form of energy, so when you compress the gas some of the energy you put in is stored as potential energy in the compressed gas and some is lost as heat that escapes, both through the casing, pipe work etc and also through the exhaust air. This means you've already lost some energy from that used to drive the compressor as heat.
Next you pass the hot, compressed, air to the air motor. This extracts some of the potential energy in the compressed gas, but not all of it, because there needs to be enough "left over" pressure to move the air out of the exhaust port, just like a car engine.
If you make the system closed, like a hydraulic system, then all you do is reduce the amount of useful energy that the air motor can deliver, because you will increase the exhaust pressure by piping it back to the compressor. The amount of energy extracted is directly proportional to the pressure difference across the air motor.
If you were to build a closed system like this, and manage to perfectly insulate it, then the temperature of the air inside would rapidly increase to the point where something would fail I expect. Just like a closed cycle steam engine, you would need some form of external cooling to make the thing work. This cooling would extract energy from the system as heat. The rate of heat loss is proportional to the difference in temperature and follows a non-linear characteristic. The hotter something is the more energy it loses per unit time (see Newtons Law of Cooling for an explanation). This means that the energy loss from the heat in a closed system like this would quickly reach pretty high levels.
If you want more background on adiabatic compression, then take a look at this Wiki page and some of the links to similar areas of thermodynamics: http://en.wikipedia.org/wiki/Adiabatic_process
What you have been describing is a perfect adiabatic process, something that doesn't exist.
BTW, the rubber band analogy is a good one, as rubber bands get hot as they are stretched, this heat gets lost and therefore they always return less energy when allowed to relax than it took to stretch them.
Please ask questions on the forum, rather than by PM, as it helps others and you'll get a better range of answers.