Minor point: This is at least the second time you've hinged an argument on the gas being "thin enough".
Yes, but gasses
are very thin. Collissions between gas particles can be assumed to be 'rare', in the sense that at any given time they are unlikely. So it is very unlikely that a molecule would hit the door and another molecule at the same time, for instance. These effects can only be expected to cancel similar rare coincidences.
If you're dealing with individual molecules, then you're not dealing with 'pressure'.
Read the OP. The engine is
not drawn by the same scale as the hatch. Only the hatch is a nano-scale device.
I think we're assuming it's not a closed system: the purpose of the turbine is to extract energy from the system for work elsewhere.
This is sort of what I had in mind, but I guess that removing energy from the system doesn't cut it, we'd have to
add energy to get away from the detailed balance. Presumably.
But the rates for those conditions are not the same. I gave 4 mechanisms for molecules to enter/exit, before, let me introduce two more:
I don't think those mechanisms are right, 2 seems wrong (and is not needed for the explanation anyhow). Let me try to correct them as per my suggestion in post 81:
1) Gas from outside transfers energy to door to open it, gas from outside enters, door closes and transfers energy to wall.
2) Gas from outside transfers energy to door to open it, rebounds outside, gas from inside exits, door closes and transfers energy to wall.
2b) Gas from outside transfers energy to door to open it, rebounds outside, gas from outside enters, door closes and transfers energy to wall.
3) Wall excites door to open it, gas from inside gets to the door, door excites escaping gas (ejecting it like the door was a baseball bat).
4) Wall excites door to open it, gas from outside gets in, door excites gas already outside (ejecting it like the door was a baseball bat).
4b) Wall excites door to open it, gas from inside gets out, door excites gas already outside (ejecting it like the door was a baseball bat).
5) Gas from outside transfers energy to door to open it, rebounds outside, door closes and transfers energy to wall.
6) Wall excites door to open it, door excites gas already outside (ejecting it like the door was a baseball bat).
So 1 and 3 are indeed reverses, so are 2 and 4, 2b and 4b, and 5 and 6. But 2, 2b, 4 and 4b are rare events (because it is unlikely that we have several molecules close at any one time). The reverse bias to the bias introduced in the OP is that of 3. The other mechanisms only confuse the matter.
My answer is that the entropy created by the heat created by the damping of the spring outweighs the entropy lost by moving the balls into a less random configuration.
No, that's not a problem. The heat in the spring is of no lower quality than any other heat in the system. The problem is that we're not moving balls into a less random configuration, because what we gain by the hatch working as a hatch, we lose by the hatch working as a baseball bat that ejects balls out of the box.
The atoms in the spring and trapdoor are jiggling randomly due to Brownian motion, which will prevent the mechanism from working in a useful manner (like we would expect macroscopically).
I don't think it prevents it from working, it just introduces a second function for the door which works contrary to the intended one.
What if you put the turbine at the top and the door at the bottom, doesn't heat rise.
Only if you have a temperature difference to begin with, this effect doesn't create it in the first place.
The trapdoor is heated by collisions with the gas and opens and closes randomly, allowing a particle through the wrong way as often as one pushes past.
Yes, although I think this is better and more intuitively stated as saying that it doesn't merely
allow the particle through, it actively
pushes the particle out. Because, if we say it just passively allows it, we have nothing that explains why it doesn't equally allow particles to
enter.
You could have saved yourself a lot of time by just looking it up in a book.
It wouldn't have saved me any work because this would be canceled by losses in handling the information.
He's repeatedly rejected, even gotten testy about it, assertions that random openings can swamp the case he's interested in.
But actually it can't. It's the random
closings that provide the 'negative' bias, not the random openings. The openings equally let gas through in either direction. My problem with these assertions was that they contained no explanation for a 'negative' bias.
So you are positing a valve that is so sensitively calibrated that it is perfectly set to the current entrophy setting of the room, such that it doesn't open when subjected to gas molecules moving at the normal velocity, but does open when hit by a few molecules moving somewhat faster than average.
Not at all. The valve is a normal, macro-scale valve (I provided you with links). Just like the engine is a normal, macro-scale engine. Again, we
know valves work. I'm a mechanical engineer, trust me, they do. If you don't want to trust me, try my links.
You can't change scales when you want to get the answer you want.
Of course I can change scales. We can have a small hatch and a big valve. Or rather, millions upon millions of small hatches and one big valve.