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So, Maxwell's Demon is a thought-experiment in which a
little imp guards a shutter which connects two chambers
of
gas. He only opens the shutter when he sees a fast-
moving
gas molecule moving from left to right, or a slow-moving
one moving right to left. As a result, the gas on the
right
will eventually consist of fast-moving molecules (hot)
whilst that on the left consists only of slow-moving
molecules (cold). Thus, a temperature gradient is
created
for arbitrarily little work (ie, the work done by the
demon
in opening and closing the shutter).
Maxwell's Demon has been extensively analysed and
debunked, and basically it won't work.
So. Maxwell's Piston.
We have a tight-fitting piston enclosing a volume of gas
in
a cylinder, and a little demon watching the gas
molecules.
The piston is on a ratchet, so that it stays put once it has
been moved forward.
If we just push the piston, it gives an extra speed to any
gas molecules that hit it while it's moving in. This
makes
the gas hotter. The energy to heat the gas comes from
the
work we have to do to push the piston against the force
of
the gas molecules hitting it (ie, on a gross scale, the
pressure of the gas). This is all fine and dandy.
However, suppose our demon waits until it can see that
none of the gas molecules are about to hit the piston.
He
then seizes his moment to move the piston in by a tiny
fraction. Because the piston hasn't been hit by any gas
molecules during the movement, no work has been done.
Equally, because no gas molecules have hit the piston
while it's moving, no gas molecules have been sped up,
and
hence the temperature of the gas has not been
increased.
This too is all fine and dandy. Except that now we have
managed to compress the gas without doing any work
and
without heating it up. Which is odd.
Szilard Engine
http://blogs.discov...-to-extract-energy/
A discussion of the relationship between energy and information in thermodynamics [Wrongfellow, Dec 22 2012]
[link]
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//without doing any work// I know it seems like the dishes get done automatically, and new wings get built with no visible human effort, but believe me to the scullerymaids and hod carriers it feels a lot like work. |
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Energy storage at that level isn't only atomic(literally) Newtonian KE. |
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no demon needed, just build a ratchet that works at subatomic distances and introduces no friction. such a quantum ratchet would allow you to compress the gas an immeasurably small amount further than you would otherwise be able. also, don't fail to forget that your piston and cylinder need to be made of an infinitely stiff material impervious to any compression and that the two must be mated together with similar rigidity. also, no inertia. perhaps you can build a rig to compress a single molecule of gas? |
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I think this is too focussed on the moment of causation instead of perhaps the follwing moment of effect. By reducing the volume of the space, no matter if any molecules were contacted in the process, the molecules will be more excited because they will ultimately bounce off of cylinder and the piston, and when they do so, they will be moving a lesser distance with the same energy. |
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//without doing any work//
What, your piston is massless? (W=fd, f=ma)
Hmm, never noticed before that Work=mad... |
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//What, your piston is massless?// No, but it is
frictionless (I'm allowed that in a thought
experiment). Thus, however much energy I put in
to get it moving, I can in principal recover when it
stops moving. |
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// the molecules will be more excited because
they will ultimately bounce off of cylinder and the
piston, and when they do so, they will be moving
a lesser distance with the same energy// That
sentence doesn't lend itself to analysis. What is
"excited"? And what does it mean to move "a
lesser distance with the same energy"? |
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Even if the piston has mass, if it moves against zero force then
no work is done and no energy is required. "Every object
continues in a state of rest or uniform motion, unless compelled
to change its state by an external impressed force". |
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Initially, the piston has no velocity, therefore no momentum or
kinetic energy. To decrease the volume contained (assuming a
frictionless seal) it must accelerate, aquiring translational
velocity and thus momentum and kinetic energy. |
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Having decreased the contained volume (losselesly, as there is
no friction) it must then decelerate, giving up its momentum,
before the gas molecules once again strike its face, exerting a
force. |
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Theoretically, as long as all the energy is recovered after each
move.ent, the volume of the gas can be decreased reductio ad
absurdum, until you have a volume delta-v containing a very
small amount of Neutronium. |
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[WcW] Atomic scale ratchets are supposedly
impossible, as they are as likely to slip as not (see
Brownian Ratchet). I've never been entirely
convinced of this fact, however. |
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I'm inclined (pi/4=45deg) to think this reduces to a discussion of the energy required for observation (how does the demon observe the gas molecules?) |
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Since the system is stochastic, the demon doesn't actually need
to observe the molecules.
If there were just one molecule, then based on the volume of the
cylinder, the temperature, and the mean free path, a time
window could be estimated when the molecule is not interacting
with the piston; if the piston moves during this time, no work is
done. |
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// I am no rocket scientist. If I were, I would not be working as a janitor in a state prison. |
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What a great line, I enjoyed that. Reads like the start of a good novel. |
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// Energy storage at that level isn't only atomic(literally)
Newtonian KE.
— FlyingToaster, Dec 22 2012//
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Come on then; out with it!
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^ lessee... electrons spin out to higher orbits, molecules bend to different angles... |
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The positions of the particles aren't actually
definable, but are probability states. By moving the
piston you are changing the probabilities of the
positions of each contained gas molecule and
thereby introducing kinetic energy. So saith the
Voice. |
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[Wrongfellow]'s link says it all. If you have some information about a system, and some heat, then you can use that information to do some work, or (locally) reduce some entropy; entropy and information are fundamentally linked. |
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I don't see any reason in theory why it wouldn't work as described - that is, the final volume would be smaller but the temperature is the same. |
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It is not a thermodynamic free lunch, because information is never free; you used up at least as much information about the momentary location of molecules as the extra information contained in the smaller volume of gas. |
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You could achieve the same result by applying work to the piston, and removing the generated heat; either way, you pay in full for the reduction in entropy inside the cylinder. |
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//You could achieve the same result by applying
work to the piston, and removing the generated
heat// Fair enough. I had assumed that there was
conservation of energy - otherwise it would fall
prey
to the same flaws as Maxwell's Demon. |
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So we can either compress the gas in the normal
way (without ratcheting during collision-free
moments), requiring energy to push the piston,
which we can then recover as heat; OR we can
compress the gas using the Demon, requiring no
energy to push the piston but also generating no
heat. Either way, the conservation of energy
holds. |
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Howevertheless, it does raise the interesting
possibility of being able to compress a gas without
raising its temperature. That ought to be good for
something. |
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Not so. The entropy of the smaller volume is lower, and it is possible to use that to convert some heat into work, but the internal energy of a gas does not depend on its volume. To say it has 'more potential energy' is not accurate. |
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More to the point, the amount of work that can be done by the expansion of the gas depends on the circumstances - whether the expansion is adiabatic or isothermal, for example. So there is not really any such thing as 'the' potential energy of a volume of gas, and it's a misleading term here. |
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// requiring energy to push the piston, which we can then
recover as heat // |
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You can't "recover" that energy, no more than you can recover
the energy from the cooling system or exhaust gases of an
internal combustion engine back into useful work - that would be
an anentropic heat engine, which is almost impossible. |
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Recover was possibly the wrong word; but the energy of the work is later present as heat, and thus energy is conserved. Note that he said //energy ... recover as heat//, but did not imply that that heat can be used to do work. |
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So I'm an engineer and I don't understand the point of this idea. Maybe that's why it's on the halfbakery. Custard powered piston |
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Ohhh... Then this idea has a theme song, Cake's "Satan is my motor" |
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Bang, bang, Maxwell's Demon Piston
went straight o'er my head;
I'd love to like it but I'm not sure
I grasp just what it said. |
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Joan was pivotal,
Studied compressivital
Science in the home.
Late nights all alone with a gas jar
O-o-o-oh. |
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MaxwellBuchanan,
Biologic science man
Called her on the 'phone:
Can I take heat out of the picture
Jo-o-o-oan? |
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But as she turned her back on the boy
Entropy changed her mind
Bang bang etc. |
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On all but one minor technical point: "Don't Stop Believing"
or
"Eighteen and Life"? BION, it works with both. |
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It's sure an interesting thought experiment, but any macroscopic amount of gas will contain enough particles for them to behave as a statistical ensemble, rather than as individual items. So there will never be a moment when there are no particles interacting with the piston... Or rather, the probability of that occuring could be calculated using the methods of statistical thermodynamics, and it would be vanishingly small for any real-world sized piston and reasonable gas pressures. |
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The Beatle's lawyer called, but I told him parody was fair play. |
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The speed and scale of the piston movement would probably, in my imagination anyway, place the action in the electromagnetic realm and therefore the problem would have a capacitory component. Changing of a gap and all that. |
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//any macroscopic amount of gas will contain
enough particles for them to behave as a statistical
ensemble// |
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Yes, but that's not the point, any more than it's the
point for Maxwell's Demon. If you like, imagine a
long but very narrow (say, 1µm) capillary filled with
gas at a low pressure, and fitted with a piston. The
numbers then become manageable. |
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As [wrongfellow] and [spider] said, the use of
information to determine the correct time to move
the piston results in the required increase in entropy
in the total system. TANSTAAFL still applies. |
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Maxwell's piston won't work for the same reasons that Maxwell's demon can't.
Anyway, I think both Maxwell deserve a bun :-) [+] |
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You could also have Maxwell's Ratcheting motor; a shaft is mounted with many spring-loaded ratcheting spools of fine thread. Each piece of thread is tied on to a gas molecule. As the molecules zoom about with their brownie in motion, they alternately pull on the thread, or allow it to be reeled in. All the pulls act to turn the shaft, at the end of which is a generator, or a clockwork penquin winding mechanism, or a paper-christmas-tree-unfolder, or something else useful. |
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I suppose you could argue that the threads steal energy from the molecules, cooling them down, but they can get that heat back from the walls of the containment vessel. So the machine is running on the background heat of the universe. |
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[Poc] Look up a brownian ratchet, as I mentioned
above. Basically, a ratchet at that scale will either
fail to advance or slip backwards enough that no net
motion is achieved. |
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[Kansan]
/* FIXME: */
True , but the statistical mean of momentum ( p=m*v ), and consequently the statistical mean of energy would be the same for heavy and light particles in an homogeneous mix. |
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He's right about the velocity, though, since the mass term is so disparate. |
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There's also potential for stratification if the velocity falls low enough, even under a measly 10N of gravitational force. Gas centrifuges can separate isotopes with much smaller mass ratios, but demand much higher centripetal forces. |
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Statistical measurements are a red herring. One can
simply build the piston with a box containing
sufficiently few molecules that the ratchet is
otherwise possible. |
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But if we cut the number of gas molecules and the size of the piston sufficiently, we find that we are indeed trying to put a tiny harness on a single atom. perhaps after we are done with that it can play the universe's smallest violin to celebrate our success. |
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If you turn the vessel inline with gravity the gas will balance for any giving weight of piston. The statistical collection will look as if a molecule is always against the piston. Is there a time when the piston is about to fall and has space before the next molecule? No gravity will make sure the gap is closed. |
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I'll agree with the no work part but it would heat up.
(the demon told me so) |
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