Nanotech free energy

[Merko]

Wait a moment. I think I have it figured out now. There is a reason why it would be more likely for a molecule to exit the box, when the hatch is swinging open due to random vibrations.

Assume that the hatch swings open from vibrations. Assume that a molecule enters the gate, partially. Now the hatch closes again.

In this scenario, the hatch will push the molecule out of the box, regardless of where it came from. And so we have a bias that moves molecules out of the box. This bias cancels the first bias, and so there is no net effect.

Case closed?

 

[Merko]

Or maybe not. Because when the hatch swings open due to random vibrations, it also 'clears' an area on the inside of the box from molecules. Eg, any molecules approaching the opening have a probability of hitting the opening hatch and getting deflected. Molecules coming from the outside don't have this problem.

 

[Ziggurat]

Right, but it appears to me that there is no reason why we must assume a detailed balance to be the case, than to satisfy the second law of thermodynamics.

You don't need the 2nd law to derive detailed balance. It is, in many respects, more fundamental than the 2nd law.

And again, it does nothing to explain these mechanisms. The exact opposite of a molecule hitting the hatch, opening it, and entering, would be a molecule approaching from inside, the hatch vibrating open, the molecule entering the opening, the hatch vibrating back

The hatch doesn't "vibrate" back, it swings back because it's spring-loaded.

This appears to be an extremely unlikely sequence of events, unlike the reverse.

That's only because your intuition in this case is unreliable. First off, the hatch has EXACTLY the same chance of flipping open due to a gas molecule hitting it as it does to open because of thermal vibrations in the wall. Second, you forget how often a gas molecule will hit the door, open it, but simply bounce back without entering at all.

This is because there is absolutely no causal link between the molecule approaching and the hatch opening, and also no explanation for the propensity of the hatch to close and hit the molecule on its way out.

The hatch closes because it's spring-loaded. The propensity to hit the molecule on the way out is because the energy for opening/closing is supposed to be larger than the typical thermal energy (so that the door doesn't essentially just stay open), so most escaping atoms are moving slow compared to the door (which MUST swing very fast in order to open in time for incoming gas molecules to squeeze by).

 

[DavidS]

A heat engine requires a source of energy, and a cold sink.

The cold sink requirement comes from SLT. It's clear that the device, if functional, violates SLT for exactly that reason.

The question I thought was at hand is whether we must appeal directly to the SLT to refute the device, or whether SLT-independent reasoning can prove the device impossible so we engineers won't wake up screaming in terror. At least not for that reason.

A piston need not be a heat engine.

Also useful for the odd doorstop, bookend, or desk lamp.

In this case, it's a pressure engine: it uses differences in pressure, NOT in heat, to drive the engine.

Ah... that makes it part of a heat engine: trading the pressure energy in for work.

After running a simulation (because physics is hard), I'm fairly certain this setup would work

Bad news: Simulation is hard, too. At least as hard as all the physics you have to translate into the simulator. I presume, at least, that the electrons' lack of ears means the sound of crunching numbers won't cost them any sleep.

Now all we have to do is figure out whether your simulation properly represents all the phenomena we haven't yet thought of -- but most of us expect to -- that would keep the device from violating the second law. That is, the simulation didn't solve the problem, it just moved it.

Short hand answer: temperature is linked intimately with energy scales in quantum mechanics. A given temperature has a characteristic energy for excitations (basically describing probabilities of excitations with that energy occuring). The energy scale for gas atoms must be such that some gas atoms have enough energy to trasfer to the door to excite the door into its open (higher energy) state. After the door opens, we want in to close again. And we want it to stay closed. In order for the door to close and stay closed (as opposed to bouncing open and closed), we need the door to be able to transfer that energy to the wall in a dissipative manner. The wall must have modes of excitation with that energy so that it can absorb the energy of the door, or the door will bounce back open. And here's the problem: if the wall can absorb excitations at that energy, it can also create excitations at that energy. If it is at the same temperature as the gas (which is going to be at the same temperature as your gas), then the probability of the gas exciting the door and the probability of the wall exciting the door are going to be the SAME. Which means that you cannot keep the door from swinging open randomly and letting gas out from inside, and you cannot create a pressure differential. The ONLY way to prevent the door from opening in the absence of an incoming molecule from outside is to siphon off energy from the wall - in other words, to actively cool the wall to a lower temperature, so that energy flows from the door to the wall and not vice versa. But actively maintaining the wall at a lower temperature, despite a continual input of heat, requires energy (just like running your refrigerator). And the energy required to do this will suck up any energy you could get from your pressure pump, even assuming perfect efficiency (and you're just losing energy if there's any inefficiency anywhere).

I think we've got a winner.

 

[RecoveringYuppy]

Second, you forget how often a gas molecule will hit the door, open it, but simply bounce back without entering at all.

Personally I like the phrasing you developed a few posts back focused on reversibility. But I think that a qualitative argument that might match Merkos revolves around the cases that open the door but rebound. I would think that he might accept the premise that the atom rebounding out the opening constitutes a bias toward atoms escaping. Atoms following the rebounding atom out experience no opposition, atoms attempting to enter have to get past the rebounding atom. He may accept this as an previously unaccounted for bias that works against the bias he's focused on.

Focusing solely on the cases of an atom entering the opening from the outside (which seem to be the only cases in dispute) we have these cases:

1. Atom has not enough energy to open the door and rebounds. Not an issue.
2. Atom has enough energy to open the door but not proceed and rebounds.
3. Atom has just enough energy to open the door long enough for a single atom to enter but none to escape (I'm to some degree accepting the existance of this case merely for the sake of argument).
4. Atom has enough energy to open the door and enter but may also leave the gate open for other future exchanges before closing.
5. Atom has enough energy to open the door and destroy the door in the process.

I would contend that case two represents an unappreciated case biased towards atoms leaving the chamber for reasons mentioned above.

I would also think, but can't prove without a lot of tedious specification of a particular device, that the energy range corresponding to case 2 is going to be wider than case 3.

 

[Ziggurat]

Right, but it appears to me that there is no reason why we must assume a detailed balance to be the case, than to satisfy the second law of thermodynamics.

Why would we believe in detailed balance other than the 2nd law? For the simple reason that we believe that the probability of transition from a state is proportional to the probability that the state is occupied. Does that depend upon the 2nd law? Not really.

This is because there is absolutely no causal link between the molecule approaching and the hatch opening,

It doesn't MATTER if there's a causal connection between two parts, what matters is the TOTAL probability of the ENTIRE event. What is the probability that a molecule approaches the hatch from inside, versus the probability that a molecule approaches the hatch from outside? Basically the same. What's the probability that an approaching molecule from outside has sufficient energy to pop open the hatch? About the same as the probability that the hatch will open on its own. A molecule approaching from inside can be ejected regardless of its energy, but only an energetic molecule from outside can be let in. The low probability of a given outside molecule having sufficient energy compensates for the low probability that the door will open for an approaching molecule from inside, and the total flow rates WILL balance. Again, that your intuition tells you otherwise ONLY indicates that your intuition is not a good guide. Which is quite often the case when working with physical systems radically different than our day-to-day experience.

 

[Merko]

I would think that he might accept the premise that the atom rebounding out the opening constitutes a bias toward atoms escaping. Atoms following the rebounding atom out experience no opposition, atoms attempting to enter have to get past the rebounding atom. He may accept this as an previously unaccounted for bias that works against the bias he's focused on.

No, this doesn't seem plausible at all. First, it would be very rare that two molecules are there at the same time, given a thin enough gas. Second, this effect would be canceled entirely by the increased chance that TWO molecules following each other from the outside would enter at the same time, single file. Because, a molecule from the inside could in the similar fashion be deflected by the entering molecules.

However, I think the reversed bias is that I suggested in post 81. I think this solves it. I feel the effect I outlined in post 82 is probably very small and is canceled by some other very small effect.

I would also think, but can't prove without a lot of tedious specification of a particular device, that the energy range corresponding to case 2 is going to be wider than case 3.

I don't think so. Again, the gas molecules can be heavier than the door, and we can use the normal equations for conservation of motion here.

so most escaping atoms are moving slow compared to the door (which MUST swing very fast in order to open in time for incoming gas molecules to squeeze by).

Valid observation.

Second, you forget how often a gas molecule will hit the door, open it, but simply bounce back without entering at all.

No, because that is irrelevant, as it might equally allow molecules to enter, or to leave.

A molecule approaching from inside can be ejected regardless of its energy, but only an energetic molecule from outside can be let in.

No, this is wrong. A slow outside molecule may enter for the same reason that a slow inside can, namely that the hatch has vibrated open.

But again, I feel the effect I suggested in post 81 solves the case.

 

[RecoveringYuppy]

No, this doesn't seem plausible at all. First, it would be very rare that two molecules are there at the same time, given a thin enough gas.

OK, well it is your intuition that's being argued against here so you get to decide which argument impresses you.

Minor point: This is at least the second time you've hinged an argument on the gas being "thin enough". Your point 7 in your OP says that in principle you could connect these hatches in series. If being "thin enough" is important to the operation of this machine then there will be some limit to how many of these things you can productively place in series.

 

[blutoski]

That obviously doesn't work, because there's no pressure difference, and the turbine never turns. The point of the chamber and hatch is that it (supposedly) creates a pressure difference.

If you're dealing with individual molecules, then you're not dealing with 'pressure'.

OTOH: if you're dealing with 'pressure' (lots of molecules), then what you're saying is that you're seeking a special type of hatch that defies pressure: allowing gas to go from low-pressure to high-pressure, right?

Sort of like saying:
"I've invented a perpetual-motion waterwheel. This black box represents the 'valve' that allows water to flow upstream, back to the waterfall. I'm still working on that part."

 

[blutoski]

The problem, once again, is not that this violates conservation of energy, but that it violates the requirement that entropy not decrease in a closed system. It's a 2nd law violation, not a 1st-law violation.

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.

Unless I missed the part where the work is redistributed to the system, say, by operating the gate, or being dissipated as photons to the molecules outside.

 

[Ziggurat]

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.

Doesn't matter, the same principle applies. The restriction that entropy not decrease in a closed system is the same as saying that for an open system, any decrease in the entropy of the system must be offset by an equal or greater increase in entropy of the system's surroundings. Extracting work from a system, however, does NOT require an export of entropy. This means that if you can extract work at the same time as you've decreased total entropy (as would be the case if this device worked), you have violated the 2nd law of thermodynamics.

 

[Ziggurat]

No, this is wrong. A slow outside molecule may enter for the same reason that a slow inside can, namely that the hatch has vibrated open.

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:

5) The door opens and a low-energy gas molecule enters the chamber without transfering energy to/from the door
6) The door opens and a low-energy gas molecule exits the chamber without transfering energy to/from the door

5 and 6 are time-reversal versions of each other, and they will have the same rates in both directions and so cancel. But we ALSO have my previous number 3 as a method for slow molecules to exit, and the time reversal of that (for molecules entering, number 2) is NOT slow molecules entering, but fast molecules.

But again, I feel the effect I suggested in post 81 solves the case.

That's related to the above, yes.

 

[Dilb]

Bad news: Simulation is hard, too. At least as hard as all the physics you have to translate into the simulator. I presume, at least, that the electrons' lack of ears means the sound of crunching numbers won't cost them any sleep.

Now all we have to do is figure out whether your simulation properly represents all the phenomena we haven't yet thought of -- but most of us expect to -- that would keep the device from violating the second law. That is, the simulation didn't solve the problem, it just moved it.

The simulation I ran was just a classical simulation, with the gas as small balls which undergo random, perfectly elastic collisions, with a door on a damped spring separating two rooms. The "molecules" did tend to enter the door more than exit it. I certainly don't think my simulation properly represents what happens in the real world, but the reason it doesn't work should have a better explanation than just saying "the door won't work, the rates will be equal, because otherwise it would work and violate the second law of thermodynamics".

 

[Ben Tilly]

The simulation I ran was just a classical simulation, with the gas as small balls which undergo random, perfectly elastic collisions, with a door on a damped spring separating two rooms. The "molecules" did tend to enter the door more than exit it. I certainly don't think my simulation properly represents what happens in the real world, but the reason it doesn't work should have a better explanation than just saying "the door won't work, the rates will be equal, because otherwise it would work and violate the second law of thermodynamics".

So here's a good question. Suppose that we set this up with macroscopic bouncing balls. (Let's assume that we have truly elastic balls.) What you've just said is that the proposed device will tend to collect the balls on one side of the wall. Why doesn't that violate the second law?

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. Which means that the working of the spring is a significant part of the operation of the machine, and has to be a significant part of the analysis.

Which thought triggered a memory, I searched on it and came to http://en.wikipedia.org/wiki/Von_Neumann-Landauer_limit - which says that there is a lower limit on how much heat must be released by an irreversible flip of a bit. So in the context of this engine, there is a minimum amount of heat that you must release in having the spring close the door. This represents a minimum increase in entropy. I firmly believe that a detailed calculation would find that this increase in entropy always exceeds the decrease caused by moving one more atom inside the partition.

Cheers,
Ben

 

[Squishua]

2. This device breaks the second law of thermodynamics and so it's impossible.

It does. But this law is more of a conjecture anyway.

It is no more conjecture than saying that same set of winning numbers will not be drawn three consecutive times in the state lottery. Sure, it's "only" statistically unlikely, but these are mighty steep odds.

And these are the odds against it doing any useful macroscopic work once. Working continuously would be along the same statistical lines as winning every lottery time after time after time...

The odds are damning.

So.. where am I going wrong? In one of the attempts above, or is there something else that I just haven't thought about?

For one, you might consider that the "molecule-sized" hatch "works" at the atomic scale, which is quite different from the macroscopic scale.

The hatch is bumpy and granular just like the molecules. 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).

You can't win and you can't break even.

An interesting gedankenexperiment though.

 

[sinsanity2006]

What if you put the turbine at the top and the door at the bottom, doesn't heat rise.

 

[DeviousB]

The door swings open because it has had energy imparted to it by the molecule. So where exactly does this energy go? If it is absorbed by the swing or the frame in some way (usually through heating), then entropy increases and the 2LOT is not violated, if we imagine a perfectly elastic door and spring (or doorframe and spring), then once hit by a molecule, the door will continue to swing open and shut and not function as an adequate partition between the two sides.

Once again, covered in point 3 of the OP.

Actually, no. Point 3 refers the the energy of the molecule. The whole point of Smoluchowski's Trapdoor is that it appears to work because a naive analysis usually does not correctly account for the door.

If the door is light enough - and the spring weak enough - to admit a particle, then when at thermodynamic equilibrium with the rest of the system its kinetic energy is such that it does not function as a one-way door. If it is cooled to maintain its function then the entropy gain through cooling can be shown to be greater than the entropy loss through the operation of the door.

Of course, very few respectable scientists actually believe it can be circumvented. I also don't believe it can be circumvented. I don't believe that this device would actually work. But it is definitely not enough to say that it can't, because so far, it has not been proven.

In fact it was proved by its proposer, Smoluchowski, in 1912 ("Experimentell Nachweisbare der Üblichen Thermodynamik Widersprechende Molekularphänomene" - M. von Smoluchowski, Physikalische Zeitung 13). His (correct) analysis of an equivalent situation to yours showed that any mechanism - such as a spring-loaded trapdoor - is prevented by its own Brownian motion from functioning reliably as a one-way valve. 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.

Smoluchowski's work was in response to Maxwell's assertion that the second law "has only a statistical certainty". Smoluchowski 'designed' a feasible, mechanical 'Maxwell's Demon' and demonstrated that it could not convert heat into work in violation of 2LOT.

Part of the reason scientists believe in the 2nd law so strongly is precisely because of Smoluchowski's work. An automatic, mechanistic MD does not work and, at the time, the idea of an actual decision making MD could be dismissed as a fantasy.

And if a century old paper in German is too obscure for you, your device has even been built and tested (albeit inside a computer): -

"Maxwell's Demon, Rectifiers, and the Second Law: Computer Simulation of Smoluchowski's Trapdoor" - P.A. Skordos, W.H. Zurek.

 

[DeviousB]

And you may have been thinking about this for 10 years, but Smoluchowski's Trapdoor was covered in my U/G TD course, and that was over 20 (ack!) years ago!

You could have saved yourself a lot of time by just looking it up in a book^*.


*Mine is in the attic, so I cribbed most of the above from here.

 

[AWPrime]

That's not the problem. Any sustainable gradient, even a small one, could in principle drive an engine.

Only if the engine is frictionless and weightless. Any engine has a minimun energy threshold.

 

[RecoveringYuppy]

His (correct) analysis of an equivalent situation to yours showed that any mechanism - such as a spring-loaded trapdoor - is prevented by its own Brownian motion from functioning reliably as a one-way valve. 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.

I wonder if Merko accepts this? To me, it doesn't seem to be addressing his point. He's repeatedly said that he thinks he's accounted for random motions and that the random motions, which he agrees aren't a one-way door operation, don't eliminate the one case he thinks is biased. He's repeatedly rejected, even gotten testy about it, assertions that random openings can swamp the case he's interested in. He claims they only reduce the efficiency of the effect he's talking about. And the resolution he finally talked himself in to rests on him talking himself in to a belief in an opposing bias existing in some other case.

Do you know of any articles that might address a question I had during this conversation: What is the practicality of building a door that has a low "door inertia" to high "gas momentum" ratio? Would such a door necessarily face imminent destruction or could one be built with a practical life time?