An infinitely long Maxwell’s demon in a vacuum

In which the second law of thermodynamics plays spoilsport in the high dreams of an honourable Gujju.


UPDATE Sep 27: Work intervened. More on this in a bit, but I thought I should say something before then. Like Saikishan points out in the comments, the Carnot engine argument is flawed. The idea of generating power from the temperature rise caused by the train is laughable. I’ll say why. I’ll also argue why I think the idea that energy can be extracted from the small scale motion of turbulence is also deeply flawed. Soon.

There’s this article doing the rounds about the Indian central government getting a letter from a gullible Gujarati man who thought he had a brainwave when he realised that moving objects drag the medium they are in (air) behind them, and leave eddies of flow in their wakes. “All that wasted energy! Let’s put a windmill there and extract it all, why don’t we?”

So went he forth and sent a letter by post to the Prime Minister’s Office. (The article makes double mention of the fact that he sent his letter by post. That’s either wonderfully subtle mockery, or just blind luck.) And apparently the PMO saw fit to send this letter to the Railways asking for expert opinion.

The PMO, in turn, forwarded it to the Railways Ministry, asking it to explore the “techno-economic” feasibility of the idea, and sought regular updates.

The expert opinion was, of course, that this is a useless idea:

“A train will pass the windmill in less than 20 seconds. Even if there is a train every 15 minutes, a windmill can operate for only 25 minutes per day. This will not be viable economically. Further, the energy produced by the windmills would have to come from the trains only, which will consume extra energy[…]”

I have no problem with people sending silly ideas to engineers in the railways. I’m sure whoever got the job of explaining why the idea is silly had a lot of fun with it. I thought I would too.

So what’s wrong with sticking a windmill next to a train? The good people of the railways point out that this would be a huge investment that’s only ever going to be ‘switched on’ 25 minutes a day. Philistines, I tell you. What stops them from working with infinitely long trains and infinitely many windmills? Unfortunately, even with infinitely long trains and infinitely many windmills, there’s the little matter of the second law — the no-free-lunches law of thermodynamics.

Stick a windmill–indeed or any mechanism–next to a train and whatever energy the mechanism produces has to come out of the fuel the train burns. (There would be additional losses too.) As proof by reductio ad absurdum, imagine an ideal engine (a Carnot engine) running the train; i.e. the train’s already running at the maximum possible efficiency. The addition of the windmill draws extra work out of the fuel that the train is burning, and fucks with the second law. And as we all know, the second law is Tony Montana.

The infinitely long train idea is out, then. How about a mechanism that captures energy from the random motion of the turbulence that the (finitely long) train leaves behind in its wake? I can think of two inter-related problems with this.

The first one is logistical: what is the mechanism you have in mind that “knows” when the train has passed by? Because if the mechanism is in place when the train is passing by, it will affect the flow around the train, and therefore change the drag on the train, and therefore effectively draw energy from the train’s fuel source. At which point we’re back to fucking with Tony Montana.

The second problem is fundamental. Can you extract energy from the random motion in a medium? The idea of extracting energy from the wake behind a train is a rehash of the very old problem of Maxwell’s demon: a mechanism that can separate the ‘hot’, i.e. faster moving, molecules in a gas from the ‘cold’ ones. If you think about it, all you need is two compartments with a tube connecting them which only allows ‘hot’ molecules to pass in one direction, and only allows ‘cold’ molecules to pass in the other direction. And soon enough, one of the compartments will be full of ‘hot’ gas, and the other full of ‘cold’ gas. And of course, nothing of the sort is physically possible without violating the second law. Why this is so has to do with information and energy being equivalent, but I shan’t say more about this here.

In conclusion, windmills need large-scale movement of the air around them, i.e. they need wind, in order to extract energy. And changing the large-scale flow around a moving object has to be paid for with interest in increased drag, owing to the second law. The second law of thermodynamics also precludes any attempt at extracting energy from the small scales (albeit in a different way from above).

3 thoughts on “An infinitely long Maxwell’s demon in a vacuum”

  1. If one were to apply the same sense of logic as ( As proof by reductio ad absurdum, imagine an ideal engine (a Carnot engine) running the train……)

    Consider 10 birds, each powered by a carnot engine. Their efficiency therefore is maximum and cannot be enhanced by 2nd law.

    But if those same 10 birds flew in formation, we know that their overall efficiency is enhanced.

    Similarly the overall efficiency of an aeroplane powered by a carnot engine can still be enhanced by adding passive drag reduction elements.

    So where does the contradiction come from ? The bird or plane cannot a carnot system for it has aerodynamic losses. Putting them in formation only reduces those loses and hence does not violate 2nd law. I can extend the same to the train. Even if it is powered by a Carnot engine, the train as a whole cannot be a carnot system. Hence your first logic does not apply ? Am I missing something ?

    The way I see it themodynamically is as follows. The train is transferring is doing work on the air, which becomes stored as energy in the air. Laws of thermodynamics only determine how much of that energy is recoverable. They do not imply that extracting any energy automatically implies the work that is done by the train increases.

    Forget windmills or extracting kinetic energy from the wind in any way for now. I guess you would agree that the energy spent by the train ought to be equal to the energy gained by the ambience (1st law). Now if we were to wait till everything comes to rest, the energy would eventually be all converted to potential energy and reflect in increased temperature of the air. I can always connect a heat engine between that air and air from a very distant region that is yet to be affected and get some work. Mind you, at this time the train has also stopped and thus I havent made the train do any more work that what it did during its journey. Ofcourse 2nd law would determine the portion of that energy that can be converted to work, which would be DT/T, which would be very small for any practical purpose. Nevertheless, I have extracted a non zero energy from the wind without increasing the work on the train.

  2. Coming to the Maxwell demon. If one puts tiny paddle wheels in gas at rest , then it appears as if we can extract energy from the random molecular motion in any gas. This would mean violating 2nd law, i.e. converting heat directly into work without a second reservoir. Where is the contradiction ? The answer is that the paddlewheel will also be made up of molecules which will vibrate based on their temperature. If the paddlewheel is at the same or higher temperature, the random vibrations of the paddle wheel would cancel whatever torque that is produced by molecules that randomly impinge on it. It is therefore possible to extract any energy only if the paddle wheel has lower level of vibrations, ie. at a lower temperature. Hence 2nd law is not violated. A more sophisticated argument is the Feynmann Ratchet.

    However, such a problem does not exist with extracting energy from the small (but very large by any molecular scale) eddies in the turbulent flow. They are not thermal vibrations. So nothing prevents us from putting tiny paddlewheels (whose thermal vibrations would be much smaller scale) and extract energy from the small turbulent eddies. But does that affect the large scale turbulent motion and hence the drag on the train ? That is a controversial area, one that pertains in some way to my current problem. Based on whatever evidence I have and based on observations such as the spread rate of a turbulent jet doesnt depend on Reynolds number, I would like to argue that the coupling between the large and small scales is virtually absent in free-shear flows.

    Hence while I dont argue that it is indeed an economically or technologically feasible idea to be able to extract energy from the wind due to a train (without contributing an equal or higher load on the train), I dont see how it is fundamentally impossible based on what thermodynamics I know. Thermodynamics can indeed be strange, so if I did miss out anything, please do clarify.

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