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).