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I was thinking about how you might grow plants inside without sunlight powered only by LEDs. But to get the energy for the LEDs, one might drill a hole down into the Earth's magma and put a steel pole. Then the heat from the magma would heat up the pole and you might be able to generate electricity at the top from the heat.

I was wondering, if the pole was for example 1cm in diameter, how deep would you have to drill it to generate electricity for one LED?

This assumes that the heat would make it's way to the top of the steel pole without dissipating. Hopefully it would as steel conducts heat better than rock.

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closed as off-topic by Bill N, John Rennie, Jon Custer, Kyle Kanos, ZeroTheHero Mar 3 at 1:56

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  • $\begingroup$ Mind you, steel is a pretty lousy thermal conductor relative to copper or aluminum (like 10x worse or more). $\endgroup$ – Jon Custer Feb 28 at 4:15
  • $\begingroup$ yes, but i'm thinking steel might be less likely to melt. Then the copper might just dissolve into the magma. Maybe you could generate the light near the magma and funnel it up with fibre optics. Or maybe the magma itself emits light. $\endgroup$ – zooby Feb 28 at 4:30
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    $\begingroup$ You need a thermo-electric generator for this application. $\endgroup$ – David White Feb 28 at 6:06
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You're fighting a tough battle there. The deeper you drill, the warmer it gets. But the farther you have to transport the heat. Even assuming you had nearly perfect insulation, the rate you can deliver the heat is low.

For thermal conductivity (the rate that you can pull heat up through your rod), we can use $\frac{Q}{t} = \frac{\kappa A (\Delta T)}{d}$. The longer the rod, the slower the heat comes up.

If you have to go four times as far to double the temperature difference, you're not getting anything good from the power. Imagine that you could hit something really hot (like 2000K), and it was only a mile down. Then using an aluminum rod we could expect: $ (205 W/m K)\pi (.005m)^2(1700K)/1610m = 0.017 W$.

So with unrealistically optimistic geography, we get a tiny amount of heat delivered (and then you have the difficulty of turning that tiny bit of heat into usable power).

Waiting for the heat to diffuse through the rod (even for high conductivity metals) is just too slow. More efficient is to use lower heat levels, but transport the heat via a fluid to the surface.

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