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The Thermoelectric effect allows for electrical energy to be created, based on a difference of temperature. In fact the Radioisotope thermoelectric generator is based on this principal and does/has supplied energy to several NASA vehicles.

Space is cold, and the inside of human occupied vehicle is warm. So if you just made the shell of your ship a big Thermoelectric Generator, and kept the inside at a comfortable temperature, how much electrical energy would you produce?

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    $\begingroup$ Usually it's the other way round. You have to expend energy on keeping the inside at a comfortable temperature by dumping heat through the radiators. $\endgroup$ – Deer Hunter Jul 28 '13 at 12:13
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    $\begingroup$ Interesting, but I presume you couldn't convert the heat to el. energy efficiently. Seebeck effect TE generators have, according to Wiki, "...typical efficiencies around 5–8%.". Problem is, this comes at an expense of the heat converted into el. energy (well, obviously LOL), and you end up cooling the inside of your spaceship that much faster, requiring more heat,... ad infinitum. And then also the problem that @DeerHunter mentioned. You're losing heat faster than you'd like it to, so you really want to insulate, rather than speed up the heat exchange by radiating it to space. $\endgroup$ – TildalWave Jul 28 '13 at 12:21
  • $\begingroup$ Current spacecraft aren't big enough to use human metabolism, but by the square-cube law eventually there is enough heat produced by people inside the ship to keep the ship warm. These huge ships would have enough heat to produce some power through thermocouples. (Basically burning food for heat, then powering thermocouples with that heat. People in the middle) $\endgroup$ – Jeremy Kemball Aug 12 '13 at 18:24
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This question is intriguing because of the nature of the thermal cycles. This is the maximum theoretical efficiency of a thermal cycle (Carnot cycle), no ifs, ands, or buts about it.

Carnot efficiency

You can obtain very low temperatures from space, because space is at a low temperature. You'll often hear the Cosmic Microwave Background (CMB) cited for this, but that's overly optimistic. A radiator could theoretically couple to that temperature, but in practice you would have to shield line-of-sight from every star in the sky. Practically, the averaged temperature of CMB + stars is a better lower bound, and you'll never get anywhere near to that.

If a blackbody was exposed to Earth's radiation and space in LEO, but was shielded from the sun, it could get to -30 degrees C. Obviously deep space probes don't have to worry about Earth radiation, and you could thinkably shield from that anyway.

We're left with the conclusion that T_C, in the Carnot limit, can be made very low. That suggests a very real possibility of a thermal cycle between the radiator and "room temperature". An engineer will hem and haw at the mention of this, but you could have a thermal cycle between those two things at 90% efficiency. I think we need to recognize that the answer to the question, as asked, is "yes".

Now, onto the qualifiers. There are a lot of penalties for ever setting up something like this.

  1. Space stations have to spend money on insulation to begin with, so you would increase that cost (dramatically), in order to avoid heat flow bypassing your radiator.
  2. What physical mechanism would you make this thermal cycle out of?
  3. The system would affect the energy balance of the station. It would have to be a part of the heat engineering from the ground up.

The only thing this really tells us is that it's not a serious near-term consideration. There are good reasons that we don't have a experience base for #2, for instance. There's a lot of work going on with recovery of waste heat, but often over small T differentials, but we don't often consider heat rejection at very low temperatures. It would only come into play for heat recovery systems in liquid nitrogen plants, for instance. If memory serves me correctly, I think thermoelectric systems depend on a very high temperature source. Everything is turned on its head when changing the temperature ranges like this. But there might be good options out there. This would be an interesting study area, because we just don't see those super low temperatures on Earth naturally. So it would rarely make sense to use it for heat rejection. Keep in mind, however, that good heat engines are not guaranteed. Thermal plants on Earth can often only produce 30-40% efficiency when the theoretical limit is 70% or so. That's because higher efficiency systems just won't scale up like we need. It's hard to say what efficiencies we could get.

But we wouldn't do it soon because space radiators are extremely large in size, modern designs require lots of mass, and insulation costs money too. The physical limit is area, from thermal radiation laws, but these are often made of metal sheets, or other things which are heavy. This is reasonable when you consider they'll have to hold in a fluid at pressure (and leaking is bad). The real limit is robustness for the space environment, ability to go up in a rocket, and the ability to unfurl itself into space. If you could spread out a much lighter sheet, it will cool much faster. But how could you recoup that coldness? And how is it going to hold up? In the distant future, space heat rejection systems have a lot of room to obtain very good performance through large, fragile systems in zero gravity. Same goes for insulation.

The heat balance with the station isn't completely self-defeating. This would only work if used with a station that was virtually perfectly insulated to begin with (long way off), but the "useful work" would be put back into the station. That creates an interesting situation where you get back a lot of the energy you consume. Low temperatures have economic value just as high temperatures do. But you'll have some other heat source (the sun, for instance) anyway, so any proposal for heat cycles coupling from station temperature to space also have to compete with coupling to the higher temperature. The ultimate design for heat movement between reservoirs would have to be considered in a holistic sense. But I could see how the OP's idea would make sense in a station powered by PV panels, for instance.

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    $\begingroup$ ...or how about another planet? Mars' average surface temp of 218K gives a Carnot limit of ~25%, with any 'waste heat' going into the planet itself. Also interesting (IMO) is considering a base somewhere like the moon, where it's really only 30-40K in the shade, giving a 'lunothermal' system a Carno limit of over 80%. $\endgroup$ – pjz Nov 9 '15 at 21:16
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An RTG is based off of the flow of heat. You have to have a way to make heat flow from one spot to another spot. You can't directly just use one end directly to space, there just isn't anything there. What you end up having to do is use radiators, which will radiate the heat in to space, but these tend to be warmer than the spacecraft itself, as they have waste heat. In addition, efficiency numbers for a thermocouple are always less than 10%, and could be much lower than that.

So, where would the heat come from, if not from an RTG? It would either have to be waste heat from the electronics, or heat coming from the Sun. Waste heat can typically be prevented in most cases by careful design, and usually isn't a significant problem. From the sun is possible, but solar cells have an efficiency of around 20%+, and sometimes quite a bit higher than that. As solar cells are more efficient, why use thermocouples?

Bottom line: in theory, one could use a thermocouple to produce a small amount of electricity from "Waste heat" that is radiated out of a radiator. But the best case, it could provide a small amount of heat that could improve your efficiency slightly.

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    $\begingroup$ Let's not forget that these ancillary systems waste mass. Precious mass budget may be going down the drain. $\endgroup$ – Deer Hunter Jul 28 '13 at 12:56
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    $\begingroup$ Not sure what "can't directly radiate to space" is supposed to mean. Of course you can directly radiate to space. Any object with a view factor to space a temperature above absolute zero radiates to space. Radiators are just devices specifically design to radiate. Typically by being thermally connected to the heat source being rejected, having good radiative properties (i.e. high emmissivity), large area, and a good view factor to space. $\endgroup$ – Adam Wuerl Jul 28 '13 at 15:31
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    $\begingroup$ I assumed @Pearson meant you couldn't conduct/convect/transfer heat directly to space, so you have to radiate. $\endgroup$ – Rory Alsop Jul 28 '13 at 19:05

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