Well, let’s do some quick napkin math– Background (Google searches) (1) Per capita global energy consumption is 22000kwh/yr, which is ~8kw (2) ISS runs on 75-100kw for a crew of ~7 or so (3) S9G reactor for Virginia class sub generates 210MW for a crew of 134 (4) Average US household comes out to ~1.5kw in electricity alone
So. If we’re setting an arbitrary limit of 10MW, that means we are limited to (1) a population of 1000, (3) a population of 7ish, (4) a population of ~6000
I’m going to discount (4) entirely, because that ignores the non-electrical energy consumption which would still have to be done with electricity in space.
Note that every other case also doesn’t cover the entire energy cost of living, because the per capita average and the ISS average doesn’t include growing food, which is free solar power on earth, and specifically case (1) is significantly buffered by people worldwide that use minimal/no power due to having a planet that handles life support for them. Nuclear sub is probably not a great comparison either, because it’s designed to operate in combat conditions and never be refueled. But they are pretty much entirely self-sufficient outside of food.
ISS is probably the best comparison, assuming regular shipments of supplies and no industry. That gives us a rough population of 60-100 per megawatt. I did specify “significant” and “transorbital”, meaning we can’t assume consistent supply shipments. So let’s cut that number in half (random guess), and we have a population of 30-50 per megawatt. Now, there are people that live in villages of 30-50 people, but those villages often rely on infrastructure and industry of larger towns. You can’t really just find a field and plant corn in space. Every space habitat is going to need some sort of industry to make it economically viable. That means workers, that means more power. Let’s guesstimate that we cut the viable population in half again. 15-25 people per megawatt. Now I think this is a viable assumption given the disparity between household consumption (say half your power is electrical, so life support is 2-3kw) and per capita consumption (which divides total power consumption, industry included, giving another 5-6kw per capita to industry).
Smallest town that had productive industry I’ve ever lived in had a population of ~10,000, with about 1500 of those people employed in the factory. Given above napkin math at 15-25p/Mw, which is 40-60kw/person, that puts us at 400-600MW of power for a self sufficient habitat/space ship capable of supporting a population of 10k. Given that the small town I just referred to has a total power consumption of 187MW, we get that same factor of roughly 4x we came up with above.
So for a future space station analogous to Rural Bumfuck, East Nowhere (pop. 10,000) were looking at half a gigawatt of juice. That’s a lot of thermal energy.
Also, S-B law works in kelvin so going from 18C to 90C is only a 33%(^4) increase. Any reasonable space radiator at that point would likely have a multiple coolant loop system. Heck, I’d expect it to be the reverse of current nuclear design, with heat being dumped into a molten salt loop that goes into the radiators themselves at hundreds if not thousands of degrees.
I think the opposite. But we’ll get to that.
First, let’s eliminate transportation. Cool. Done. Now, every space station/space ship is entirely self sufficient, in a contained civilization sense. Go back to that company in a small town I referenced (I worked a contract there for a bit): those 1500 people are producing a pretty basic, but very specific doohickey that exists in pretty much every building we’ve built since the 70s. That production facility represents ~40% of the global market share. Now it is a basic doohickey, so there’s only six separate production lines that feed into the final doohickey. And each building has hundreds, if not thousands of similar specific doohickeys. Spaceships would be more complicated, so let’s just assume a thousand similar doohickeys, six production lines feeding in, one person per production line and were up at 6000 factory workers. Given the previous ratio of 17:3 of population to workers, our minimum theoretical station population size just expanded to 40,000. Multiply previous estimate for 10k by 4. And that’s not considering the feedstocks-one of those production lines was essentially just CNC machines…but they bought barstock iron. That’s another production line. Oh, and the iron has to come from somewhere, so we’re talking mining operations. New limitation: we can only build on asteroids that have ample supply of every mineral resources we need. Plus, each one of those production lines means more spare parts means more production lines. We lose all economy of scale. Minimum population goes up again.
Second, I’ve lived in a lot of places on earth, and even the least hospitable ones, like when I was in the northern USSR or down in Mexico, you had 3-4 months out of the year where you could just open the windows and switch off the heat/cooling. You don’t get that in space. And we see this with the ISS, too. A power system of ~84-120kw supports a crew of ~7 plus or minus a few. I’m guessing most of that power goes to life support. Compared to the power I draw in my house, that implies that living on a habitable planet offsets roughly 80% of the power expenditure for life support.
Third, that’s why I’m comparing primarily household consumption to the ISS. I draw a bit over a kw, and the ISS draws about 10 per person. Thermal losses happen upstream of that. I’m sure the iss solar panels (and solar panels also deal with thermal losses which might now be less than 50%, but last I seriously looked into it were 66% with perovskite cells) are actually exposed to significantly more power than their 240kw max output.
And yes, there are orders of magnitude in difference between the poorest and the richest on earth. This is why I think the 8kw number per capita is actually a low estimate. The difference being that building a dirt house in a prairie is more than adequate life support on earth. Can’t really build a space shack out of sod and expect to do much living in it. I addressed the need for transportation earlier. Matter of fact, one of the theories for why neanderthals died out while modern humans survived is because we did trade and they didn’t figure out transportation.
Cooking, water cycling, etc is already figured in. The ISS does cooking and water heating perfectly fine. Agriculture also wouldn’t be that big of a problem, actually. You just need to build a greenhouse and add a cooling system to account for the increased heat gain of having a greenhouse on your ship. I guess you’ll want some backup grow lights for going past the asteroid belt.
My point is that cooling requirements are cooling requirements. Whether you’re cooling down GPUs or you’re cooling down people, the only question is one of scale. How many GPUs do you need to cool, and how many people do you need to cool? Right now, we can cool off half a dozen, maybe a dozen people on a ship. Having that be the upper limit for space populations means we aren’t going to space in any significant way, indefinitely. If we want to have even small space stations of a few thousand people, we will need to solve a cooling problem comparable in magnitude to a data center in space.
Personally, I’m okay with Google or whatever spending their R&D budget on it. Government grants have been gutted enough, let Google burn cash on it and then put the cheap Chinese knockoff on your future spaceship.