# What is the minimum practical size for buildings heated by small nuclear reactor?

In the book Early Riser by Jasper Fforde, humans hibernate in large dormitories. These circular buildings range in size from 20 to 60 floors, with around two dozen rooms per floor. While the residents slumber they are kept nice and warm.

The heat is generated by a hot pot. The hot pot is a small nuclear reactor. A lone steward stays awake during the winter operating the hot pot by partially inserting and removing control rods to regulate the temperature. The reactor is set up to produce heat, not electricity.

This seems like a good way to heat a very large building. Even small nuclear reactors have to be quite large and expensive to function properly and safely. The buildings residents are almost always asleep while the building is occupied, so there is almost no energy usage except for heat. What is the smallest building size that would match with the energy output of a small nuclear reactor?

• What is "small" when you attach it to nuclear reactor? – L.Dutch - Reinstate Monica May 16 '19 at 18:42
• Basically any size equal or larger than the reactor, assuming you're requiring the reactor to be in the building. – GrandmasterB May 16 '19 at 18:57
• Interesting article on some of the modern small / portable designs that may be of interest for you: powermag.com/big-gains-for-tiny-nuclear-reactors From the sound of it, these would not need control rod operators. They're basically big batteries. – GrandmasterB May 17 '19 at 6:32

# Any size would be practical, including a single individual

Though we don't call them such, Radioisotope heater units are technically small nuclear reactors, which only give out about a watt of heat. The description that you gave requiring an operator and control rods does imply a larger unit, but there is no reason to believe that this single purpose nuclear heater type reactor couldn't be designed at a variety of small sizes.

• Great, didn't know about those, seems obvious they should exist in retrospect. +1 – A Rogue Ant. May 16 '19 at 18:36
• I was going to answer "a pup tent", but you got there first. Radiothermal generators come in power ratings from a few watts to a few kilowatts, and of course can be ganged to produce more heat if needed. – Zeiss Ikon May 16 '19 at 18:37
• If the "control rods" were in fact neutron reflectors, they'd be an excellent way of turning up the heat when needed. All those pictures of a plutonium ingot glowing red hot were taken after it had been covered up in exactly that way for a little while. – Starfish Prime May 16 '19 at 18:38
• I am not a specialist, but in a nuclear reactor the fission is accelerated by modulating the neutron flux, while in the device you propose it is all left to nature. I don't think they can qualify as reactors. – L.Dutch - Reinstate Monica May 16 '19 at 19:01
• @L.Dutch The definition of nuclear reactor is "An apparatus or structure in which fissile material can be made to undergo a controlled, self-sustaining nuclear reaction with the consequent release of energy." While it doesn't correlate to what we expect from modern nuclear reactors, Jasper Fforde was not incorrect to classify them as such in his book with the description he gave, and they can indeed be made smaller than what he described. – Mathaddict May 16 '19 at 20:21

Using the decay calculation of plutonium 238: we must use ~1.75 grams of P-238 per watt. This seems to be inline with the heat production of typical radioisotope heater units

... (providing) about one watt of heat each, derived from the decay of a few grams of plutonium-238

Let's assume: each room is 7 feet x 7 feet x 7 feet (the minimum bedroom size in NYC), each floor has 24 rooms (we can pretend heating systems, stairs, and hallways don't take up volume). This means a 20 floor facility would be 164,640 cubed feet. Using this map I'm going to guess we are in zone 3 (because that's where NYC is). This means to heat our facility we need ~7 Million BTUs or ~2 Million watts.

To produce 2 Million watts through radioactive decay, we need 3500 Kg of P-238. The mass of P-238 is 0.019 kg/cm3, so we need ~66.5 cm3 in Plutonium alone.

I think that since the plutonium is just naturally decaying, it doesn't need to be cooled (someone please confirm). However I have no idea how to go about shielding the radiation produced by the Plutonium. I think you would be pretty safe with something about the size of 7 feet x 7 feet x 7 feet.

Suggestion: look into how many rooms this could supply with power https://en.wikipedia.org/wiki/S8G_reactor

• If you need 3.5t of plutonium and it weighs ~19g/cc, you'll need a bit more than 66.5cc... 3'500'000g/(19g/cc) = (3'500'000/19)cc = 184'210cc which is a cube nearly 60cm on a side, other than that, looks ok. Although I wouldn't want to be in a building with a 2MW space heater with no off switch... – Samwise May 16 '19 at 22:59
• Great sources! In the book the dormitories were circular. The elevators and ventilation was in the center core. – Stephen Meschke May 17 '19 at 16:07

## Portable Nuclear Reactors

OP states:

Even small nuclear reactors have to be quite large and expensive to function properly and safely


This would be better written as:

Even small *civilian* nuclear reactors have to be quite large [...]


Assuming you aren't bound by anti-proliferation treaties and you can use higher enrichment than our current generation of civilian reactors, you can make a reactor very compact, even if your definition of "reactor" is strict enough to require control rods.

The Demon Core was roughly the size of a grapefruit, so your minimum "reactor" size is probably about 2-3 times that, to support a little more material, control rods, neutron reflecting surfaces, and a support box.

Just... don't open the box.

• But I must know what's inside, even if it kills me – DKNguyen Apr 14 at 20:43