What pressure would be needed to cause fusion of water?

[prodigylock]

TL;DR Summary

Theoretically, what pressure would water need to be subjected to force the oxygen and hydrogen to fuse into heavier elements and how much energy would it release.

So in a DnD story, someone made a bomb by putting 3375ft^3 of water into a 0.5ft radius sphere and caused it to make a nuke. I was thinking if this was possible then what would actually happen, so I spent an afternoon looking for the answer and only got the pressure and density.
6445773,7307163375188090110591252 kg/m^3
186976087900000000000000000 PSI
Would the pressure result in the hydrogen and or oxygen fusing and if so how much energy would all of it make if this indestructible sphere disappeared at one point.

 

[berkeman]

Summary:: Theoretically, what pressure would water need to be subjected to force the oxygen and hydrogen to fuse into heavier elements and how much energy would it release.

So in a DnD story, someone made a bomb by putting 3375ft^3 of water into a 0.5ft radius sphere and caused it to make a nuke. I was thinking if this was possible then what would actually happen, so I spent an afternoon looking for the answer and only got the pressure and density.
6445773,7307163375188090110591252 kg/m^3
186976087900000000000000000 PSI
Would the pressure result in the hydrogen and or oxygen fusing and if so how much energy would all of it make if this indestructible sphere disappeared at one point.

Welcome to the PF.

This is where you need to start -- it's not just pressure that is involved in starting a fusion reaction...

https://en.wikipedia.org/wiki/Lawson_criterion

 

[Vanadium 50]

6445773,7307163375188090110591252

Good heavens. If Sister Mary Albert saw you write something with that ridiculous precision, she'd rap your knuckles with her ruler.

Have you established that this reaction is even exothermic?

 

[Baluncore]

So in a DnD story, someone made a bomb by putting 3375ft^3 of water into a 0.5ft radius sphere and caused it to make a nuke.

How could you possibly compress water by that much?

The container would expand as molecular bonds stretched, resulting in rupture of the containment.

If you calculate the energy needed to compress the water, you will find that it needs as much energy as is released by a nuclear bomb.

 

[prodigylock]

I forgot to mention but this theoretical container is indestructible.

As I couldn't find a source on a Liquid adiabatic process I couldn't calculate if the compression would generate enough heat to make plasma and cause the sphere to become ignited.

It should not be exothermic since the only way would be with beta decay but that would take too long on this scale to sustain the reaction but I'm not that good with this(hence the reason I asked here) so that's what I wanted to find out what would happen.

 

[Vanadium 50]

Well if it's not exothermic, where does the energy come from for the kaboom?

 

[prodigylock]

The energy for the kaboom came from quick math and assumptions and that's why I wanted to explore the idea further. As far as I have read the oxygen from the water might be able to fuse into si-28 and an alpha particle. Later through the Triple-Alpha process, it would make 2 gamma rays and some carbon-12. So that would produce some energy and one of these might fuse with the protium but I'm not too sure about that.

 

[snorkack]

Well if it's not exothermic, where does the energy come from for the kaboom?

You don´ t need any energy. Well, zero point energy.
Even at zero pressure, a water molecule in vacuum, you will have small but nonzero rate of tunnelling, mostly for the two simple reactions:
p+p=d+e⁺+ν_e
p+p+e^-=d+ν_e
Note that p-p fusion has the lowest Coulomb barrier. Whether it takes place due to pure zero point energy (pure pycnonuclear fusion), with appreciable contribution of heat or mainly as thermonuclear fusion, it is preferred.
Of course, as either the pressure/zero point energy or temperature is increased, higher Coulomb barrier reactions will contribute:
p+¹⁶O=¹⁷F+γ
¹⁶O+¹⁶O=³²S+γ
¹⁶O+¹⁶O=²⁸Si+α
¹⁶O+¹⁶O=³¹P+p
et cetera
Therefore, seal water in a pressure vessel and since heat generated by pycnonuclear fusion cannot escape, it slowly heats up to thermonuclear.
The original premise is water compressed to density of about 6400 kg/l, making about 700 kg/l of protium. At that density and no temperature, what is the lifetime of protium to pycnonuclear fusion?

 

[mfb]

The container is a massive bomb without any fusion already. Just release the interior which is under some ridiculous pressure and it will explode violently. At this density you can forget molecular bonds or even atoms. The electron degeneracy pressure will be ~10¹⁸ Pa, giving that bomb an energy of the order of 10¹⁶ J or a few megatons of TNT equivalent.

Any plausible mechanism to compress the material will probably heat it up a lot, too. You end up with a pressure and density way higher than in the core of the Sun. Might be enough for a lot of hydrogen fusion, followed by more fusion reactions later.