How much does a human being explode if we dissociate all the molecules?

[Leo_Bloom]

It’s about time we got to this point. I was sick of always assuming spherical cows.

[LSLGuy]

@chorpler

I couldn’t stop wondering about this, so after refreshing myself on electrostatics and Coulomb’s law and the like, and plugging a calculation into Wolfram Alpha, I got a result of about 5.4x10[sup]28[/sup] joules of energy for 10[sup]28[/sup] electrons packed into a half-meter-wide sphere without any counterbalancing charge. Wolfram Alpha helpfully informs me that this is about 145 times the energy the sun outputs every second, so it seems like it would be pretty dangerous to use a Niven-style disintegrator on a spherical human in a vacuum.

Bolding mine.

I had the same thought but was too lazy to act on it. Thank you. And a mighty fine GQ calc it is.

Which demonstrates clearly just how important it is that electrons and protons have exactly the same charge, not merely approximately the same charge. Even a difference of 1 part per 10[sup]20[/sup] would still disassemble every atom in all the matter in all the universe.

[chorpler]

@LSLGuy

Bolding mine.

I had the same thought but was too lazy to act on it. Thank you. And a mighty fine GQ calc it is.

You’re welcome. Although I’m not 100% sure I did it right. I originally did a similar calculation after reading a Harry Potter fanfiction (okay, it was a fanfiction of “Harry Potter and the Methods of Rationality” … which I guess makes it a fanfanfiction, or maybe a meta-fanfiction) where a transfiguration student wonders what would happen if they transfigured something on their desk into a pound of free electrons, and gets royally chewed out by the school authorities and told not to do that.

However, I found a similar question on the XKCD forums here, which makes me think I did it fairly correctly.

[Carl_Pham]

If you turn your subject into essentially a load of compressed gas and your magic ray ensures that the temperature remains the same, then what you have is essentially the free expansion of a gas at some initial high pressure at room temperature. The front will move outward at approximately the speed of sound, that being the canonical rate of propagation of density waves in which the restoring force is entropy (which is the case here), at least until the pressure drops to a point that’s comparable to the surrounding medium, and ignoring some modest nonidealities in the first few microseconds when it still has a liquid-like density.

So that’s a boom, but not a really nasty boom, which requires supersonic front propagation (driven by temperatures in the explosion much higher than room temperature). The approximate energy release can be worked out by just calculating the pV work required to compress the final equilibrium volume at 1atm and room temperature to the starting volume. You’ll be ignoring nonideality, Joule-Thomson effect, and all kinds of other stuff, but those would be minor corrections.