How much energy would a Proton at Planck temperature have, and what effect would it have if it was released into the atmosphere at ground level.
This question was motivated by Flash episode “Revenge of the Rogues”. Minor spoilers below.
[SPOILER]The Flash is battling Captain Cold and Heatwave, a scientist who should know better comments that Captain Colds gun works at absolute zero the coldest temperature possible while heat wave works at the hottest temperature possible (Planck temperature) so if you cross the beams they should cancel out. Not realizing that when you average 1.4x10^32 C with 0, you still get something that’s pretty darn hot.:smack:
So I wanted to try and work out what the minimal damage of such a heat gun would actually be.
[/SPOILER]
Well, a single proton, or any single particle, can’t really have a temperature, since temperature is a statistical property of a large number of particles. But if we restate that as “a particle in a group of particles which collectively have the Planck temperature, and which has the average energy for particles in that collection”, then it would have the Planck energy. That’s certainly a lot for a single subatomic particle, but it’s not unprecedented on the human scale: Think of a full gas tank.
Of course, that’s also in a single particle. One would expect that Heatwave’s weapons generate many more particles than that. A hundred or a thousand gas tanks would make for quite an explosion. A mole of gas tanks would be far more than that, yet.
Also note, by the way, that there’s no particular reason to believe that the Planck temperature is the maximum possible temperature, nor are most of the other Planck quantities known to be absolute bounds. If there is an absolute bound for some quantity, it’s reasonable to guess that it might be somewhere in the vicinity of the corresponding Planck scale, but it might be half of it, or pi times it, or the like, or it might be something else entirely, or there might not be any absolute bound at all. We just don’t know.
THanks for the response. I realized that it doesn’t exactly make sense to talk about the temperature of a single particle, but the idea I had is mind is pretty much what you used for your calculation, basically thinking a conversion from temperature to average kinetic energy per particle. So looking up the energy density of gasoline, we are talking in the ball park of around 2,000 megajoules?