One Particle in a Vacuum

I recently watch a lecture by Neil Tyson where he said the closest thing we have to a vacuum is interstellar space. I believe he said there will be one atom per 1 cubic meter or something close to that. I know that pressure equalizes, meaning that a higher pressure systems will move towards low pressure systems to reach an equilibrium. So I was wondering how that works. Do all the atoms in space try to get equidistant from one another to maintain reach an equilibrium pressure. If you made a 1 cubic foot sphere and put a single atom in it. Does pressure play a part there? Would the atom find the center of the sphere and stay there? Would it just bounce around unconcerned with equalizing pressure?

I'm sorry if this seems scatter brained. Whenever I watch a Neil Tyson video my brain is overloaded with curiosity.

-

One productive way to think about gas pressure is to think about how it feels to get with a ball. The ball is moving, it hits you, bounces off and you feel a bit of force in the same direction as the ball was moving. If the ball is bouncier, it looses less energy in the collision. We generally assume that gas atoms perfectly elastic, that they lose no energy in collisions. And when they're completely unstructured, that's a pretty reasonable assumption.

Gas pressure is the result of the ridiculous number of collisions that gas particles have. So a single atom in a chamber would indeed just zip around inside that shell and bounce off the walls. Bouncing elastically off the walls.

-
So in space do they fly around uninterrupted until they happen to collide with something else? They aren't drawn toward or away from things. They are just bouncing around by collisions? – Hoopdady Mar 8 '13 at 16:43
Technically they are still influenced by gravity and other long range forces, which are very weak at those distances, and also colliding into each other. – Wolfram074 Mar 8 '13 at 16:52

No, if you put a single atom in a sphere, it will probably keep bouncing randomly. Any time you measure it's position within the sphere, it is equally likely to be at any other position than the center, just as Wolfram074 said.

But, if you put, say 10 atoms, inside the same sphere, they'll arrange themselves such that, if you take, suppose one-fifth of the sphere, it is likely that you'll find 2 atoms inside that volume. That is what gas density means.

Your example confuses you, because you suppose an atom inside a sphere of 1 cubic meter, whereas what Neil Tyson meant is that if you take a 1 cubic meter section of the universe, it is likely that you'll find one atom.

Hope that helps!

-
That makes since, but it scares me when you say "probably". ;-) – Hoopdady Mar 8 '13 at 16:46
Me too, but that's all you can say in Physics nowadays. :) – Cheeku Mar 8 '13 at 16:48
Heck, even when thermodynamics was all classical, it was all you could say then too, the number of particles was just so absurdly large. – Wolfram074 Mar 8 '13 at 16:55