Thermodynamics Thought Experiment: I Hurt My Brain. Help!
Alright, help me find the flaw in my logic here. There must be one. It's killing me.
Imagine two boxes totally enclosed except for a passage connecting them. The opening to the passage is a wide funnel into one box that narrows down to a thin tube into the other box. The passage is extremely long such that the funnel walls are almost perpendicular. The enclosed system contains bouncy balls sparsely and evenly distributed throughout. The volume enclosed by the two boxes is significantly larger than the volume in the connecting tunnel. Shake the whole system vigorously for a significant amount of time and what would you expect at the end? I'm guessing the box with the wide opening would contain less balls than the box with the narrow opening. Right?
Now scale the whole thing down so the bouncy balls are air molecules. You don't have to shake the system anymore. They're bouncing around constantly on their own. After time passes, wouldn't one box contain more air molecules than the other? If that's the case, the increase in density on one side with no corresponding volume change would heat the air. Conversely, the drop in density on the other side would cool the air. And if that's the case, we just created order from disorder without expending any work and broke the second rule of thermodynamics.
So it can't be right.
It's like Maxwell's Demon without the demon. In Maxwell's case you could point to the work being done by the demon and say "there's your entropy". In this case there is no demon.
Help.
