Suppose an ideal airtight room, filled with air, no changes in volume, amount of air or energy.
On the one hand, "hot air rises" (less dense, flotation, convection...) ((there's gravity, we are on Earth))
On the other hand, temperature tends to equalise (thermodynamics, heat flow, conduction, convection, diffusion, ...)
Do these two effects end up in a dynamic equilibrium in the end, resulting in some heat gradient? Or does the first effect just disappear in this ideal scenario?
From real life, and what I've absorbed from my vague unscrutinised encounters with thermodynamics over the years, I feel the answer should be the latter, but my understanding votes for the former. Maybe it's the former but to a negligible degree?
My confusion comes from the undersanding that, even in equilibrium, some molecules have higher energies than others (that's how evaporation works IIUC). Wouldn't they tend to rise?