Now to help me understand this, i will need a time based description of how this occurs in a particular instance.
Imagine a planet covered in an atmosphere of ideal gas. On this planet we have our super-long insulated upright tube, but at this moment, its a vacuum; nothing is inside of it.
To fill it with gas, the top cap is opened and gas flows into it. Once the pressure inside equalizes, it is re-sealed.
Now the fact that we have had gas move with gravity, the particles that are lower down, have gained more heat energy due to the conversion of potential energy, into kinetic energy and are hotter 'at the moment at least'.
now that it is left to become static how does temperature even out?
I find it hard to understand how, when a particle from a lower position, will loose energy to gravity when it changes location, to collide with a particle at a higher position.