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The equilibrium condition for your isolated column of air is hydrostatic equilibrium and a uniform temperature throughout. This is the condition that maximizes entropy. There is a non-equilibrium local max in entropy for your isolated column. This local max also is in hydrostatic equilibrium but has temperature falling with increased altitude at the adiabatic lapse rate.sophiecentaur said:Consider a simple column of a gas air, in equilibrium in an insulated cylinder. In an equilibrium situation the air at the bottom of the column will not rise if it is MORE DENSE than the air above it.
This isolated column is not a good model of the Earth's atmosphere. The Earth's atmosphere is not an isolated system and it is far from thermal equilibrium. The atmosphere is primarily heated from below and radiates into space from above.
The atmosphere is typically closer to that local max (adiabatic lapse rate) than it is to the global max (constant temperature), so the atmosphere is typically driven toward that local max in which temperature decreases with altitude. But not always. Sometimes thermal inversion layers set up in the atmosphere. Rising air stops at the inversion layer -- until it finally punches through. That's when all kinds of havoc such as tornados can result.