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First, I apologize for the sloppy title. I had a tough time phrasing this as a concise question.

For a column of air at a given pressure, density decreases (the air expands) as temperature increases.

At the same time, however, adiabatic cooling seems to represent the opposite phenomenon. As a parcel of air rises, it expands due to a decrease in ambient pressure. This expansion results in fewer collisions between air molecules, thus its temperature decreases.

In other words, higher temperatures cause air to expand, but expansion causes air to cool. Does this result in a kind of feedback loop (i.e.: air expands, thus cools, thus contracts, thus warms, thus expands...), with temperature and density ultimately reaching a kind of equilibrium? Or are these two phenomena totally unrelated? Is there something else I'm misunderstanding altogether?

Thanks for any clarification and I hope this question makes sense!

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    $\begingroup$ I think this would be a better question for Physics.SE. I don't see any relation to aviation. $\endgroup$
    – Bianfable
    Nov 23, 2021 at 19:08
  • $\begingroup$ @Bianfable Hmm, that may be fair. The question occurred to me through studying aviation weather theory, so this is where I thought to ask it. $\endgroup$
    – Ethan B
    Nov 23, 2021 at 19:21
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    $\begingroup$ This answer on Physics explains it; the error you've made is the reason for expansion. The answer also addresses the stratosphere where the temperature rises as you go higher. I also agree it's OT here. If the linked answer didn't help, you may want to ask a moderator to migrate the post over to Physics by raising a custom flag. $\endgroup$
    – user14897
    Nov 23, 2021 at 20:14
  • $\begingroup$ "density decreases (the air expands) as temperature increases" – yes, when you add energy while keeping pressure constant. That is how a hot air balloon works. If expansion is caused by reduced pressure, temperature decreases. $\endgroup$ Nov 23, 2021 at 20:36
  • $\begingroup$ Under extreme conditions, such as a rocket exhaust, there may be something along the lines of your thinking in the form of the diamond pattern. Not seen in weather as heating/cooling and volume changes are many orders of magnitude smaller. See the SR-71 Blackbird jet exhaust. $\endgroup$ Nov 24, 2021 at 0:52

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"density decreases (the air expands) as temperature increases" – yes, when you add energy while keeping pressure constant. That is how a hot air balloon or a thermal works. If expansion is caused by reduced pressure, temperature decreases.

What happens in the atmosphere is normally described as an isentropic process.

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    $\begingroup$ I think this is the relevant point I'm looking for. When energy is added and pressure remains constant, the temperature increases and the air expands. But because the pressure is constant in this case, there isn't a subsequent adiabatic decrease in temperature, so the infinite regress or feedback loop suggested in my original question does not occur. Correct me if I'm wrong or misunderstanding. $\endgroup$
    – Ethan B
    Nov 23, 2021 at 21:30
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    $\begingroup$ @EthanB Yes, that's it. It helps to ask yourself whether a process would need the addition or removal of energy and where this should come from. $\endgroup$ Nov 23, 2021 at 22:01
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There are 5 players in your question, found in:

the gas equation P = nR/V × T, and relative humidity

For your question:

Density decreases as temperature increases

we can see lower density (nR/V) and higher temperature T will yield the same pressure and a greater volume.

Higher temperature causes the air to expand

The air parcel is now lighter than the surrounding air and rises.

But expansion causes the air to cool

The "contraction" is only due to temperature decrease. With no change in pressure, no energy is going into the system to drive heating through compression. (Remember rising air is constantly moving into lower pressure). The contraction will be a thinning of the rising air column, as seen with the "classic" mushroom or anvil cloud. It is simply a reduction in volume as temperature drops, with pressure remaining equal to surrounding air.

All fine and good until: relative humidity gets too high. Moist air cools with expansion at a lower rate than dry air, and the lighter water vapor also contributes to its bouyancy.

Now the air rises much faster and higher, potentially leading to a thunderstorm.

ultimately reaching a kind of equilibrium

So, yes, with weather the phenomena are related through pressure, and humidity plays a key role. Dry air, heavier than surrounding air of equal pressure but higher humidity, can be heated by compression as it sinks. These are the famous Chinook or Foehn winds. As the dry air sinks, the surrounding air of higher pressure compresses it. This is the opposite of adiabatic cooling.

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  • $\begingroup$ Correct! See edits. $\endgroup$ Nov 23, 2021 at 21:17

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