How the temperature of the Earth's surface affects the air pressure above it

[GilSE]

TL;DR Summary

From one hand - hotter air is "lighter", from another - hotter air does a higher pressure

If the surface is heated, air above it will also heat, its temperature will rise. It will cause two processes: while temperature of gas rise, its pressure will also increase, but, also, as the air molecules get more energy, they will go higher from the earh surface, concentartion of the molecules near the surface will decrease, hence, the air pressure should decrease, too ($p=nkT$, $n$ is number density). So, which of these factors will prevail?

 

[Frabjous]

There are additional mechanisms. For example, differential heating of air is a cause of wind.

 

[Vanadium 50]

This is far from a system at equilibrium. Thinking about it that way is likely to be unhelpful.

 

[Lnewqban]

Please, see:
https://en.wikipedia.org/wiki/Thermal

http://www.atmo.arizona.edu/students/courselinks/spring15/atmo336/lectures/sec1/structure.html

While the temperature of certain mass of air located at sea/ground level increases, its atmospheric pressure remains the same, and its volume increases (meaning its density decreases).

As that mass of air goes higher from the Earth surface, it is cooled by the surrounding air located at higher altitudes.

 

[Philip Koeck]

As that mass of air goes higher from the Earth surface, it is cooled by the surrounding air located at higher altitudes.

That's a bit circular!
Why is the surrounding air cooler in the first place?

I would say air that rises cools due to (roughly) adiabatic expansion.

In general it might be a good idea to look at stationary models of the atmosphere and ignore wind and temperature changes due to the time of day. Maybe that can give a rough idea of what's going on.

One model is the adiabatic model which says that air cools off when it rises and therefore it should be colder higher up. It turns out that the temperature decreases linearly with altitude in this model.
From that it's possible to work out how pressure decreases.

An interesting question is of course how realistic such a model is?

 

[berkeman]

TL;DR Summary: From one hand - hotter air is "lighter", from another - hotter air does a higher pressure

If the surface is heated, air above it will also heat, its temperature will rise. It will cause two processes: while temperature of gas rise, its pressure will also increase, but, also, as the air molecules get more energy, they will go higher from the earh surface, concentartion of the molecules near the surface will decrease, hence, the air pressure should decrease, too ($p=nkT$, $n$ is number density). So, which of these factors will prevail?

It sounds like you should take some classes in meteorology and invest in some supercomputer time.

https://www.researchgate.net/figure...spheric-Sciences-University-of_fig9_249416022

 

[Philip Koeck]

TL;DR Summary: From one hand - hotter air is "lighter", from another - hotter air does a higher pressure

If the surface is heated, air above it will also heat, its temperature will rise. It will cause two processes: while temperature of gas rise, its pressure will also increase, but, also, as the air molecules get more energy, they will go higher from the earh surface, concentartion of the molecules near the surface will decrease, hence, the air pressure should decrease, too ($p=nkT$, $n$ is number density). So, which of these factors will prevail?

Are you asking what actually happens in the atmosphere of the earth (with sun and wind and clouds) or are you just wondering about basic physics?
For the latter it's better to consider a model system rather than the actual atmosphere.

 

[GilSE]

That's a bit circular!
Why is the surrounding air cooler in the first place?

I would say air that rises cools due to (roughly) adiabatic expansion.

In general it might be a good idea to look at stationary models of the atmosphere and ignore wind and temperature changes due to the time of day. Maybe that can give a rough idea of what's going on.

One model is the adiabatic model which says that air cools off when it rises and therefore it should be colder higher up. It turns out that the temperature decreases linearly with altitude in this model.
From that it's possible to work out how pressure decreases.

An interesting question is of course how realistic such a model is?

Oh, I did some calculations assuming the atmosphere adiabatic. My idea was that the total number of particles in the air collumn is constant, so I could find pressure at zero height. What I've got is that zero level pressue doesn't changed when the temperature change. Hence, I thought that two factors mentionted above just compensated each other in the model, when in reality some factor prevail for some reason.

Though, it still could be a wrong calculation. I'm going to do it again and post there.