Variation of air temperature with altitude

[eneacasucci]

TL;DR Summary

Variation of air temperature with altitude, considering the approximation of perfect gas, which transformation explains this phenomena?

Considering the approximation of perfect gas, I don't understand why at higher altitude the temperature is lower.
Intuitively it is clear to me, but I do not understand the kind of transformation that takes place; the gas is free to expand and the pressure too is not constant, since it decreases at higher altitudes. Then also the temperature decreases but I don't understand if we can see this decrease of temperature from this formula PV=nRT or if it is an isothermal transformation so the temperature of a certain mole of gas doesn't change due to the free expansion but for other mechanisms of heat transfer (like conduction and convection).

I've also tried to think about the ocean, when we go deeper the pressure increases but there is a liquid, and a liquid is not compressible, so the pressure there is not associated to a change in temperature, which is due mainly to convective motion.

 

[apostolosdt]

Regarding your last paragraph, if I recall correctly, ocean water remains incompressible down to about 3 km depth, and then it gradually becomes compressible.

As for the rest of your post, using the perfect gas theory for the atmosphere is a very risky approximation. For example, what are the boundaries of your system?

 

[Bystander]

https://www.google.com/search?q=bar...390i650l2.103136j0j7&sourceid=chrome&ie=UTF-8 ; https://www.science.org/doi/10.1126/science.192.4234.46 .

 

[eneacasucci]

Regarding your last paragraph, if I recall correctly, ocean water remains incompressible down to about 3 km depth, and then it gradually becomes compressible.

As for the rest of your post, using the perfect gas theory for the atmosphere is a very risky approximation. For example, what are the boundaries of your system?

Maybe considering a certain number of moles that travel from the bottom to the top increasing altitudes, since hotter air moves upward... but still the boundaries are not clear....

 

[Frabjous]

Pressure decreases at altitude so moving air expands and undergoes adiabatic cooling.

Space has a temperature of a few kelvin which is a cold boundary for the atmosphere, although one needs to also take radiation transport into account.

 

[eneacasucci]

https://www.google.com/search?q=bar...390i650l2.103136j0j7&sourceid=chrome&ie=UTF-8 ; https://www.science.org/doi/10.1126/science.192.4234.46 .

For the isothermal atmosphere model so a hotter mass of air that travels higher, at lower pressures, doesn't change its temperature due to the change of pressure, right? then why the temperature of air is lower? is it due to heat transfer with the "universe"? (sorry it sounds stupid but I can't think about anything else)

 

[Bystander]

TL;DR Summary: Variation of air temperature with altitude, considering the approximation of perfect gas, which transformation explains this phenomena?

PV=nRT or if it is an isothermal transformation so the temperature of a certain mole of gas doesn't change due to the free expansion but for other mechanisms of heat transfer (like conduction and convection).

What "free expansion?"

 

[eneacasucci]

What "free expansion?"

I was thinking about this one https://en.wikipedia.org/wiki/Joule_expansion but maybe it is not the right example to talk about atmosphere

 

[Bystander]

I was thinking about this one https://en.wikipedia.org/wiki/Joule_expansion but maybe it is not the right example to talk about atmosphere

What do you think you/the gas is working against?

 

[eneacasucci]

Pressure decreases at altitude so moving air expands and undergoes adiabatic cooling.

Space has a temperature of a few kelvin which is a cold boundary for the atmosphere, although one needs to also take radiation transport into account.

Is there an explanation that clears that the transformation is an adiabatic cooling?

The boundary with the space is clear to me and makes sense (with cooling due to conduction I guess and maybe also some convective movements). What about radiation transport?

 

[eneacasucci]

What do you think you/the gas is working against?

There isn't a surface like a container or something, there is just the gravitational force... but not a material boundary, just air with other air around

 

[Bystander]

just the gravitational force..

..., annddd, ...?

 

[eneacasucci]

..., annddd, ...?

I would say atmospheric pressure due to the other air present?

 

[Bystander]

I would say atmospheric pressure due to the other air present?

@Chestermiller : this has pulled an "Ouroboros" on me; any suggestions?

 

[eneacasucci]

@Chestermiller : this has pulled an "Ouroboros" on me; any suggestions?

Yes, It is like Nietzsche's snake biting its own tail. At present my conclusion is that hot air going upward, at lower pressure, does not vary its temperature due to this pressure change, but that the temperature varies because of the greater proximity to cold space.

 

[Baluncore]

At present my conclusion is that hot air going upward, at lower pressure, does not vary its temperature due to this pressure change, but that the temperature varies because of the greater proximity to cold space.

In that, I think you are wrong.
The ionosphere is very much hotter than the lower atmosphere.
https://en.wikipedia.org/wiki/International_Standard_Atmosphere

 

[Chestermiller]

A parcel of air rising to higher altitudes is surrounded by similar parcels which do not exchange heat with one another because they are at the same temperature. However, because the atmospheric pressure is decreasing as they rise, they experience adiabatic reversible expansion. This is responsible for the so-callled "adiabatic lapse rate" of the air in the troposphere (up to 10-15 km). However, above the tropopause, in the stratosphere, the air temperature is rising with altitude due to absorption of solar photons by ozone and air in the ultra-violet.

 

[russ_watters]

Yes, It is like Nietzsche's snake biting its own tail. At present my conclusion is that hot air going upward, at lower pressure, does not vary its temperature due to this pressure change, but that the temperature varies because of the greater proximity to cold space.

This can't be correct, because space isn't "cold", it's just empty. There's nothing up there for the air to exchange heat with.

...except by thermal radiation against the CMB and the sun, which can't be the reason because the gradient (in the troposphere) doesn't change much between day and night.

There's no good reason to make up your own explanation here when the accepted explanation works fine.

 

[fresh_42]

https://www.google.com/search?q=bar...390i650l2.103136j0j7&sourceid=chrome&ie=UTF-8 ; https://www.science.org/doi/10.1126/science.192.4234.46 .

... time to update my calculator thread. Thank you!

 

[eneacasucci]

This can't be correct, because space isn't "cold", it's just empty. There's nothing up there for the air to exchange heat with.

...except by thermal radiation against the CMB and the sun, which can't be the reason because the gradient (in the troposphere) doesn't change much between day and night.

There's no good reason to make up your own explanation here when the accepted explanation works fine.

It wasn't my explanation but I was trying to sum up what was said, after which came the comprehensive answer by @Chestermiller

 

[Vanadium 50]

What is this thread about? If it is how the atmosphere really works, shouldn't it be in Earth Science? And the OP should be prepared for a complicated answer with a lot or interacting things going on.

If, OTOH, it's on how well a particular simplification does, we should decide which one we are talking about,

 

[fresh_42]

What is this thread about? If it is how the atmosphere really works, shouldn't it be in Earth Science? And the OP should be prepared for a complicated answer with a lot or interacting things going on.

If, OTOH, it's on how well a particular simplification does, we should decide which one we are talking about,

And that everybody will understand why it is complicated, here is an impressive image:

https://scied.ucar.edu/learning-zone/atmosphere/change-atmosphere-altitude
(UCAR at Boulder, CO)

 

[Vanadium 50]

I was kind of wondering what "And that" by itself meant! (For those who missed it, @fresh_42 posted that and then filled in)

If we were to do it over, we probably would not talk about "the atmosphere" as a single body. (Nor "air" as a single material) but there;s no sense crying over spilled terminology.

 

[cjl]

Regarding your last paragraph, if I recall correctly, ocean water remains incompressible down to about 3 km depth, and then it gradually becomes compressible.

As for the rest of your post, using the perfect gas theory for the atmosphere is a very risky approximation. For example, what are the boundaries of your system?

Whether ocean water is compressible or not really depends on how much compression you deem to be significant. It compresses even just between the surface and a few feet down, but the amount of compression is really quite small.

Seawater has a bulk modulus of around 2.3*10^9 Pa, so at 3km, with a pressure of about 3*10^7 Pa, you'd notice a bit over a 1% increase in density. Measurable, sure, but still surprisingly small.

 

[fresh_42]

Whether ocean water is compressible or not really depends on how much compression you deem to be significant. It compresses even just between the surface and a few feet down, but the amount of compression is really quite small.

Seawater has a bulk modulus of around 2.3*10^9 Pa, so at 3km, with a pressure of about 3*10^7 Pa, you'd notice a bit over a 1% increase in density. Measurable, sure, but still surprisingly small.

What is it at the bottom of the Mariana Trench? I'm just curious because there are fish down there so I assume it cannot be too high.

 

[Vanadium 50]

What is it at the bottom of the Mariana Trench

I think it's still seawater. (How could I resist such a line?P

Pressure is around 1100 atmsopheres. But the putative fish are fine because there is no pressure differential and so no force.

I say putative because I do not know if fish really go that deep. The problem isn't pressure - it's food.

 

[Bystander]

I say putative because I do not know if fish really go that deep. The problem isn't pressure - it's food.

https://en.wikipedia.org/wiki/Mariana_Trench

 

[cjl]

What is it at the bottom of the Mariana Trench? I'm just curious because there are fish down there so I assume it cannot be too high.

Around a 4-5% increase in density vs surface. Again, certainly measurable, but not particularly large.