Variation of air temperature with altitude

  • #1
eneacasucci
50
12
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.
 
Physics news on Phys.org
  • #2
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?
 
  • #4
apostolosdt said:
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....
 
  • #5
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.
 
  • Like
Likes russ_watters
  • #6
  • #7
eneacasucci said:
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?"
 
  • #9
  • #10
Frabjous said:
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?
 
  • #11
Bystander said:
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 :olduhh:
 
  • #12
eneacasucci said:
just the gravitational force..
..., annddd, ...?
 
  • #13
Bystander said:
..., annddd, ...?
I would say atmospheric pressure due to the other air present?
 
  • #14
eneacasucci said:
I would say atmospheric pressure due to the other air present?
@Chestermiller : this has pulled an "Ouroboros" on me; any suggestions?
 
  • #15
Bystander said:
@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.
 
  • #16
eneacasucci said:
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
 
  • #17
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.
 
  • Like
Likes eneacasucci and russ_watters
  • #18
eneacasucci said:
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.
 
Last edited:
  • #20
russ_watters said:
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
 
  • #21
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,
 
  • Like
Likes russ_watters and fresh_42
  • #22
Vanadium 50 said:
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:

vertpro_comet.jpg


https://scied.ucar.edu/learning-zone/atmosphere/change-atmosphere-altitude
(UCAR at Boulder, CO)
 
  • Informative
Likes berkeman
  • #23
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.
 
  • #24
apostolosdt said:
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.
 
  • Informative
Likes apostolosdt and fresh_42
  • #25
cjl said:
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.
 
  • #26
fresh_42 said:
What is it at the bottom of the Mariana Trench
I think it's still seawater. :wink: (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.
 
  • #28
fresh_42 said:
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.
 
  • Like
Likes fresh_42

FAQ: Variation of air temperature with altitude

What is the general relationship between air temperature and altitude?

Generally, as altitude increases, air temperature decreases. This is known as the lapse rate. In the troposphere, which is the lowest layer of Earth's atmosphere, the average lapse rate is about 6.5 degrees Celsius per kilometer (or roughly 3.5 degrees Fahrenheit per 1,000 feet).

Why does air temperature decrease with altitude in the troposphere?

Air temperature decreases with altitude in the troposphere primarily because of the decreasing air pressure. As altitude increases, the air becomes less dense and cannot hold as much heat. Additionally, the ground absorbs sunlight and warms the air directly above it, so the further you move away from the ground, the cooler the air becomes.

Are there any exceptions to the decrease in temperature with altitude?

Yes, there are exceptions. One notable exception is the stratosphere, which lies above the troposphere. In the lower stratosphere, temperature initially remains constant with altitude and then increases with altitude due to the absorption of ultraviolet radiation by the ozone layer. This phenomenon is known as a temperature inversion.

How does the lapse rate vary in different atmospheric conditions?

The lapse rate can vary depending on atmospheric conditions. For example, in a dry atmosphere, the dry adiabatic lapse rate is about 9.8 degrees Celsius per kilometer. In a moist atmosphere, the moist adiabatic lapse rate is lower, around 5 to 6 degrees Celsius per kilometer, because the release of latent heat during condensation partially offsets the cooling.

How does altitude affect weather and climate?

Altitude significantly affects weather and climate. Higher altitudes tend to have cooler temperatures, which can influence local weather patterns and ecosystems. Mountains can also create barriers that affect wind and precipitation patterns, leading to phenomena like rain shadows. Additionally, higher altitudes have lower air pressure, which can impact human health and activities.

Similar threads

B Applying Bernoulli's equation to problems involving a perfect gas
Replies
8
Views
914
I Derivation of ideal gas heat capacity relationship
Replies
6
Views
1K
I Temperature change due to mixing liquids, heating and heat losses
Replies
8
Views
1K
I Why is estimation of ##\frac{Pv}{RT}=1+BP+CP^2+...## interesting?
Replies
2
Views
1K
I The relationship between reversible and irreversible processes
Replies
5
Views
1K
I Why does hot air have low pressure? (wind formation)
Replies
16
Views
2K
I How to understand experiment to measure heat capacity of solid?
Replies
1
Views
1K
I Non-adiabatic expansion in Diesel and Otto cycles
Replies
1
Views
633
I Perfect gas in a box with a piston
Replies
8
Views
1K
B How the temperature of the Earth's surface affects the air pressure above it
Replies
7
Views
599

Hot Threads

Recent Insights

Back
Top