Colder with increasing altitude.

[russ_watters]

Dave, if

\frac{V_{1}}{T_{1}}=\frac{V_{2}}{T_{2}}

and V₂ = 2V₁

then

\frac{V_{1}}{T_{1}}=\frac{2V_{1}}{T_{2}}

∴ T₂ = 2T₁

from which we end up with Charles's Gas Law, which states that, at constant pressure, the volume of an ideal gas is directly proportional to its temperature.

http://en.wikipedia.org/wiki/Charles's_law

Adiabatic cooling (aka, adiabatic expansion) does not happen at constant pressure.

What you are describing is what happens at the surface: it is heated and expands at constant pressure. That's what causes it to rise.

 

[russ_watters]

Well spotted. DaveC's description clearly does not meet the constant pressure requirement of Charles' Law. To meet that, heat would need to be added to maintain the pressure, and at a doubled volume the temperature would also double.

Which is why that's not what happens. Again, Dave said adiabatic cooling.

http://apollo.lsc.vsc.edu/classes/met130/notes/chapter6/adiab_cool.html

 

[SHISHKABOB]

Adiabatic cooling does not happen at constant pressure.

well, right, I was just pointing out the error in terminology

I was *only* pointing out that Charle's Gas Law, which Dave mentioned, requires constant pressure. It was offtopic, I guess, technically, because I wasn't trying to add anything to the discussion of why it gets colder with increasing altitude.

 

[russ_watters]

Yes, you're right, sorry. Dave used the right term for what was happening but applied the wrong equation. That's what I get for only reading half a post.

 

[sophiecentaur]

I have read some threads on this topic, but I am still confused. Why does temperature drop as you go up a mountain? I have read that since pressure depends on the weight of the air on top of you and as you increase your altitude the amount of air over you decreases, therefore pressure decreases, gas expands and expansion makes its temperature drop. The rising hotter air gets continually cooled due to expansion (or would it start rising at all?). Gas loses internal energy when it has to expand against a force, i.e. do work. But isn't exactly the same amount of work the gas does received as internal energy of the lump of gas next to it that the work is being done upon?

This thread seems to have lost its way a bit (so what's new?)
I quote the original question and the simplest answer must explain the steady state, static condition, not involving convection / mixing / adiabatic cooling / heating by the ground etc..
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 can occur even when it is 'warmer', as long as the pressure is greater. So a temperature / pressure profile can occur which will not allow convection but where the temperature at the bottom is higher than the temperature at the top.
The atmospheric pressure is approximately halved for every 5km increase in height (for constant temperature). Applying
P₁V₁/T₁ = P₂V₂/T₂
to this simple model of a column seems to indicate that a mass of air at sea level at a temperature 300K will occupy a smaller volume than the same mass of air at 5km height (half the pressure), if the temperature at 5km is greater than 150K. (Someone else please check this)
This result is extreme and not realistic but it makes the point, I think. There are many other factors at work but it does put to bed the notion that the Hot Air must rise up through the Cold Air.

 

[D H]

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.

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.

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.

 

[SHISHKABOB]

Yes, you're right, sorry. Dave used the right term for what was happening but applied the wrong equation. That's what I get for only reading half a post.

oh it's no problem at all :P I probably should have been a bit more explicit in my post

 

[sophiecentaur]

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.

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.

Why should you say that? My model uses PV/T and thus includes non-uniform temperature. My column would have a temperature gradient maintained to fit and hydrostatic equilibrium is fine under those circs, surely. I don't think that heat flow up or down the column via the gas would be significant or that it would introduce a difference in the result; the temperature gradient would still be there, even with some conductive heat flow. What has entropy to do with this simple model?
My point in suggesting the model was that it would be a good first-step to eliminate all the factors that you say affect a real atmosphere. I didn't claim that it was a good model (I specifiied that the other factors are ignored in it) but the one thing that it does do is to show that hot at the bottom and cold at the top is a sustainable situation. I wouldn't, for a minute, suggest ignoring all your other factors but I think you would agree that, looking at them all at once, as a first step into learning about the Atmosphere, could be a bit daunting. One thing at a time, wherever possible. The OP could probably benefit from a very easy start on the whole business. If I have insulted his intelligence then I apologise to him.

This may be yet another occasion when it would help if the level of the original question could be classified in some way and could help in getting the answering comments pitched appropriately.

 

[D H]

What has entropy to do with this simple model?

It has everything to do with it. An isolated system will move toward a configuration that minimizes energy and maximizes entropy. Your simple model says that temperature should not increase with altitude. The second law of thermodynamics suggests that the atmosphere should seek a uniform temperature state. Your example says likewise. This is, I think, the heart of the OP's confusion.

The way out of this apparent paradox is that the Earth's atmosphere is far from equilibrium conditions. Once you get far enough away from equilibrium, a nearby local min in energy / local max in entropy can dominate over the global min / global max.

 

[sophiecentaur]

OK, I accept that the energy situation would not be thermal equilibrium - any more than a hovering helicopter energy situation would be equilibrium. Nonetheless, a helicopter can hover and my column can sustain that temperature gradient over it with no mass movement of air. That's all I'm saying. Where the energy comes from is another matter but, as you say, it will involve some extra entropy increase somewhere else.
Something that did strike me was that the temperature difference can be much greater than what we find in practice. That, of course, is due to all your other perfectly reasonable arguments.
Shall we say that we could have 'mechanical' equilibrium in my model (which is what I meant).

 

[Bob S]

A good explanation of why air gets colder with increasing altitude is the adiabatic expansion of air as the pressure decreases. See discussion of adiabatic expansion of air, and how it applies to our atmosphere in http://farside.ph.utexas.edu/teaching/sm1/lectures/node56.html, and see equations 329 et seq.

 

[chingel]

That is an interesting idea that the air wouldn't rise at all, because the air higher up, even though it is colder, is even less dense due to the decrease in pressure.

I am still having problems with the other explanation of rising and cooling. Bob S, wouldn't the adiabatic cooling cause adiabatic warming of the air around it? And if it does, does it matter if the warm air rises and stays there or just gives its heat off there and circulates again, wouldn't the effect still be warming the upper layers?

 

[russ_watters]

I am still having problems with the other explanation of rising and cooling. Bob S, wouldn't the adiabatic cooling cause adiabatic warming of the air around it?

Yes! A warm air mass rises and cools while a cool air mass falls arount it and warms.

And if it does, does it matter if the warm air rises and stays there or just gives its heat off there and circulates again, wouldn't the effect still be warming the upper layers?

Yes, there is a net heat transfer out of the atmosphere, but that doesn't imply that the convection cell has to be warmer at the top than at the bottom. It just has to be warmer than space.

 

[chingel]

Doesn't the energy lost by the expansion have to go somewhere? Isn't that place the air around it, not just that cool air falls and warms there, but the expanding air itself warms it? Beforehand gravitational potential energy was talked about. But isn't the gravitational potential energy increased during initial warming of the air, once it starts rising and expanding, as much air as is expanding should contract and fall, leaving the height of the whole atmosphere and its gravitational potential energy the same.

I am getting the impression that it doesn't heat the upper layers, because when it gets there its temperature has decreased, but doesn't that mean the lost thermal energy has gone into the air around it and it already has warmed it?

 

[sophiecentaur]

Work is done in raising the mass of air. That accounts for a lot of the energy transfer.

 

[russ_watters]

Doesn't the energy lost by the expansion have to go somewhere?

The air masses exchange mechanical work when one expands and the other contracts. Consider a double-ended piston with air filled cylinders: heat one side up, then release the piston and the hot side will expand and cool while the cool side contracts and heats.

 

[russ_watters]

Work is done in raising the mass of air. That accounts for a lot of the energy transfer.

This gets complicated by how comprehensive you want the definition of the system to be:

1. If you just focus on the expanding parcel of air, it may look like it is gaining gravitational potential energy...
2. ...but realistically, it is rising because of buoyancy, so the atmoshere is actually losing gravitational potential energy.
3. ...but since this is a convection cycle, it is constantly fed by heat and if it is in a steady-state will result in zero net upwards or downwards movement of air and thus no gravitational potential energy change.
4. ...but the real Earth has day and night (as well as solar activity cycles), so during the day the atmosphere is warmer and expands (locally), increasing its gravitational potential energy while at night it gets cooler and contracts, decreasing its gravitational potential energy.

The way I would analyze this is as shown in my previous post, which corresponds to #2: gravitational potential energy is irrelevant to the main issue of the thread.

 

[stacybyars]

Great question and answers here. I thought this question would be easier to answer but I learned more than I bargained for.

This point fro Pkruse was fascinating: "Also, clouds are a radiation heat shield to keep more heat on the ground. So above the clouds the air is also losing heat to the cold of space much more quickly"

 

[Borek]

This point fro Pkruse was fascinating: "Also, clouds are a radiation heat shield to keep more heat on the ground. So above the clouds the air is also losing heat to the cold of space much more quickly"

I suppose I will be corrected, but I think this statement is misleading.

Air above clouds doesn't lose heat faster - it gets cold faster. That's not the same thing.

Assuming clouds layer works as insulation air above is not heated from the bottom. That means after losing the same amount of heat air above clouds gets colder than the same air losing the same amount of heat but being heated from the bottom.

If the air is isolated from the heating and gets colder faster, speed at which it loses heat goes down much faster than in the case of the air heated from the bottom - after all air loses heat to space only by radiation, and amount of energy emitted is proportional to T⁴. That means in the same amount of time amount of energy lost is smaller, not larger.

 

[stacybyars]

Thank you for clearing this up!

 

[haruspex]

A good explanation of why air gets colder with increasing altitude is the adiabatic expansion of air as the pressure decreases. See discussion of adiabatic expansion of air, and how it applies to our atmosphere in http://farside.ph.utexas.edu/teaching/sm1/lectures/node56.html, and see equations 329 et seq.

That a parcel of air expands, and therefore cools, as it rises cannot stand alone as an explanation for why it is cooler with increasing altitude. If the atmosphere were the same temperature (and same composition) all the way up, there would be no convection. So we have to start with why that is not the situation.
The U Texas site linked above gets part of the way there, explaining that the lower atmosphere is heated from below. To complete the picture, you have to have the upper layers of the troposphere losing heat upwards. If the atmosphere were composed entirely of O2 and N2, there would be no mechanism for this, and it would all be at the same temperature as the Earth's surface. The presence of GHGs - H2O mostly - is the key. These allow the atmosphere to lose heat by radiating IR in all directions, warming the Earth on the one hand, but losing heat to space on the other. THIS is the primary reason it is cooler with increasing altitude.

The above would lead to temperature dropping with altitude even faster than is observed. That's where convection comes in. The warmer low layers are less dense than the layers above and rise. If that were the end of the story then we'd be back in the position of uniform temperature. Adiabatic cooling limits the ability of convection to equalise temperatures. This, secondary, reason explains why the temperature drops with altitude at the rate observed.

I use the mental model of a sand dune thrown up by waves. The waves create a steep slope; gravity tends to flatten it out again; the properties of the sand grains prevent gravity flattening it totally, leaving a characteristic 'angle of repose'.

 

[chingel]

Work is done in raising the mass of air. That accounts for a lot of the energy transfer.

Does buoyancy decrease the fluid's or gas's internal energy and temperature? Work is done, but isn't it done by the gravitational potential energy?

 

[sophiecentaur]

Unless the total mass of the Earth's atmosphere is constantly being lifted away from the Earth's surface then there can't be any net change in GPE, can there? What goes up must come down, as my Grandfather used to say.

 

[D H]

That a parcel of air expands, and therefore cools, as it rises cannot stand alone as an explanation for why it is cooler with increasing altitude. If the atmosphere were the same temperature (and same composition) all the way up, there would be no convection. So we have to start with why that is not the situation.

There would be no conduction, but not necessarily no convection. To have no convection the atmosphere would have to be isothermal and be in hydrostatic equilibrium.

The answer to your question, "why is that not the situation", is simple: The planet surface is at a different temperature from that of the atmosphere. Planetary rotation (at a rate other than the orbital rate) alone will make this happen. You don't need greenhouse gases to get advection. Those greenhouse gases however do play a very important role.

The U Texas site linked above gets part of the way there, explaining that the lower atmosphere is heated from below. To complete the picture, you have to have the upper layers of the troposphere losing heat upwards. If the atmosphere were composed entirely of O2 and N2, there would be no mechanism for this, and it would all be at the same temperature as the Earth's surface. The presence of GHGs - H2O mostly - is the key.

I agree that the presence of greenhouse gases is the key to how our real atmosphere behaves. I disagree as the lack of greenhouse gases would not create an isothermal atmosphere, at least not near the surface.

An atmosphere that is transparent to both incoming solar radiation and outgoing thermal radiation would be very different from our actual atmosphere. With a transparent atmosphere there would be huge day/night temperature extremes on the planet's surface, similar to those on the Moon. These huge swings would drive the behavior of the atmosphere near the surface. Daytime temperatures in the atmosphere near the surface would drop at the adiabatic rate (the dry adiabatic rate; a transparent atmosphere rules out H₂O) as surface air heated by the planet rises. The rapid daytime heating of the surface precludes an isothermal atmosphere, at least near the surface during daytime. There would be an isothermal atmosphere above a rather low altitude that varies with time of day, nearly touching the Earth at the dawn boundary.

----------------------------------------------------------

To get back to the OP's (chingel's) confusion, one needs to look at what causes temperature to vary within the atmosphere. There are four primary mechanisms:

• Conduction at the surface of the Earth,
• Adiabatic cooling/heating as parcels of air rise/fall,
• Atmospheric mixing as those moving parcels mix with the air around them,
• Radiative transfer, which is only possible due to the presence of greenhouse gases, and
• Diffusion, or molecular level heat transfer.

Diffusion would slowly drive the atmosphere to an isothermal state were it not for those first four mechanisms. Diffusion is very slow compared to those first four, making diffusion pretty much a non-factor given that those first four mechanisms do exist.

It's important to understand that second process, adiabatic cooling and heating. This is where I think chingel still has problems. A rising or sinking parcel of air isn't subject to conduction; that happens at the Earth's surface. The parcel is mixing only at its periphery, and only slightly, so that is a non-factor. Radiative transfer is typically slow, so that too is a non-factor. There is effectively no heat transfer with the environment, so adiabatic conditions apply. Couple this adiabatic behavior with the decrease in pressure with increasing altitude and the parcel must decrease in temperature as it rises. It's a simple matter of thermodynamics.

The parcel will stop rising eventually. If nothing else, it will hit the tropopause. There is very little mixing between the troposphere and stratosphere because a temperature inversion exists at the boundary between the two layers. Typically a rising parcel will stop rising long before the tropopause. One reason is that the environmental lapse rate is typically less than the adiabatic lapse rate. Rising air under such conditions quickly cools to a point where the temperature is equal to that of the surrounding environment. This stops the rise in its tracks. This is a stable atmosphere; not much is happening here.

The environmental lapse rate can at times be higher than the adiabatic lapse rate. The rising air continues to rise, eventually reaching a point where the relative humidity is 100%. The release of energy from condensation counteracts the cooling to some extent (the moist adiabatic rate is only 6°/km, about 4°/km less than the dry rate). These rising parcels of air in an unstable atmosphere are what give us our weather. The net result is to cool the surface of the Earth and heat the atmosphere.

Radiative transfer has the opposite effect. It acts to raise the temperature of the surface of the Earth and reduce the temperature of the atmosphere. Radiative transfer and advection battle one another. Note that there is no radiative transfer without greenhouse gases. Our weather depends on those greenhouse gases.

 

[olivermsun]

There would be no conduction, but not necessarily no convection. To have no convection the atmosphere would have to be isothermal and be in hydrostatic equilibrium.

Wouldn't it be sufficient for the atmosphere to be at or above the adiabatic lapse rate (rather than requiring the atmosphere to be isothermal)?

 

[D H]

Wouldn't it be sufficient for the atmosphere to be at or above the adiabatic lapse rate (rather than requiring the atmosphere to be isothermal)?

Below, not above. A lapse rate above the adiabatic rate is unstable. A lapse rate below adiabatic does stop convection.

However, such a condition would not persist long without conduction, convection, and radiative transfer. With none of those disturbing / distributing processes, diffusion would drive the atmosphere toward isothermal conditions.

 

[olivermsun]

You're right, below. Negative sign confusion.

 

[haruspex]

The planet surface is at a different temperature from that of the atmosphere. Planetary rotation (at a rate other than the orbital rate) alone will make this happen.

True, the diurnal cycle would create some convection, but it would have to be quite brief and moderate; it would transfer heat upwards far more efficienctly than conduction carries heat back down, yet the two would have to be in balance. The average air temperature would exceed that of the ground, and most of the time there'd be a strong inversion.
More importantly, it does not affect my main point: adiabatic cooling cannot be the primary cause for the existence of the gradient. Something else must cause it, which causes convection, which in turn is limited in its equalising effect by adiabatic cooling.

To get back to the OP's (chingel's) confusion,

chingel had at least two confusions. Everyone else on this thread is discussing the one made explicit, how adiabatic cooling works. But chingel's question demonstrates a more basic confusion, apparently shared by the majority, that adiabatic cooling is the primary cause of the decline in temperature with altitude.
If I asked you what caused sand dunes in the desert you wouldn't say it was the angle of repose; you'd say it was the wind.

 

[SHISHKABOB]

If I asked you what caused sand dunes in the desert you wouldn't say it was the angle of repose; you'd say it was the wind.

without the wind, the sand would be in a big lump

no sand dunes

 

[olivermsun]

... adiabatic cooling cannot be the primary cause for the existence of the gradient. Something else must cause it, which causes convection, which in turn is limited in its equalising effect by adiabatic cooling.
...
If I asked you what caused sand dunes in the desert you wouldn't say it was the angle of repose; you'd say it was the wind.

So you would prefer the explanation that radiative equilibrium, moderated by convection (where the adiabatic cooling comes in), is the "cause" of the decreasing temperature with altitude?