Generally speaking, I understand why hot air rises and cold air falls. Gravity causes cold air, which weighs more than hot air, to be pushed down. But there a lot of situations where I have a hard time understanding how this concept applies.

For example, it makes sense that roofing is a hot job, since hot air rises in a house up to the roof (and also because the sun shines on a roof more directly and a roof is often black which makes it reflect sunlight as heat). But why does it feel so much cooler at the top of a mountain than at the bottom?

How can it be so cold at an altitude of several thousand feet that airplanes need ice protection systems, since at higher altitudes one is closer to the sun? And how can we make sense of the fact that the temperature a few feet deep in the ground stays ~50°F year round, but down in the core of the earth it is extremely hot?

 

Adiabatic Cooling

 

Oh dear! Thermodynamics was one of my weak points in physics, and I could never keep straight the definitions of the words "adiabatic" and "isothermal".

I came across a college lecture about "The adiabatic atmosphere" which seems relevant:

Of course, we know that the atmosphere is not isothermal. In fact, air temperature falls quite noticeably with increasing altitude. In ski resorts, you are told to expect the temperature to drop by about 1 degree per 100 meters you go upwards. Many people cannot understand why the atmosphere gets colder the higher up you go. They reason that as higher altitudes are closer to the Sun they ought to be hotter. In fact, the explanation is quite simple. It depends on three important properties of air. The first important property is that air is transparent to most, but by no means all, of the electromagnetic spectrum. In particular, most infrared radiation, which carries heat energy, passes straight through the lower atmosphere and heats the ground. In other words, the lower atmosphere is heated from below, not from above. The second important property of air is that it is constantly in motion. In fact, the lower 20 kilometers of the atmosphere (the so called troposphere) are fairly thoroughly mixed. You might think that this would imply that the atmosphere is isothermal. However, this is not the case because of the final important properly of air: i.e., it is a very poor conductor of heat. This, of course, is why woolly sweaters work: they trap a layer of air close to the body, and because air is such a poor conductor of heat you stay warm.

 

Adiabatic Cooling

Great answer.
The Wiki entry mentions Chinook winds as an example of Adiabatic heating.
I was at that Casino yesterday, great Friday seafood buffet but the machines weren't very hot.

 

Adiabatic Cooling

Right. And because moist air carries more heat than dry air per unit volume, it continues to rise (hotter = less dense) and gives us clouds and rain. If you took away gravity, the Earth would be in bad shape for humans.

John

 

...If you took away gravity, the Earth would be in bad shape for humans...

Ummm...weather would be the least of our problems...

 

Right. And because moist air carries more heat than dry air per unit volume, it continues to rise (hotter = less dense) and gives us clouds and rain.

Just to be clear, it is the water vapor that carries the additional heat...in the form of 'latent heat of vaporization'. Condensation of the vapor as the surrounding air cools increases the temperature, resulting in further updrafts, more condensation, etc. A positive feedback loop. This is why moist air is unstable and causes 'weather' -- up to and including the most powerful hurricanes.

 

Regarding question about the temperature of the ground being constant at about 50 degrees (F) while the core of the Earth is extremely hot (about 10,000 degrees), that is because of the "Geo-Thermal Gradient".

Heat from the core is usually conducted in a three dimensional radial pattern. However, there are "Hotspots" where the crust of the Earth is thinner (or completely separating because of mantle convection), at subduction zones, or over superheated channels in the mantle.

Hotspots create a semisolid material called "magma" which can migrate to the surface and trigger volcanoes.

 

Generally speaking, I understand why hot air rises and cold air falls. Gravity causes cold air, which weighs more than hot air, to be pushed down. But there a lot of situations where I have a hard time understanding how this concept applies.

For example, it makes sense that roofing is a hot job, since hot air rises in a house up to the roof (and also because the sun shines on a roof more directly and a roof is often black which makes it reflect sunlight as heat). But why does it feel so much cooler at the top of a mountain than at the bottom?

How can it be so cold at an altitude of several thousand feet that airplanes need ice protection systems, since at higher altitudes one is closer to the sun? And how can we make sense of the fact that the temperature a few feet deep in the ground stays ~50°F year round, but down in the core of the earth it is extremely hot?

First off, forget about the whole "closer to the sun" thing. If you are at 26,000 ft you are (about) five miles above sea level. That's five miles out of ninety-three MILLION miles. To put that in perspective, in (northern hemisphere) winter we are about three million miles closer to the sun than we are in summer, so I don't think that five miles buys you anything.

If you look at the air consider what would be required for it to be happy to stay where it is, you can consider that one packet of air that is sitting on top of another packet of air and the packet on top has to be at a slightly lower pressure than the packet on the bottom because it is supporting less air above it than the bottom packet. How much lower the pressure is depends on the density of the top packet, which in terms depends on the temperature. So then you have to ask what the relationship between the temperature of the top and bottom packets has to be in order to give the necessary pressure relationship to just account for the density of the packet. What you end up with in doing so are the nominal lapse rates of temperature, pressure, and density as you go up in altitude. You can do this for an idealized atmosphere that has no energy being dumped into it from solar heating or ground heating, or you can take into account these, and other, factors to get more realistic models, but even the simplest one gives a very good first-order approximation to what is actually observed (on average).

 

Actually if the atmosphere is in pressure equilibrium, the temperature of any given layer can be the same as for the any of the layers above or below it.

The air in an elevator shaft is a simple example where the pressure is greater at the bottom than the top. However, if there is no heat source and the air isn't moving, the temperature at the ground floor is usually is the same as at the top.

As for weather, the layer near the ground is absorbing sun light and radiating infrared and it's usually warmer than the layers above it. However there can be an "inversion" where a warmer layer rests on a cooler layer. An inversion will prevent convection of warm air from below and this phenomenon can cause severe air pollution.

The Raleigh Taylor Effect is another phenomenon where a flat warm layer is trapped below a flat cooler layer and this prevents convection.

 

Actually if the atmosphere is in pressure equilibrium, the temperature of any given layer can be the same as for the any of the layers above or below it.

Nope. Do the math. If you assume the temperature is the same throughout the column then you can't get a stable density/pressure profile.

As for weather, the layer near the ground is absorbing sun light and radiating infrared and it's usually warmer than the layers above it. However there can be an "inversion" where a warmer layer rests on a cooler layer. An inversion will prevent convection of warm air from below and this phenomenon can cause severe air pollution.

The Raleigh Taylor Effect is another phenomenon where a flat warm layer is trapped below a flat cooler layer and this prevents convection.

All kinds of effects can come into play when you are talking about the interaction of different air masses and the various heating/cooling mechanisms that can be involved.

 

Just to be clear, it is the water vapor that carries the additional heat...in the form of 'latent heat of vaporization'. Condensation of the vapor as the surrounding air cools increases the temperature, resulting in further updrafts, more condensation, etc. A positive feedback loop. This is why moist air is unstable and causes 'weather' -- up to and including the most powerful hurricanes.

You seem to have missed my point completely. Your answer, adiabatic cooling, certainly occurs, but that is only half of the answer. Whether hot air (i.e., less dense air) rises is dependent on gravity/acceleration. In fact, the Memsic line of accelerometers is based on that very fact. It is also worth remembering that an air and water vapor mix is less dense than dry air at the same temperature and pressure.

The TS also asks about ice protectors on aircraft. They are not needed in air that is dry.

John

 

It's all PV=nRT, folks, where n & R are constants for the gas under consideration. Volume is proportional to Temperature/Pressure.

The air at the ground has the weight of all the air above on it, causing higher pressure, and thus lower volume (higher density). The higher molecular density causes more molecular collisions, which makes it warmer. This causes the gas to expand, which makes it want to rise (lower density). After rising to a place in the atmosphere where it is happy with its density, there are fewer molecular collisions, and it cools off. Which makes it want to sink back down.

Add in water vapor, with evaporation and condensation taking or adding heat, respectively, to the air, and you get a much more dynamic picture, along with precipitation, as the gas laws are sidestepped by one of the principle components deciding not to be a gas anymore.

 

It's all PV=nRT, folks, where n & R are constants for the gas under consideration. Volume is proportional to Temperature/Pressure.

The air at the ground has the weight of all the air above on it, causing higher pressure, and thus lower volume (higher density). The higher molecular density causes more molecular collisions, which makes it warmer. This causes the gas to expand, which makes it want to rise (lower density). After rising to a place in the atmosphere where it is happy with its density, there are fewer molecular collisions, and it cools off. Which makes it want to sink back down.

Add in water vapor, with evaporation and condensation taking or adding heat, respectively, to the air, and you get a much more dynamic picture, along with precipitation, as the gas laws are sidestepped by one of the principle components deciding not to be a gas anymore.

Higher molecular density does not make it warmer. If that were the case then the air is a scuba tank would be extremely hot -- yet it is the same temperature as it's surroundings (in steady state).

The TS is talking about why the lapse rate is what it is and the discussion should first focus on stable, dry air to set a simple framework.

 

Visible light from the sun goes right through the atmosphere. Only a very narrow band if infrared light is absorbed by the trace quantities of CO2 and water vapor in the air. On the way down, there is some scattering but very little energy is lost (absorbed) by the atmosphere. The majority of light-to-heat conversion happens when the light hits the ground, a building, something. Any light that is reflected upward, continues upward unless it is absorbed (again by CO2, water vapor or clouds (ice or droplets).

So, the guy above that said, it is all about the ideal gas Law equation, was wrong. It is all about Absorbance - light interacting with matter.

The air blows horizontally and, therefore, the air that hits your face on the mountain top was not near the warm earth surface to get warmed by conduction or convection. Air over lakes warms less rapidly than air over land. Water vapor in air changes the density significantly (lower) and causes all kinds of issues (see Inversion) https://en.m.wikipedia.org/wiki/Inversion_(meteorology)

There is a lot going on but, most questions are answered by the way the sun heats the earth - and the inversions that happen to cause anomalous behavior.

 

Higher molecular density does not make it warmer. If that were the case then the air is a scuba tank would be extremely hot -- yet it is the same temperature as it's surroundings (in steady state).

The TS is talking about why the lapse rate is what it is and the discussion should first focus on stable, dry air to set a simple framework.

Not true. When you 1st compress the air in your scuba tank, it gets warmer. Then the heat transfers back to the surroundings because heat flows from higher temp to lower temp. When you extract the air from the tank, it is instantly cooler because of pressure relief and moisture evaporation as the pressure is released. It's true that solar heating of the ground is a key point I was leaving out, but pressure heating is real, especially with moisture content.

 

Not true. When you 1st compress the air in your scuba tank, it gets warmer. Then the heat transfers back to the surroundings because heat flows from higher temp to lower temp. When you extract the air from the tank, it is instantly cooler because of pressure relief and moisture evaporation as the pressure is released. It's true that solar heating of the ground is a key point I was leaving out, but pressure heating is real, especially with moisture content.

Of course it gets warmer as it is being compressed -- that is why scuba tanks, for instance, are filled slowly and usually while sitting in a bath of water. But your claim was very simple -- that because a gas is more dense that there are more collisions and therefore it is warmer. Not true. The gas sitting there in that filled scuba tank that has reached equilibrium is much, much more dense than the air surrounding it. Thus, by your reasoning, there are more collisions and therefore it must be warmer.

 

There are 3 variables: P is proportional to T/V. Increase P while holding V constant, and T goes up. There's your scuba tank. You remove heat from it while it pressurizes, so it's not adiabatic.

In air, P is fixed at a given altitude, more or less. Increase T and V increases. The V increase causes the air to rise until it matches the density of surrounding air at a new altitude, but it's warmer than the surrounding air, having just risen. Adiabatic step is done, so now the surrounding cool air cools the newly risen air mass. This may cause condensation in the newly risen mass, and it will cause the volume to decrease and sink back down again, as anyone who has felt the cold air from an impending thunderstorm can attest. That cold air has just made a round trip from ground to stratosphere to ground.

I will say I was wrong about the primary mechanism of the heating. Pressure does cause heating, but an equilibrium would be reached without rise and fall of air. The external heating of sun on earth destabilizes that equilibrium.

 

To simplify things, imagine a planet that has an atmosphere but that is just drifting around in space (or perhaps in orbit so far from its sun that it receives negligible heat). This planet is completely dead, in terms of anything that would disturb the air, so we have no weather or air mass circulation. Now, over a long enough time the atmosphere would condense because the planet would cool toward the cosmic background temperature as it radiates heat away, but for now let's consider that the air holds sufficient total energy to place the air at the surface at a reasonable temperature -- or we could even stipulate that the planetary body itself, due to internal processes or latent heat, keeps the surface of this perfectly spherical planet at a constant reasonable temperature (let's say that this reasonable temperature is, oh, 15°C. And let's say that the surface pressure of the air, which is composed of, say, about 80% N2 and 20% O2 with nothing else, is about 15 psi. Finally, let's say that the gravitational constant at the surface of this planet is about 10 m/s². The point is that, even under the static conditions described, the pressure and temperature of the air would decrease as you rose in elevation and you can calculate the lapse rate of both. In fact, the temperature lapse rate would turn out to be the ratio of the gravitational constant to the specific heat of the air at constant pressure, which in this case would be around -10°C/km.

 

Regarding the previous post, if the atmosphere of the planet in was initially at a uniform temperature for all heights above the surface, it would seem the temperature would tend to remain uniform.

However in the real world, the atmosphere will lose heat due to infrared radiation into free space. Because of the lower density, the upper layers are more transparent to the radiating process and they would cool faster than the lower ones. Therefore the temperature would in fact decrease with increasing height.

This is consistent with the Second Law Of Thermodynamics which says that heat will progressively transfer from a region of higher temperature (the bottom layer) to the top layer which is at a lower temperature because heat is ultimately lost by radiation into space.

The overall temperature would eventually approach (but not achieve) uniformity and rate of heat transfer would approach zero. However, because there is some residual heat at the lower level, the temperature would be seen as decreasing (very, very slightly) with increasing height away from what's left of the heat source.