# Why is the temperature outside the airplane lower than the ground temperature?

seems the airplane is nearer to the sun, so the sun should more directly shine on the plane. But when I travel, the airplane temperature is much lower than the ground. Why is the temperature so low?

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Mountain cliffs are also near sun, but still you can find it colder.. –  SS-3.1415926535897932384626433 Jul 4 '12 at 11:08

The reason is that the air way up high is cold, and the airplane is in contact with a huge amount of air because it is moving so fast.

The sunlight at high altitudes doesn't heat the airplane by any significantly greater amount than it does when the airplane is on the ground, at least the difference is miniscule. The distance to the sun is so enormous that the slight change due to the airplane being in the air has absolutely no measurable effect, but there is a small effect due to the fact that the airplane is higher in the atmosphere, so less of the sunlight has been scattered by the atmosphere at the high altitude. Neither consideration makes much difference, this doesn't matter.

The thing that does matter is how the atmosphere absorbs heat from the sun. The atmosphere is really bad at capturing heat. If the Earth were a mirror, and the sunlight just bounced off the surface of the Earth, the Earth would be at close to absolute zero temperature, because the atmosphere is nearly transparent. But this is not what happens--- the light hits the ground, and is absorbed by dark things, like plants and ocean-water. Then this energy is reradiated in the infrared into the atmosphere, where certain gasses like CO2 and methane, reabsorb some of the heat and trap it in the atmosphere. Finally, there is infrared light that is escaping into space, and this keeps the Earth from heating up indefinitely. The whole thing is in a steady state.

But the part of the atmosphere that absorbs the infrared light is close to the ground. CO_2 is a heavy gas, since oxygen is heavier than nitrogen so O_2 is heavier than N_2, and adding a carbon atom to O_2 definitely makes it heavier still. The density of gasses in the atmosphere is given by the Boltzmann law--- the density goes as

$$e^{-{mg h\over kT}}$$

this is the potential energy divided by the thermal temperature (assuming T is constant, which is a bad approximation, but it gives you a zeroeth-order understanding). This means that the heavy gasses have an exponential decay of concentration relative to the light ones, and at the top of the atmosphere, it's all N_2, and very little O_2 and extremely little CO_2. The attenuation length is proportional to the mass, and CO_2, with atomic weight 46, is 1.6 times as heavy as N_2.

This means that the top of the atmosphere is poor in heat-capturing CO_2 (although it has methane), so it is largely transparent to the sunlight coming in and to the infrared light going out. This means it is really cold. This also makes the segregation effect of temperature and mass stronger, so that the oxygen at cold high altitudes is reduced by even more than the naive Boltzmann estimate above, because at low temperatures, the difference in attenuation length of different mass gasses increases proportionally to the inverse absolute temperature.

The airplane is touching the air, and is losing energy from the surface to the air until the airplane body is at the same temperature as the surrounding air.

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There's a slight mistake in this answer: although the atmosphere is transparent to visible light, it's really, really good at absorbing and emitting in the infra-red range, to the point that it behaves as an almost perfect black body. The top is cold because it's good at emitting, not because it's bad at absorbing. If you don't believe me, use the Stefan-Boltzmann law to calculate the Earth's temperature assuming it's a black body, and you'll get the temperature of the stratosphere. The reason the surface is warmer is the greenhouse effect. –  Nathaniel Jul 4 '12 at 9:15
See, for example, asd-www.larc.nasa.gov/ceres/brochure/rad_bal.gif for figures on how much IR is absorbed and remitted versus transmitted. –  Nathaniel Jul 4 '12 at 9:15
You have forgotten water vapor, which is the main "green house gas" en.wikipedia.org/wiki/Greenhouse_gas Water vapor is 36% to 72% contribution depending of course on humidity at the time to the green house effect. The only reason AGW targets CO2 and methane as crucial is through a feedback with H2O hypothesis, introduced into their large General Circulation models that bootstrap the CO2 contributions. Models that are wrong vs most experimental data. –  anna v Jul 4 '12 at 13:50
@Nathaniel: Ok, I'll fix it. –  Ron Maimon Jul 4 '12 at 14:44
@Nathaniel: What's the absorption length in infrared? Is it 1 km, 100 m? –  Ron Maimon Jul 4 '12 at 15:04

According to Gas law temperature and pressure is related using this equation. $PV=nRT$ ,that is pressure is directly propositional to temperature. At very high attitude pressure is very low so the temperature should also be low (the air pressure near ground is higher than air pressure at high altitude).This cause the decrease in air temperature

Your argument from the ideal gas law does not hold. You assume that because $P$ decreases $T$ has to follow. The gas in the upper atmosphere contains less particles per volume, i.e. $n$ will be smaller, therefore $T$ does not necessarily decrease. –  Alexander Jul 4 '12 at 13:52