Why is the atmosphere colder at higher altitudes?

Posted by in Musings




My roommate and I got into a serious debate the other day about the cause of varying atmospheric temperature changes at different altitudes.  I argued that the discrepancy resulted from differences in pressure, which according to the Ideal Gas Law, invariably results in lower temperatures.  He on the other hand, being a PhD student in Energy Resources, believed that the geothermal energy of the earth itself was warming the air at lower temperatures.  In fact, we both became so invested in the argument that our debate stretched over multiple days, and each of us was certain our point of view was correct.  He finally decided to take matters into his own hands and find any scientific articles (READ: NOT Yahoo Answers) to uncover the truth. What he (we) figured out surprised us both.

Turns out we were BOTH wrong.  Or technically, MOSTLY wrong.  Before I explain what is the RIGHT argument, I’ll better explain our point of views.

Ideal Gas Law (my argument)

Coming fresh off the MCAT, the ideal gas law (PV=nRT) is still deeply ingrained in my mind.  For those readers out there that are not physics-inclined, each letter within the equation stand for different physical properties of gas.  P = Pressure, V = Volume of the Gas, T = Temperature, n = amount of gas (in moles) and R = a constant number (was experimentally determined at one point or another).  Given this over-simplified equation, if any one of the variables changes, we can determine what will happen to the system.

The point I was initially trying to prove was that as pressure decreases, and assuming that the number molecules (n), the volume (V) and R are all constant, then temperature (T) must ALSO decrease in order to maintain a balanced equation.  To understand this conceptually, if you have ever deflated a pressurized tire or ball, the air escaping feels very cold.  It is basically following this mathematical equation.

However there are a few problems with this equation.  One, it assumes adiabatic expansion/cooling.  Adiabatic processes are those where there is no energy exchange with it’s surroundings, which clearly is impossible in real life situations.  The air is constantly being heated and cooled by outside processes, therefore this point is moot.  Additionally, if we arrange the equation to be P=(n/V)RT, n/V equals density.  This equation assumes density is constant, which we already know changes as a result of altitude. Thus nullifying the applicability of the Ideal Gas Law equation.

Geothermal Energy (his argument)

My roommate’s theory postulated that the energy produced by the molten core of the earth generated the heat that would actually warm the atmosphere from the ground up.  So it isn’t necessarily a result from the altitude above sea level, but more so how far away from the earth’s crust the atmosphere is.

Unfortunately, I don’t know that much about geothermal processes, and the brevity of presenting his arguement isn’t to discredit his point of view and promote my original hypothesis.  It is simply because I know very little on the subject.  Anyways, in summary this DOES actually happen, but the energy produced is minimal….only ??0.075 W/m^2, only enough energy from an entire acre to power a 60 watt bulb for 5 seconds.

Warming by the Sun, from the ground up?

According to this USA Today article, air gets colder as you go higher because air is warmed from below, from the earth.  HOWEVER, it is not, as McClure had thought, due to the Earth’s geothermal heat, but rather because the sun’s radiation is initially not absorbed efficiently by air.  Much of the sun’s energy comes in as UV and visible light, which passes through the atmosphere without much absorption.  It is absorbed by the earth, heating the Earth’s surface.  Then the surface of the earth emits infrared radiation, which IS absorbed efficiently by air.  Additionally, any living organism produces infrared radiation as a natural byproduct of normal biological processes.

Combining the infrared energy from biological sources with the natural reflection of solar energy, the air is heated from the ground up.  The level of energy vastly outweighs the amount produced by geothermal energy, with the average solar insolation is ~1000-2000 W/m^2.  That is about 20,000 times higher than geothermal energy.

(I’ve added a nice graphic that also shows the complexities of the earth’s atmosphere)

Conclusion

It seems we were both wrong.  Technically his point is partly right, but the contribution from geothermal energy is negligible.  My point, on the other hand, is based on idealistic conditions, which don’t exist in nature.  Nonetheless, I’m pleasantly surprised to find that is is indeed the sun that heats up the atmosphere….but the reverse of what intuition would have us believe.  So back to our orignal questions “Why is it colder at higher altitudes?”….it seems we looked at the problem completely backwards!

It’s pieces like this that are the reason I started this blog.  When you are as incessantly curious as I am, you’ll always find something that will amaze you.