Mount Everest and Adiabatic Cooling

Say you are on a trip to Nepal, and you’re hanging out with friends in Kathmandu a few days before you set out to climb Mount Everest. You remember about Adiabatic Cooling, something you learned in that one Geography class with that cool teacher that was always wearing cool bowties every day.

You tell your friends that you can calculate out what the temperature would be at the various base camps along the way, and also at the top of Mount Everest.

The trail up Mount Everest and the elevations of the camps along the way.
SRC: http://www.atmos.umd.edu/~meto200/meto200.liftingcondensation_files/image002.gif

You get out a piece of paper, a pencil and your phone. Using your google-fu you quickly find the relevant information, perform the calculations and tell them that at base camp one the temperature would be about 12.5F right now, the temp at Camp 2, half way up would be about -5.5F right now and it would be about -22.1F at the summit.

If the temperature at Kathmandu is about 79F, the temperature at the
Mount Everest Base Camp is about 12.5F. When Adiabatic Cooling occurs,
it has two rates. The Dry Adiabatic Rate and the Saturated Adiabatic rate.
The Dry Adiabatic Rate is about 5.5F/1000ft and the Saturated Adiabatic Rate
is about 2-3F/1000ft. 

This is super cool, your friends are impressed and you have gained cool science cred with them, but what they really want to know is how it works.       

On earth, air moves around as an air mass. Air masses are volumes of air defined by their temperature and how much water they contain. When an air mass moves up, and over something like a mountain it cools down as it goes up in elevation. This is because of a process known as Adiabatic Cooling, as a gas goes up in elevation the pressure, forces acting upon the air, lessen so it has a chance to expand. As it expands, the temperature of the air mass goes down because the total heat energy that the air mass has is now spread over a larger area.  

Once this air reaches the lifting condensation level, the level where the air temperature has reached the dew point and can start forming clouds, the temperature still decreases, but at a slower rate.

The temperature about half way up, at Camp 3 is about -5.5F
 and the temperature at the summit is about -22.1F 
Because the LCL was reached getting to the base camp
only the SAR was used in the calculations.