Why are mountains' weather cold instead of hot?

Answer 1

Gebob is by far closest to the answer. It does involve the ideal gas law but also something called adiabatic expansion. As you increase elevation, the atmospheric pressure decreases simply because there is less air above you at higher elevations. When a mass of air travels up hill by the wind, the decreasing pressure allows the air to expand. During the expansion the amount of internal energy (or heat) contained does not change. The constant internal energy is called an adiabatic condition. The pressure vs. temperature relation for an ideal gas undergoing an adiabatis process is:

T2 = (P1/P2)^((1-k)/k) * T1

Where T1 and T2 are the initial and final absolute temperatures and P1, P2 are the corresponding pressures. k is the specific heats ratio which is 1.4 for air (it is a measured property of the gas)

For example, a change in pressure from sea level (14.7 psi) to 5000 ft (12.0 psi) will change the absolute temperature from 80 F (540 R - need to use absolute temperatures) to:

T2 = (14.7/12.5)^((1-1.4)/1.4) * 540 R = 515 R

For a drop of 25F.

Answer 2

At low pressure, temperature decreases according to an approximation of the Ideal Gas Law:

T2 = T1 * P2/P1 (From PV = nRT)

Thus, for a given volume of gas, as P2 decreases with respect to P1, T2 decreases with respect to T1

From a molecular standpoint, there are fewer molecules around, thus less thermal vibrations/heat content.

Answer 3

As warm air rises from the ground, it cools, resulting in the temperature change.

Answer 4

very simple elevation.