## Temperature on the mountain

Why is it that you feel cold on the mountains when you are actually nearer to the Sun? By right, it should be hotter.

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 Mentor Because you aren't that much nearer to the sun - what's a few thousand feet compared to 90 million miles? There are a number of reasons why it is cooler at higher altitudes, but the main one is that as warm air rises and the pressure drops (because there is less air above pushing down), the air expands and cools according to the ideal gas law.

 Quote by russ_watters Because you aren't that much nearer to the sun - what's a few thousand feet compared to 90 million miles? There are a number of reasons why it is cooler at higher altitudes, but the main one is that as warm air rises and the pressure drops (because there is less air above pushing down), the air expands and cools according to the ideal gas law.
The temperature of air is dependent on its internal energy and not on the volume expansion. If quoting, PV = nRT, we have, $$P_1V_1 = P_2V_2$$. The temperature does not change, no?

Further, when the warm air rises and cools, shouldn't it "drop down" to a lower altitude?
If the air cools down when it rises to a higher altitude, the energy lost must go somewhere but where?

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## Temperature on the mountain

 Quote by touqra The temperature of air is dependent on its internal energy and not on the volume expansion. If quoting, PV = nRT, we have, $$P_1V_1 = P_2V_2$$. The temperature does not change, no? Further, when the warm air rises and cools, shouldn't it "drop down" to a lower altitude? If the air cools down when it rises to a higher altitude, the energy lost must go somewhere but where?
Boyle's Law, $$P_1V_1 = P_2V_2$$ assumes that temperature is held constant. You can't use that here.

Think of it this way, as altitude increases, pressure decreases. If pressure decreases, the interaction between molecules, i.e. collisions will be less. An expanding gas cools. If you don't believe this, look at a standard altitude chart here and notice the temperature distribution with altitude.

http://www.pdas.com/e2.htm
http://aero.stanford.edu/StdAtm.html

Here is a nice reference on the computations:
http://www.pdas.com/hydro.pdf

Mentor
THIS site goes into more detail and points out that it is an adiabatic process (no heat exchange with the environment), so it must cool as it expands.
 Quote by FredGarvin Boyle's Law, assumes that temperature is held constant.
...and thus requires heat transfer.
 Quote by touqra Further, when the warm air rises and cools, shouldn't it "drop down" to a lower altitude?
Yes, it does sometimes set up a convection, but regardless, it will still be warmer lower and cooler higher except in rare cases of a temperature inversion. Ie, you can't have convection unless it is warmer lower and cooler higher.

 An added point of interest ... There can be enormous temperature differences generated by adiabatic effects. For example, a strong wind called a foehn wind (such as we get in the town I live in) will cool wet air on the upward side of the mountains and heat it up on the dry side. But because dry air heats at about 10degC per 1000m as opposed to 6degC for wet air the temperature on the lee side can be much hotter. Sometimes there is a temperature difference of 15deg here, at sea level, between one side of the mountains and the other.

 Quote by FredGarvin Boyle's Law, $$P_1V_1 = P_2V_2$$ assumes that temperature is held constant. You can't use that here. Think of it this way, as altitude increases, pressure decreases. If pressure decreases, the interaction between molecules, i.e. collisions will be less. An expanding gas cools. If you don't believe this, look at a standard altitude chart here and notice the temperature distribution with altitude. http://www.pdas.com/e2.htm http://aero.stanford.edu/StdAtm.html Here is a nice reference on the computations: http://www.pdas.com/hydro.pdf
An expanding gas cools because it did work. I can't imagine what the air is doing work unto. Isn't need free expansion, and so, there is no work done, and hence temperature stays the same?
If the expanding gas does cools, where has the heat energy transferred to?
I don't understand.

 Quote by touqra If the expanding gas does cools, where has the heat energy transferred to?
There is basically no heat transfer externally. This

http://daphne.palomar.edu/jthorngren..._processes.htm

is a reasonable, and simple, explanation.

 While average environment temperature decreases with altitude by about -6°C/1000m, the intense midday radiation is felt on our skin as higher temperature. At night this heat is emitted as infrared more easily in the thin air, so we feel colder. Note that this interaction with the mountain surface is what makes the slope temperature gradient so much less than the adiabatic gradient of 10°C/1000m.

 Quote by touqra An expanding gas cools because it did work. I can't imagine what the air is doing work unto.
1. Sunlight strikes the ground and warms it.
2. Decay of radioactive elements underground also warms the surface of the earth.
3. The heat from the ground is transferred to the air.
4. Warm, low altitude air does work by expanding against atmospheric pressure.
5. Expansion results in lower air density.
6. Cooler, denser air falls down and displaces it, forcing it up.