If hot air rises, why are mountain tops so cold?

Cause of the snow.

Because they lack a ceiling, which you obviously have.

The reason it's actually colder is because, as you go up in the atmosphere, the Earth's atmosphere feels less pressure the higher up you go. So as the gas in the atmosphere rises it feels less pressure, which makes it expand. When the gas expands it does some work. And and if it's doing work, it must be losing some energy; and if it loses energy, its temperature must drop because we define temperature as the average energy of the particles. Therefore, if the energy of the particles is lower, the temperature must be lower.

but the mountain tops are cold

Because the air gets colder as altitude increases.

Bro, you done talked shite about the Arizona State hos and now JA, why dont you show us a pic of the smoke show you pounding out currently?

because of decompression. As the air gets pushed up the mountain side the air isn't under as much pressure and there is a cooling effect.

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If hot air rises, why are mountain tops so cold?

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The density of air is lower thus lower pressure.

PV=nRT

Additionally you are dealing with lower molecular weight air molecules the higher you increase in elevation so the "n" in the ideal gas law also decreases.

Molecular weight of air molecules:

CO2 = 44 at only 0.4% is the heaviest molecule an likes of hug the ground...good for plants and why we have tree lines at high elevations.

O2 = 32 at about 20%. Get too high and O2 gets too low for oxygen life. It's good for us that O2 is relatively heavy and likes to hug the ground.

N2 = 28 and is about 79%.

H2O = 18 in the form of water vapor and varies in percentage based on humidity levels. It's one of the lightest air molecules and likes to rise and condense above the heavier molecules to form clouds.

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Ozone layer absorbs a lot of the UV rays coming it. It warms up. It also doesn't mix, because it's warmer as you go up.

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Isn't ozone unstable, that is it is very reactive and reacts with other air constituents back to O2 and needs be replenished continuously by UV light from the sun?