Heat rises, why is it cold at high altitudes?

[Feodalherren]

So I was at a ski-resort last weekend and this question just came to me out of nowhere. Hot air usually rises. Shouldn't that logically lead to high altitudes being warmer than low altitudes?! It's true for the ocean, but air seems to defy this law. Why is that?

 

[chill_factor]

This is not exactly true. For the atmosphere, the temperature minimum is not at the ground, but rather at a height of around 60 km. Afterwards, light from the sun can impart enough energy to the low density gas particles above that to significantly increase their average kinetic energy. below this layer, the gas is too dense for solar radiation to significantly increase the average kinetic energy since there are more particles per volume, but same amount of sunlight, so each particle gets less. Below the temperature minimum layer, there is an effective heat source: the ground.

 

[sophiecentaur]

The "heat rises" statement only works for a region of air and the regions around it. A body of air will rise if the surrounding air is at a slightly greater pressure. So warmer air will float up as it is displaced by cooler air around it.
It's really another issue why all the air in the atmosphere is cooler at a greter height and there are many different models of the atmosphere, with different levels of complexity. One good reason is that the Earth is heated by sunlight and the resulting IR radiation heats the air above. The higher levels of air get less of this radiation. Also, when air rises by convection (like cumulus clouds) it cools down as it expands.
But this only applies to the lower layers of the atmosphere. The temperature goes up and down as you get higher, for various reasons. See this wiki link.

 

[olivermsun]

So I was at a ski-resort last weekend and this question just came to me out of nowhere. Hot air usually rises. Shouldn't that logically lead to high altitudes being warmer than low altitudes?!

Higher altitude = lower pressure. If you raise a certain "piece" of air to a higher altitude, it should expand and cool down a bit.

It's true that hot air rises, but there's nothing to keep rising hot air right at the top of the mountain. Either it's cool enough after it rises that it's the same density as the air around it, in which case it just stays there, or else it just keeps rising and leaves you with the cooler air on top of the mountain that you had to begin with.

It's true for the ocean, but air seems to defy this law. Why is that?

First of all, the ocean is heated from the top, not from the bottom, and so the warmer, lighter water just tends to stay at the top. Secondly there is something to keep the warm water from rising even further — it's called the top of the ocean. :)

 

[cjl]

So I was at a ski-resort last weekend and this question just came to me out of nowhere. Hot air usually rises. Shouldn't that logically lead to high altitudes being warmer than low altitudes?! It's true for the ocean, but air seems to defy this law. Why is that?

Among other things, this is related to the fact that as a parcel of hot air rises, it expands, and if there is no heat transfer between the parcel of air and its surroundings, it cools. For more details, look up "adiabatic lapse rate". This isn't the entire reason, but it does at least explain part of it (and in reality, the adiabatic lapse rate often defines the steepest the temperature gradient can be across a significant portion of the atmosphere, since if the gradient were any steeper, heat transfer would become convection dominated, which would flatten it out again).

 

[Feodalherren]

Thank you for all your answers. I think I got the gist of it. I suppose it's trickier than I thought and that's why meteorology is an entire science :).