why is it when heat rises, the top of the mountains are colder and not warmer?

Answer 1

The hot air cools as it rises because higher up there is less pressure, so the air expands....

When a gas is allowed to expand, it cools down, or draws heat from its surroundings, cooling the area around it - this is the principle an airconditioner or refrigerator uses to cool things down. (When a gas is compressed, just the opposite, it heats up - you might notice this in a dive shop where the staff is filling scuba tanks!)

You can see the effects of this in many places. For instance, when you have a big propane tank in your grill and you run the grill for a while, you might see condensation, or even frost, on the valve of the tank. That's because the gas in the tank is expanding as it emerges. As the gas expands it cools down and cools the valve it is flowing though.

So, as air ascends the mountain and expands, it will cool down. If the air is moist, it will not be able to hold all the moisture it held at a lower altitude, so the rising air will often form fog or clouds or even rain as it goes up the mountain.... this is the first stage of what is called a "rain shadow"

Answer 2

Hot air rising is only one process affecting temperature, and a relatively weak one - there's many other processes at work. In this case, it's the thinner atmosphere at the tops of mountains that makes them colder. This relation is captured in Gay-Lussac's law, which says that the ratio of pressure to temperature is a constant. Since air pressure decreases as altitude increases, temperature must also decrease as well.

Answer 3

The tops of mountains are colder because they have much less oxygen, and it is the oxygen in the lower atmosphere that retains heat.

Just like the seas - the greater depth you go to the colder it gets!

Answer 4

The air is thinner the higher the elevation. Thinner air means less ability to trap heat.