There is less pressure in the air as you go further up the atmosphere. As heat rises up it begins to feel less pressure and starts to expand. Expanding requires energy so as it expands, it’s releasing energy which causes it to get cooler. By the time you get to the top of the mountain it’s much cooler as so much energy has already been released
This is to do with pressure. The less pressure you have the colder things are. As you climb the mountain you are decreasing pressure therefore getting colder.
Heat does rise and continues to rise and cool until it gets cold and then it begins to sink towards the ground where it is heated again. This is the basis for convection and is a rough model of how our atmosphere works.
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