HEAT IS SUPPOSED TO RISE. WHY THEN, IS IT COLDER ON TOP OF A MOUNTAIN THAN IN THE VALLEY BELOW?

Heat does not rise. Low density air rises if surrounded by air of higher density. Air that is heated by contact with warm ground becomes less dense and therefore rises. As it rises, it mixes with cooler air above and cools to a point where it stops rising. Air at the top of a mountain makes little contact with the ground and is therefore cold. Air in the valley below makes a great deal of contact and is therefore warm. That is, the lower region of the earth’s atmosphere, the troposphere, is warm and in it the warmest layer is that nearest to the ground. The stratosphere above absorbs incoming radiation from the sun. The temperature here therefore increases with increasing height. So if you climb 40km above the earth’s surface, you would find that it gets much warmer again. Also, there is a much greater air volume at altitude, since the planet is a sphere: like an onionskin, each layer of atmosphere covers a larger and larger area. The ground heat therefore dissipates into this vast heat sink. As there is no lid on the atmosphere, the heat escapes from this sink into the endless void by the way of radiation.