If hot air rises, why is it usually colder in the mountains at higher elevations?
Air is nearly transparent to sunlight. This means that the sunlight reaches the ground to warm up the oceans and the land it hits. As the oceans and ground warm up, they warm the air above them. This warming destabilizes the atmosphere: warm air rises. As warm air rises, though, it moves up into an area with lower pressure (there is less air above to push down on it). This allows the air to expand, and as it expands it also cools down. The gas law, also called Boyle’s law, is an expression of this. Thus, the air at higher elevations (lower pressure) is cooler. You can do a pretty good job of predicting how much colder it will be on a mountain by just using the standard lapse rate of 3-4 degrees C / 1000 feet or 6 degrees C/km. Also keep in mind that the pressure reported in a weather forecast is generally corrected to mean sea level. If not, there would always be two major low pressure areas in the US: over the Rockies and, to a lesser extent, over the Appalachians.
