I keep hearing people saying that air rises because it is low pressure and that's what causes clouds to be formed. But, isn't hot, rising air high pressure? It's got fast moving atoms in it and that may mean that there are more collisions between the particles right? Shouldn't that mean that rising air is high pressure?
The hot air has the same pressure as the surrounding cold air. However, this pressure is created by a smaller number of faster moving molecules, hence hot air has smaller mass and rises according to the Archimedes law. In other words, the same number of molecules of hot air take larger volume.
On the other hand, if we had air confined in a rigid volume (like a pressure cooker) and heated it, its mass and volume would be constant, but pressure would be higher.
This is the difference between and isobaric vs. isochoric processes (constant preassure vs. constant volume).