Question

proove that hot air rises up

Answer 1

because hot air is not of any kind of mass or weight it loss all his property and mixtured in air and rise by the process of evaporation

Answer 2

Hot air rises because when you heat air (or any other gas for that matter), it expands. When the air expands, it becomes less dense than the air around it. The less dense hot air then floats in the more dense cold air much like wood floats on water because wood is less dense than water.