Hot air is less dense than cool air, so hot air will rise above cool air. Increasing the air temperature inside a hot air balloon makes it lighter than the surrounding air, so the balloon can lift up. The density of hot air is about 0.25kg/m^3 less than that of cool air, which means a cubic meter of hot air can lift about 0.25kg.
What is the minimum volume of hot air needed to lift a hot air balloon carrying