Why does a hot-air balloon float

A hot-air balloon is one of the more graceful sights of summer. A vast floating ball, powered only by a small propane burner, seems to defy gravity as it floats effortlessly above the ground. But what is it causing the balloon to fly, despite its considerable weight  

The small burner at the heart of the balloon heats the air within the canvas hood of the balloon. The densities of all materials -solid, liquid or gas - alter with temperature. Almost universally, we find the density p increases with cooling. Density p is defined as the ratio of mass m to volume V, according to 

It is not reasonable to suppose the mass m of a gas changes by heating or cooling it (in the absence of chemical reactions, that is), so the changes in p caused by heating must have been caused by changes in volume V. On the other hand, if the volume were to decrease on heating, then the density would increase. 

So the reason why the balloon floats is because the air inside its voluminous hood has a lower density than the air outside. The exterior air, therefore, sinks lower than the less-dense air inside. And the sinking of the cold air and the rising of the warm air is effectively the same thing it is movement of the one relative to the other, so the balloon floats above the ground. Conversely, the balloon descends back to earth when the air it contains cools to the same temperature as the air outside the hood. 

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