why does hot air rise?

When you heat a material, the particles start to move around more (kinetic molecular theory). In the case of a gas, this means that the particles will be more likely to move apart, which causes the density to decrease. Due to buoyancy, which is the property that materials will float in a less dense substance (for example, wood floats on water because it is less dense, while a rock sinks because it is denser). So a hot air balloon is full of air that is less dense than the air around it, and the mass of the balloon itself is sufficiently overcome by the buoyant force (because it holds a large volume), so the balloon floats. However, a helium balloon floats without heat because the helium is lighter (He is lighter than the different elements and compounds in air), and thus it is less dense.

Note that you can get a small balloon filled with helium to float pretty easily, but you need a relatively large balloon to get a hot-air balloon to float.

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RE:

why does hot air rise?

hot air balloon rises

helium balloon rises without heat

hot air is lighter than cool air