The same bag, holding less
Why Does Hot Air Lift a Balloon?
Heating the air inside pushes some of it out of the open mouth, so the balloon ends up lighter than the air it displaces.
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Step 1 of 5
Warm air spreads out.
Heat makes air molecules move faster and shove each other further apart, so the same air takes up more room than it did when it was cold.
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Step 2 of 5
The bag cannot grow, so air leaves.
The balloon is already full and open at the bottom. When the air inside spreads out, the surplus simply spills out of the mouth and is gone.
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Step 3 of 5
Now it holds fewer molecules than the same space outside.
The balloon's volume has not changed, but there is less air inside it than there would be if it were full of cold air. That difference is the entire lift — air at a hundred degrees is roughly a fifth lighter than the air outside.
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Step 4 of 5
The burner is the only control you have.
There is no throttle and no rudder. Firing the burner makes it climb, letting the air cool makes it sink, and a vent at the top dumps hot air quickly.
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Step 5 of 5
You steer by choosing a height.
The wind blows in different directions at different altitudes, so a pilot climbs or descends until they find a layer heading where they want to go.
A typical balloon holds about 2,800 cubic metres of air, and heating it to 100°C makes the whole thing roughly a quarter of a tonne lighter than the air it sits in.
The short version
A hot balloon empties, spilling air out of its mouth until what is left inside is about a fifth lighter than the air outside. There is no rudder: you steer by climbing or sinking until you find a wind going your way.
Try it yourself
Hold a light plastic bag open above a warm radiator. As the air inside warms, the bag lifts and tries to rise.