What principle allows hot-air balloons to ascend and descend?

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Hot-air balloons rise because hot air is lighter than cold air, following Archimedes’ principle, which states that an object will rise if its weight is less than that of the displaced fluid (liquid or gas). Modern hot-air balloons use a propane burner to heat the air inside the balloon to ascend. To descend, the burner is turned off, allowing the air to cool, and a vent is opened to let in cooler air, increasing the air density inside the balloon.