Hot-air balloons float because the air caught inside the balloon is heated up by a burner, making it less dense than the air outside. As the burner heats the air, it expands and some of the air escapes; that's what makes it less dense.

Introductory Chemistry: A Foundation
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Chapter2: Measurements And Calculations
Section: Chapter Questions
Problem 82QAP: If a solid block of glass, with a volume of exactly 100 in.3, is placed in a basin of water that is...
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Hot-air balloons float because the air caught inside the balloon is heated up by a burner, making it less dense than the air outside. As the burner heats the air, it expands and some of the air escapes; that's what makes it less dense.

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