The volume of gas contained in a balloon expands when heated and contracts when cooled according to Charles' Law, which states that the temperature and volume of a gas are directly proportional.
The reason for this can be understood on a particle level. The particles of a gas are in constant, random motion. When a gas absorbs heat, the rate of molecular motion increases. As the molecules move faster they move farther apart, have more collisions with the inside surface of the balloon and collide with more force. The volume of the balloon will increase until the pressure, which is caused by collisions, is the same on the inside of the balloon as it is on the outside.
Conversely, when the air in the balloon is cooled the molecules slow down and have fewer and less forceful collisions with the inside of the balloon. The volume of the balloon then decreases until the inside pressure is once again the same as the outside pressure.
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