# How does Charles' law relate to hot air balloons?

May 24, 2015

Charles' Law says that the volume of a gas is directly proportional to the temperature of the gas.

#### Explanation:

V ∝ T

This means that when the gas in a hot air balloon is heated, the gas expands.

The balloon has a fixed volume, but there is a hole at the bottom.

So, the extra volume flows out of the hole in the bottom of the balloon.

Since there is less air in the same volume, its density decreases.

The volume is constant, so the weight of the air in the balloon decreases.

According to Archimedes' Principle, an object floats when it weighs less than the fluid it displaces.

When the air in the balloon gets hot enough, the net weight of the balloon plus the hot air is less than the weight of the same volume of cold air, and the balloon starts to rise.

When the gas in the balloon is allowed to cool, the volume of hot air decreases.

Cold air moves in through the hole, the weight of balloon plus air increases, and the balloon starts to sink.