For our last episode, we showed some of the math that helps explain how hot air balloons rise through the air. Most people know that hot air rises, but why? The Ideal Gas Law (pV = nRT) says that if the pressure inside the balloon doesn't change (true) and the volume inside the balloon doesn't change (also true) then an increase in the temperature will cause a decrease in the number of air molecules occupying that space. That means the heated air is less dense than the outside air. A principle stated by Archimedes explains that buoyant force pushes the less dense air upward.

The balloons need to be quite large because this upward force is quite weak, a fraction of an ounce per cubic foot of air. But if you make the balloon large enough (many balloons are 90,000 cubic feet) the buoyant force can be great enough to lift the balloon (800 lbs) and its passengers.

We also showed an equation that can give, approximately, the amount of lift to expect from heating the air a certain number of degrees.

For additional info:

Wikipedia entry on hot air balloonsA nice explanation of the math and physics involved with balloons at How Stuff Works

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