The law you want to use here is called Charles' Law. (V1
) That means that if you divide the starting volume by the starting temperature, you get the final volume divided by the final temperature. It's important here to use the absolute (Kelvin) temperature, which starts at absolute zero, not some other scale which call some more abitrary temperature zero.
Here's how it works with a balloon. You fill the balloon with hot air. It eventually fills up, but you're not off the ground. If you keep heating the air, you raise T2
. That means the volume (V2
) has to get bigger to keep that side of the equation correct. But the balloon can only hold so much air. As you keep heating the air, it gets bigger and some of it starts to spill out the bottom of the balloon. Now you have even less air in the balloon than you started with.
As more and more air leaves the balloon, it get's lighter and lighter and eventually, you lift up off the ground.
Getting down is interesting too. You have 2 choices. You can either cool the air inside the balloon back down so that more air comes in or you can let more cool air in by opening a small hole in the balloon, which lets some hot air escape. It takes a long time for the air in the balloon to cool down all the way, so you usually let air back in. Hot Air Balloons have a special valve that lets some air come into the balloon without all too much coming in and causing the balloon to fall fast.
(republished on 07/30/06)