What about hot air balloons? They work by similar principles. If you heat up a gas it expands. In the case of a hot air balloon, when the gas inside the balloon expands the extra gas is pushed out the bottom of the balloon, meaning that there are fewer atoms inside the balloon, meaning that the air in the balloon is lighter than the air outside the balloon.
The amount of lifting power is controlled by how hot the air is. If you heat the air inside the balloon 100 degrees F hotter than the outside air temperature, then the air inside the balloon will be about 25 percent lighter than the air outside the balloon. So a cubic foot of air weighs about 35 grams at 32 degrees F. A cubic foot of hot air at 132 degrees F will weigh 25 percent less, or about 26.5 grams. The difference is 8.5 grams or so. So a hot air balloon has to be much bigger to support the same weight, but it will float because hotter air is lighter than cooler air.
You can get a sense for how much air contracts and expands as its temperature changes by performing the following experiment:
- Take two Ziplock bags (1-gallon size) and blow them up (you can do this by zipping the bag closed, then unzipping a small hole at one end of the zipper). Blow each bag up like a balloon and seal it while holding pressure on the last breath. You want these bags to be full -- you want the plastic on both inflated bags to be tense.
- Now let the bags sit on the counter for a couple of minutes and cool off. You pumped 98.6 degree F air into them, and you want the temperature to drop to room temperature. The bags will probably become a little less tense in the process of cooling (makes sense...) so add one more puff of air to make them tense again.
- Now stick one of the bags into your freezer for about three minutes, while leaving the other one on the counter. When you take the bag in the freezer out it will have deflated some. How much? By about 10 percent to 15 percent. It has deflated because cooler air is denser than warmer air. Compare the cold bag to the bag on the counter -- the cold bag will not be tense at all. Then a funny thing will happen as the cold bag warms up -- it will get tense again and return to its original size!
You can clearly see that warmer air takes up more space than cooler air. Therefore, warmer air is lighter than cooler air, and that is what makes a hot air balloon float!