|MadSci Net: Physics (View this file without Frames)|
You asked at what altitude a balloon would pop but I'm not so sure that most balloons would pop at all. Rather, I think most balloons would just get deflated and fall back to earth without popping. The reason for this is that when a balloon rises, it does so because of buoyancy. To see what buoyancy is, it might be easier to look at it in the context of water, e.g. in the ocean. The amount of water that something displaces determines how much it'll float; i.e., the buoyant force that is exerted on a submerged body is equal to the weight of the water that the body displaces (remember, weight is the gravitational force exerted on a mass). How much water does a body displace? This is determined by it's volume and it's shape. In order to float, the body has to displace enough water to generate a buoyant force equal to the weight of the body. This is also known as Archimedes' principle, named after the Greek scientist who lived over 2,000 years ago! Just remember that the water can support something so long as the object weighs as much as (or less than) the weight of the volume-of-water whose space it takes up; if the thing weighs more than the weight of the water that was in that space, it sinks.
Now that we have an idea of what buoyancy is, how does it apply to the balloon?? Well, you can imagine the air around you as being an ocean of air. And like the more familiar ocean of water, there is a certain amount of pressure at each depth. At ground level the pressure is high and the pressure drops as you travel higher up (just like at the bottom of the ocean the pressure from the water is high and the pressure drops as you float up to the top). Now, the shape and volume of the balloon displaces a certain amount of air and if you fill up a balloon with a lighter-than-air gas (e.g., helium), the inflated balloon will weigh less than a similar volume of air. The weight it displaces (the buoyant force discussed earlier) pushes it up and the balloon "rises" or "floats".
As it floats higher and higher, the air pressure becomes lower (the air is less dense) and the temperature also drops. As the air pressure drops, the buoyancy will actually stay the same rather than go down. This is because the air inside the balloon will expand and this will make the whole balloon expand. Since buoyancy is determined by the weight of the displaced air, even though the density of the air decreases, the expansion of the balloon still ends up displacing the same weight of outside air as it did at the lower altitude. What about the temperature? Well, the temperature will make the air around the balloon, and also the gas inside the balloon, more dense. So although the density of the surrounding air increases, the volume (and hence amount of air displaced) of the balloon decreases, thus maintaining the same weight displacement and keeping the buoyancy constant again (rather than having it go up).
Eventually, however, the material of the balloon (the latex) will do one of 2 things. In the 1st case, the latex or fabric of the balloon will expand and then not be able to expand any more. In this case, the balloon will displace a certain volume of air which won't change as the balloon continues to rise. Since the air above it is still continuing to drop in air pressure, eventually the static volume of the balloon will lead to decreased buoyancy (air gets thinner but volume of the balloon stays the same and so the same volume now displaces smaller weight of air) and the balloon will eventually come to rest at a maximum altitude where it's buoyancy and weight are equal. In the 2nd case, the fabric will start to expand so much that the gas that was trapped inside the balloon will start to escape. As the gas begins to escape, the amount the balloon can expand will peak and the balloon will again reach a maximum altitude. In either case, after quite some time, the gas will eventually leak out of the balloon and the balloon will slowly descend and fall back to the earth, deflated.
So, I think the only way to have a balloon pop as it floats up is to either have a sudden change in pressure where the fabric is subjected to more strain than it can bear or to have a weak fabric that pops at some altitude at or before it's maximum altitude (this would depend on the material of the balloon) or to have a fabric that "cracks" at the low temperatures. In general, I'd assume that the latex used for regular balloons is strong enough to allow a normal balloon to reach it's maximum altitude by expanding without popping. I'm sure there are many other factors, but this should be a general overview of what happens. I'd tell you to give it a try, but unless you live in a house with a really, really huge ceiling, you'd have a heck of a time tracking where the balloon lands! I hope this helps and please feel free to drop me a line if I something is unclear.
P.S., here are a few sites that discuss balloons and balloon flight. They mostly talk about the high altitude balloons used in research and for carrying people rather than party balloons but they're still very informative. Btw, they also have info on how high different sorts of balloons can go (from 30,000 feet to 60,000 feet to even higher!).
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