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As altitude increases external pressure exerted on the balloon slowly drops while the internal balloon pressure remains constant. The temperature also greatly decreases to well below freezing making the mylar quit brittle. If the balloon is filled to capacity with helium or hydrogen it will eventually burst due to pressure changes at about 2000 - 4000 meters in altitude. If filled to 50% capacity it will burst below 10000m due to low temperature fracturing.

The balloon will rise up, and its altitude will eventual stabilize at the height where the density of the air is equal to its own density. I'm not sure what sort of height such a balloon might attain, but it won't be reaching the edge of space or anything like that: probably just a few hundred feet; possibly a few thousand. Although mylar is pretty impermeable, the helium will leak out by degrees, and so the density of the balloon will increase. No longer buoyant, it will descend and finally land in some lonely spot: a miserable, dejected, deflated mylar rag. It will eventually be discovered by some hiker, who will be immensely disappointed if it doesn't have a message attached to it.

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16y ago

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