how do balloons work?

Inspired by a recent thread on lighter than air travel - how does the whole lighter than air thing work for balloons and zepplins and the like?

I understand the concept that if you have an object that has less density than it’s environment that gravity will create more pressure underneath it and it will rise, etc.

This makes sense for rigid objects or objects in a rigid container. But in the case of say, a toy balloon, why doesn’t the surrounding air pressure just squash the helium balloon until the helium molecules are at the same density as the surrounding air? Prefer conceptual explanations to equations…

Because the pressure INSIDE the balloon is equal to the pressure OUTSIDE the balloon - 1 atmosphere.

If you take the balloon up high, it’ll start to swell since atmospheric pressure drops - this happens with, for instance, high-altitude weather balloons. They are not fully inflated at launch so that when the balloon is at high altitudes the envelope doesn’t burst. When you see them ready to be released they look mostly deflated and wrinkled (but they are still lighter than air, obviously).

And I suppose if you could take your balloon to the bottom of a swimming pool you’d find that it gets smaller since the outside water pressure is greater than 1 atmosphere inside the balloon.

Because the two gases have different density at the same pressure. That’s what “different density” means, usually.

If you have a bag of air under water, the water pressure doesn’t squash it until the air has the same density as water, right? Same thing.

The atmosphere already does squish the helium balloon, but it doesn’t squish it to the same density, but rather to the same pressure.

Pressure depends on the number of molecules in the gas, if the termperature is kept constant. It doesn’t matter what weight the particles have, an equal number of particles will have equal pressure. So a balloon filled with a gas that is heavier than air (air is composed mostly of N2 and 02) will have the same number of molecules as the volume of air it displaces, but will be heavier, a balloon filled with CO2 will sink much faster than a balloon filled with air. A helium balloon likewise has the same number of molecules, except in the case of helium each “molecule” is actually a single He atom. So at the same pressure, Helium is about 1/4 the density of air. Hydrogen (H2) is even lighter, about 1/8 the density of air.