Balloon volume as it rises in constant atmospheric density

Question

I've been considering an hypotetical situation and it's making me a bit confused. If anyone could give me any insight, I would really appreciate it!

It is as follows:
Let's pretend atmospheric density remains constant with altitude. If I fill up a balloon at sea level and start rising it, would the balloon expand, shrink or remain the same?

My first thought it that it will expand. I filled it up at sea level, so it's inside pressure is the same as the outside. If I now start rising it, the outside pressure will decrease (since there will be less air above us), thus making the balloon expand to match it's inside pressure to the outside pressure. But this would mean the density inside the balloon is less than the density outside the balloon, which I find really counter-intuitive.
Furthermore, from what I understand, it's the density inside it that determines it's inside pressure. So it makes it all the more confusing to me that the density inside would be different from the density outside.

The only other possibility I can think of is that the question itself is flawed. The density can never be constant because the air at higher altitudes would always compress the air at lower altitudes, making it more dense.

Any thoughts?

Answer 1

You assume a constant density of the atmosphere and a balloon filled with an ideal gas. Both are in the gravitational field of earth. Then the ideal gas equation applies only to the gas in the ballon, not to the atmosphere. In this case, the atmospheric pressure decreases (approximately linearly) with increasing altitude. At any altitude, the pressure inside the ballon must alway be the same as in the adjacent atmosphere, i.e., it decreases with altitude. Thus, according to the ideal gas equation, the volume of the gas in the balloon must expand with increasing altitude.

This corresponds in good approximation to the behavior of a ballon in water, where the density is approximately constant with depth.

Answer 2

When looking at the atmosphere the ideal Gas equation should apply. This means that, when the pressure decreases with height, your density will also decrease (assuming comparatively small temperature changes). So your assumption is unphysical.

Now one could ask, what would happen, if the atmosphere was filled with an incompressible fluid, in which case your assumption would be satisfied. Then you would have to decide though, whether you want to fill your balloon with the same incompressible fluid, in which case his density would not change at all, while the balloon is rising (One might ask the question, why it would be rising in the first place, but lets not overthink this.), or you could fill it with gas, in which case, what you described would happen, but then the density of the balloon not being identical with the incompressible fluids density also should not be a surprise.