# Why does the increase in atmospheric pressure crush this empty bottle?

I'm trying to understand how atmospheric pressure works. Please have a look at this picture taken from Wikipedia.

Because this empty bottle was sealed at a higher altitude, the pressure crushes it once we bring it back to the lower altitude. I was wondering why that is since it's supposed to be completely filled with air when we sealed it at a high altitude? What would we have to do at the high altitude so that it doesn't crush at a lower altitude?

• The definition of "completely filled with air" depends on altitude. Apr 14 '20 at 20:17

Pressure is related to the average force the molecules inside the bottle are applying to surface of the bottle. When you seal the bottle at high altitudes the air inside the bottle and the air outside the bottle are pushing against the surface of the bottle with about the same force. As you bring the bottle lower in altitude the molecules inside the bottle are still pushing against the container with the same force as before but the molecules outside of the bottle are pushing against it with more force. This means there is a net "crushing" force inwards on the bottle causing it to deform as in the image.

• Thank you for your answer! I'm curious, is there a way to prevent this crushing at all when the bottle is brought to the lower altitude? To somehow increase the force of the molecules when you seal it at a high altitude so that the pressure equalizes at lower altitudes? Apr 14 '20 at 20:31
• You could add more air to it as you bring it down to increase the pressure inside so that it always matches the pressure outside. Or you could just force more air into the container when you're at the higher altitude, assuming the bottle is strong enough that it wouldn't burst. Apr 14 '20 at 20:35
• I see. So when we say high altitude, does it mean that the molecules are inherently or structurally "weaker" than the ones in the low altitude? Or is it that there are fewer molecules at a high altitude, which makes them "weaker"? Apr 14 '20 at 20:57
• There's no difference in the molecules themselves, the ratio of the gases in the air might be slightly different at different altitudes but that isn't what's causing the pressure change. There are less molecules flying around inside a bottle if the pressure is lower which means there are less molecules per second colliding with the inside of the bottle which means less force. Apr 14 '20 at 21:01
• Ahh. I see. What would happen then if we open the bottle after it's crushed at the low altitude? Would the air from the outside come rushing inside the bottle? Apr 14 '20 at 21:16

At 14000 feet air pressure is roughly 60% of that at sea level. Therefore, when the bottle was sealed at 14000 ft, the pressure of the air in the bottle was about 0.6 atmospheres. Consequently, when the bottle was brought it was filled with air at a lower pressure than the pressure of that air outside the bottle causing it to crush.

Hope this helps.

• Thank you! Does that mean that the no. of air molecules inside the bottle that was brought down is fewer than the molecules at the low altitude, which causes the crushing? Apr 14 '20 at 21:01
• @Mac_79 Yes. Or to put it another way, there is more space between the molecules inside the bottle than outside, making it easier "squeeze" the air inside the bottle. Apr 14 '20 at 21:32

Pressure at ground level is higher than at mountain top.

A thin wall experiences net differential external pressure when brought to ground. The vacuum inside the bottle which can be directly created by pumping out air from inside the bottle yo buckle it.

Buckling takes place by lower vacuum values than positive pressure capability applied inside.

Even on ground when such a container with hot steam is cooled down keeping cap tightly closed same buckling collapse occurs.

The mass of gas $$m$$ is same. Assume isothermal contraction ( constant $$T$$), Boyle's Law $$pV= mRT$$ holds good making the gas denser.