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In my thought experiment, since air exerts $14.7$ psi at sea level, the air within the cube of steel should exert the same pressure outward, $14.7$ psi. Right?

The whole thing about balanced air pressure is quite counterintuitive to me. For example why aren't things being deformed by the fact that there are two 14.7 psi forces ramming it in from the inside and outside? Aren't we left to conclude that every single container in the world can withstand a pressure of >100000 Pa?! And if you take an arbitrarily small amount of air (let's say a few thousand atoms) and pack it into a container and ship it to space, will that extremely tiny amount of air still manage to exert such a great pressure?

EDIT: Great answer, @Bill N. However I don't really get why once two equal in magnitude forces are directed at each other, nothing happens. There will still be compression. I mean, when you compress gaseous oxygen at 96 GPa (perhaps against a diamond anvil) it turns to metallic oxygen. So there is still the compression problem.

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  • $\begingroup$ Steel is strong stuff. You're worried about a mere 14.7 PSI? A steel SCUBA tank can contain 3000 PSI, and still be considered safe enough to strap onto your back. $\endgroup$ – Solomon Slow Oct 28 '15 at 2:53
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If the cube is sealed, doesn't expand and the temperature doesn't change, the pressure inside the cube will remain at 14.7 psi. That pressure is applied to all 6 sides continuously, simultaneously. Pressure in a sealed container will depend only on the volume and the temperature, not the number of sides, nor the external pressure.

On the other hand, there will be a force of 14.7 pounds of force exerted outward, normal to each face of the cube. If the cube is welded closed, I doubt that would produce any abnormal stress or strain.

Regarding your 2nd question about

why aren't things being deformed by the fact that there are two 14.7 psi forces ramming it in from the inside and outside?

Force is a vector, meaning it has direction as well as magnitude. 14.7 psi pressure on the outside of a 1 in$^2$ face results in a 14.7 pound force toward the inside of the cube. A 14.7 psi pressure on the inside results in a 14.7 pound force pushing outward. The vector sum is zero. So at sea level, the net force on each side is zero.

When a tire (or basketball, etc) is inflated to a pressure, e.g. of 14 psi, that is what we call gauge pressure meaning it is 14 psi greater than the atmospheric pressure.

Taking your sealed cube into space will probably change the temperature. The temperature would depend on how much sunlight strikes it and what color you painted the cube. My guess would be that the temperature would drop making the pressure inside the cube drop, too.

A good example of what happens with pressure in a sealed container is a bag of potato chips. Buy a bag near the coast, then take it to the mountains. That outside pressure has dropped, but the inside pressure hasn't, so the bag swells due to the net inside forces normal to the bag. Reverse the process: buy a bag in the mountains, then travel to the coast and the bag tends to collapse, until you open it.

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