PhysAssist
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No, it would weigh (mass) the same, because there's still the same number of molecules. No mass is gained when it cools. The force pressing in from the outside would appear to increase, but in reality it's constant, it's just that there is not the same force pushing back from the inside, because the molecules contract as they cool. If it was in a medium that didn't expand and contract as much as air, (or steam) you wouldn't get effects as dramatic as this:
The reason we know the force one experiences with a vacuum is caused by the weight of the air, is because absolute vacuum is the weight of the air (about -14.7 psi). If you were on top of Mt. Everest and sucked all the air out of that glass, or this barrel, the vacuum would be less, (correction: not less, but the force the glass experiences would be less) because the atmosphere would only exert about 4.9 psi on the outside instead of 14.7psi. (if it was at sea level).
Naw, absolute vacuum is absolute, however, it is actually a theoretical concept because even the hard vacuum around deep space has some ambient pressure- just not enough for us to survive or appreciate.
BTW, while you have some points re: the weight of atmosphere, and it is certainly why the can crushed, IDT that your analogy for the empty glass works.
I think it only works if the glass is upside down in a saucer of water when as the pressure inside is reduced, water gets "sucked" [actually pushed by atmospheric pressure] UP into the glass.
I do think that the suction of the mud is more surface tension, otherwise what creates the vacuum that reduces the pressure and cause atmo pressure to hold it down?
Respectfully,
Thomas