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Consider four scenarios:

(on a typical weighing scale)

  1. Measure the weight of a canister of air filled at atm pressure
  2. Measure the weight of a compressed canister of air
  3. Measure the weight of a canister with no air inside.
  4. Measure the weight of an empty canister on earth with no atmosphere

I would guess that 1 is the same as 4 and 2 and 3 weigh the same as the mass 2 plus the added or subtracted mass of air. Any explanations? This is just because a canister's volume doesn't or shouldn't change the force of it's weight being applied to the weighing scale. A weighing scale accounts for air pressure as it's applied equally on all sides and the machine is tared. When the canister is compressed the air is now heavier and tries to sink. I want to explain this more mathematically in terms of pressure resulting in a greater force on the scale. As you can probably tell, my reasoning doesn't hold much weight at the moment. (not sure if pun intended)

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  • $\begingroup$ It would good if you could rationalise your guess, and include that in your post, as this to me looks to be a homework-like question. $\endgroup$ – user163104 Aug 6 '17 at 16:59
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Keep in mind that we live at the bottom of an ocean of air, which is a fluid, so gravity is not the only factor in determining what your scale reads. There's an upward buoyant force to consider. It's this force that makes balloons full of helium rise in air. The magnitude of the buoyant force is equal to the weight of the fluid that is displaced by the can.

In case #1, the scale reading is the net downward force of gravity on the can itself, and the upward buoyant force due to the displacement of air by the closed can. Because the air in the can has the same pressure and density as the air outside, it does not affect the result. The net result is going to be almost the same as the downward gravitational force on the can alone.

In case #2, you have more air molecules inside of the can, so your scale reading will be what you get for case #1 PLUS the extra downward gravitational weight of the extra gas molecules inside the can.

In case #3, with no air inside the can, you will get case #1 MINUS the gravitational weight of the gas molecules that you removed.

In case #4, there is no atmosphere, so there is no upward buoyant force, and your scale reading is only the gravitational weight of the can itself, since it contains no gas.

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Remember that air pressure acts in basically all directions on an object. Therefore a typical weighing scale would have the same reading weighing the same object in an atmosphere and outside of an atmosphere. There is less air in scenarios 3 and 4 so those canisters should be lighter than that in scenario 1 which is in turn lighter than that in scenario 2.

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  • $\begingroup$ Almost, but not quite. Air pressure varies with height because the pressure at any given height is due to the weight of all of the air above. At a lower height, there is more air above, and therefore more pressure. So, the pressure pushing up on the bottom of any object is always slightly higher than the pressure pushing down on its top. This effect is called buoyancy. en.wikipedia.org/wiki/Buoyancy The buoyancy due to air is small, but not too small to be measured, and not too small to be significant in some experiments. $\endgroup$ – Solomon Slow Aug 7 '17 at 1:49

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