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Our teacher had us come up with our own thermodynamics experiments, so I put a glass of water inside a vacuum-capsule. Inside the glass of water I have placed a non-floating object, a small plastic ball. If I enable the vacuum, the water will begin to develop bubbles of vapor. Those bubbles attach themselves to the plastic ball and it floats.

What I want to figure out now, is how I can approximate the amount of bubbles that are necessary to lift the object. Also, does the vacuum make it easier to lift it, as the pressure on the water surface is lower?

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You want the volume of the bubbles, if they were full of water, to equal the weight of the object. The lower pressure makes the bubbles more likely to form. –  Mike Dunlavey Feb 18 '12 at 21:37
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In order for the object to float, the density of the object-bubbles system must fall below the density of water. Therefore you must determine the mass and volume of your object, and the mass of a bubble for every unit of volume. Presumably the vapor bubbles will have much lower density than the surrounding water, so keep adding volume (and minuscule mass) to the volume and mass of your object. Once you have reached the density of water you have reach the floating/nonfloating critical point. Any more vapor bubbles will cause the object to float.

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