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I'd like to ask about an experiment on atmospheric pressure. To conduct the experiment, we need an empty PET bottle and make a small cut on the lower part of the bottle. A cut no greater than one-half the circumference is acceptable. Then, we press a table tennis ball against the cut to open the cut, being sure to make the ball stay put at the cut. Next, we soak the bottle into a bucket filled with water after taking off the bottle cap. The water will flow into the bottle, but we keep a little air in the bottle. Then we close the bottle with the cap. After that, we take the bottle out of the water in the bucket. As you can see in the picture below, the water will stay in the bottle as it is, while the bottle is completely outside the water surface in the bucket.

enter image description here

The experiment and the picture is from a high-school physics book, but I just did this same experiment myself, and it is true: the water won't come out. Now I have some questions about the following homework exercise.

Which of the statements is correct about the experiment?

(A) As the soaked bottle is being lifted off the water surface, the air in the bottle increases its volume.

(B) About the picture, if some of the water at the cut evaporates, then the water level at the cut will drop.

(C) The experiment has nothing to do with atmospheric pressure.

The answer is (A), which confirms my intuition. To explain it, we can use Boyle's law and the equation $$P_\text{atmosphere}=P_\text{bottle water}+P_\text{bottle air}$$ evaluated at the cut. However, I do not know how to systematically explain choice (B). Can anyone help with it? Thank you.

Boar
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  • Although it does not address directly your question, you may find it useful to read the answers to this previous question: https://physics.stackexchange.com/questions/66658/atmospheric-pressure-experiment-using-a-cup-with-a-fluid-to-hold-a-glass-plate?rq=1 – GiorgioP-DoomsdayClockIsAt-90 Feb 02 '24 at 07:26
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    It isn't clear from your picture how the hole is cut in the bottle and how the ping pong ball seals it. Is it a circular hole with the ping pong ball pushed into the circular aperture? Or a slit with the ball pushed in to widen the slit? – John Rennie Feb 02 '24 at 07:56
  • @JohnRennie Hello, I have re-uploaded the picture. To answer your question, it's a slit. – Boar Feb 02 '24 at 14:45

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Here is a possible explanation of choice (B). If some of the water at the cut evaporates, the equation $P_\text{atmosphere}=P_\text{bottle water}+P_\text{bottle air}$ will become unbalanced. To return to balance, some of the water from elsewhere will come to replenish the vacancy due to evaporation, and so the water level at the cut won't experience a visible change. On the other hand, this replenishment will cause the water level near the bottle air to go down, from which we can infer that the pressure of the bottle air will undergo a gradual decrease according to, of course, Boyle's law.

Boar
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