A water-bottle demonstration of atmospheric pressure

[Steve Rogers]

Homework Statement

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.

Relevant Equations

$P_\text{atm}=P_\text{water}+P_\text{bottle air}$

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.

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

$$P_\text{atm}=P_\text{water}+P_\text{bottle air}.$$
However, I do not know how to systematically explain choice (B). Can anyone help with it? Thank you.

 

[Arjan82]

Your explanation for (A) is incomplete. The pressure in water is not constant due to gravity, which pressure do you mean exactly? Technically the pressure of the bottled air is also not constant, but it is good enough to take it constant, can you explain why?

Answering that will help you answering (B) as well. You should make a drawing of the bottle and al the pressures and where they occur. That really helps.

 

[Steve Rogers]

Your explanation for (A) is incomplete. The pressure in water is not constant due to gravity, which pressure do you mean exactly? Technically the pressure of the bottled air is also not constant, but it is good enough to take it constant, can you explain why?

Answering that will help you answering (B) as well. You should make a drawing of the bottle and al the pressures and where they occur. That really helps.

Dear friend,

It is tacitly assumed that the equation in my explanation is evaluated at the cut with $P_\text{water}$ denoting the water inside the bottle. I'm not sure what you meant by saying the pressure in water is not constant due to gravity, but when I talk about $P_\text{water}$, I do have $P_\text{water}=\rho gh$ in my mind. That $h$ is the difference between the level near the bottle air and the level near the cut. I hope all this helps to clarify the intended meaning. By the way, is it possible to edit a thread? Sorry, I'm a newcomer.

As to choice (B), I guess I have come up with an explanation. 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 change. On the other hand, this redistribution of water will cause the water level near the bottle air to go down.

 

[Arjan82]

It is tacitly assumed

I cannot assume anything about what you know, that's why I ask. This is a homework thread, so I'm not just going to give you the answer.

As to choice (B), I guess I have come up with an explanation.

That's the idea of a homework assignment isn't it?

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 change.

There will indeed be an imbalance in the pressures when some water evaporates. But do you need to replenish all the evaporated water from inside the bottle? You need to balance the pressures, but the pressure inside the bottle changes as well.

On the other hand, this redistribution of water will cause the water level near the bottle air to go down.

And what happens with the pressure in the air when the water level drops?

 

[Lnewqban]

(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.
...
However, I do not know how to systematically explain choice (B). Can anyone help with it? Thank you.

If the bottle was completely submerged, where the mentioned air came from?

 

[Steve Rogers]

If the bottle was completely submerged, where the mentioned air came from?

View attachment 339703

Hello, please check out the original paragraph. I said that we have to keep a little air in the bottle when we soak the bottle into the bucket.

 

[Lnewqban]

Hello, please check out the original paragraph. I said that we have to keep a little air in the bottle when we soak the bottle into the bucket.

Sorry, I missed that part.