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if I have A closed vessel that is half-filled with water. There is a hole near the top of the vessel and air is pumped out from this hole.

will the level of water rise

Sketch of closed container

apparently, the level of water doesn't always rise

I thought since there is no atmospheric pressure:

$$ P_{atm} + DgH_1=DgH_2$$

thus causing the level to rise

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  • $\begingroup$ please don't mind the bad drawing $\endgroup$ Jan 1, 2021 at 17:46
  • $\begingroup$ Re, "...thus causing the level to rise." I think that there is another possibility that you have not considered; which is, that as you decrease the ambient pressure at the surface of the water, that causes the pressure at the bottom of the container to decrease by an equal amount. $\endgroup$ Jan 1, 2021 at 17:58
  • $\begingroup$ hey but according to some source ig it necessarily does not rise and I want to know why $\endgroup$ Jan 1, 2021 at 18:00
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    $\begingroup$ Why would you expect it to rise? If you expect it to rise because of that equation, I am suggesting a different interpretation of the equation that does not require the water level to rise. $\endgroup$ Jan 1, 2021 at 18:01
  • $\begingroup$ ohhh can i get to know about the other equation ?? do u have any idea @SolomonSLow $\endgroup$ Jan 1, 2021 at 18:05

4 Answers 4

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The water level will not rise, it will actually gradually fall. This is because since there is no air pressure, the water molecules can easily escape the liquid and turn into water vapor which gradually fills the vacuum. If the container is sealed after creating the vacuum, it will fall until a certain level and then stop, because it will create an equilibrium where the number of water molecules evaporating from the liquid water will be equal to the number of water vapor molecules reentering the liquid water. If the container is not sealed then it will keep falling until there is no liquid water left.

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  • $\begingroup$ thanks but whats the difference between this and the candle experiment $\endgroup$ Jan 1, 2021 at 18:15
  • $\begingroup$ youtube.com/watch?v=LOQObaAo8GM&ab_channel=RooHaran $\endgroup$ Jan 1, 2021 at 18:18
  • $\begingroup$ can u chec this out??? $\endgroup$ Jan 1, 2021 at 18:18
  • $\begingroup$ I see what you are talking about. In the candle experiment, it is actually air pressure outside the glass that is pushing the liquid water up in order to fill the vacuum. This is possible because one part of the water outside the glass is initially in contact with the atmosphere, unlike in an enclosed box here, where there is no difference in pressure acting on the water. $\endgroup$
    – user283752
    Jan 1, 2021 at 18:26
  • $\begingroup$ ohh ok thanks i get it now $\endgroup$ Jan 1, 2021 at 18:27
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Are you thinking of a U shaped tube, where if you decrease the pressure on one side, pressure on the other forces the fluid to rise?

enter image description here

Image from Physics Libretexts

You can see how pressing on one side would make the fluid move. In the case you have shown, pressing on the top of the fluid just squeezes it.

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  • $\begingroup$ so does vaccum not cause water level to rise $\endgroup$ Jan 1, 2021 at 18:20
  • $\begingroup$ i just wanna know the reason $\endgroup$ Jan 1, 2021 at 18:20
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    $\begingroup$ Air presses down on the surface of the water. If you take out the air, it stops pressing down. Think of putting an object in the vessel instead of water. Suppose you press on the object, and then stop. Would you expect the object to rise? $\endgroup$
    – mmesser314
    Jan 1, 2021 at 18:24
  • $\begingroup$ ohh thanks a lot $\endgroup$ Jan 1, 2021 at 18:26
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What you will see happen is the water will start to boil.

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  • $\begingroup$ does the water lvl rise $\endgroup$ Jan 1, 2021 at 17:45
  • $\begingroup$ isnt this like the candle experiment??? $\endgroup$ Jan 1, 2021 at 17:45
  • $\begingroup$ what is the "candle experiment" $\endgroup$
    – mike stone
    Jan 1, 2021 at 18:17
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There are actually some counter-acting phenomena at play here.

  1. No compressibility: in a first approximation, the water can be considered as incompressible. Then we come to the conclusion that the water starting to vaporize for reduced vessel pressure.

  2. More in detail, the water density changes with temperature, and the evaporation will cool the water down, which will increase its density, and hence lower the water level further (at least, if it was initially above approx 4degC). if it was below 4degC, then cooling it will initially decrease the density.

  3. Also, water isn't completely incompressible, and lowering the vessel pressure will lead to an (albeit small) expansion. The question whether this expansion will outweigh the vaporization depends a lot on the shape of the vessel. Say, the effects could be strong enough, if you have a long thin tube, that is only open on one end, like this (yes, we're maintaining picture quality here.. :) ) :

long thin pipe vessel

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