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Amount of air in a glass



If we have an emty cylindrical glass on a flat table with a dice inside it , naturally, it will contain an amount of air inside it.

Now , if we invert this glass upside down on the table, leaving the dice still inside it but landing on the table , will the amount of air inside the glass changes?

If yes, would it be more or less, and why?

If no...why?

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Imagine putting a sheet of rubber over the mouth of the glass and turning the glass sideways or upside down. We would not expect any airflow into or out of the glass. That is, the rubber film would not bulge in or out simply because we changed the orientation of the glass.

Now place the upside down glass on the table.

Since there is no tension on the rubber film, we can carefully slide it away without any air flowing into or out of the glass.

Same amount of air.

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Normally, I would say that the dice are just a red herring to confuse us - BUT - I think they are of some significance!

When you invert the glass, the dice will fall to the table [okay, assuming
that gravity is still a player].

If you are slow to cover the dice with the glass, the dice will roll enough
that they cannot both be covereed by the glass.

Therefore: you must put the glass down pretty quickly ... this qucik movement
will create a temporary overpressure inside the glass.

At the moment you put the glass on top of the dice, the pressure inside the
glass will be higher than ambient pressure.

If the glass and the table form a perfect seal, then the pressure inside the
glass is higher than pressure outside the glass.

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perhaps the table and glass do not form a perfect seal. then the interior volume and pressure of the glass might remain constant. yet the friction/energy of the dice falling and bouncing off the glass and the table could excite/minutely raise the interior temperature of the gas requiring less atoms of gas to make up the constant volume and pressure. So less gas in the glass?

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The amount of gas in vessel depends on three factors - the volume of the container, the gas temperature and pressure.

In our case the volume and temperature are not changing. The pressure changes.

As known the air pressure decreases with increasing distance from the ground. In the first glass position the pressure therein - P1 is the average betwin Pb - bottom pressure and Pt - glass top pressure. In the second - P2 = Pb , because this is the only level of interconnected spaces. 

Since P2>P1 the amount of air in the second position will be more.


Oh! we have not given explanation regarding dice... This is to the author  :) because it has nothing to do with this puzzle.

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