How Much Air Is Needed to Lower Mercury in a Barometer from 75cm to 59cm?

[Betadine]

Homework Statement

The mercury in a barometer of cross-sectional area 1cm square has a height of 75cm. There is vacuum above it, of length 9cm.

What is the volume of air, measured at atmospheric pressure, that would have to be admitted to cause the mercury column to drop to 59cm?

Homework Equations

The Attempt at a Solution

Should I use Boyle's Law, pV = constant?

Or Pressure = hpg? But problem is that I don't have the density of air?

Very confused, despite thinking for more than a day. Can anyone please kindly help?

 

[abrewmaster]

If that's all that is given in the problem statement then I think it's fair to say you're working with room temp which should give you densities. When it asks how much air would need to be admitted is it saying into the vacuum to not make it a vacuum anymore?

 

[Betadine]

If that's all that is given in the problem statement then I think it's fair to say you're working with room temp which should give you densities. When it asks how much air would need to be admitted is it saying into the vacuum to not make it a vacuum anymore?

Thank you for the reply :)

Yes, you are right. Air is introduced into the empty space above the mercury, so that the empty space is no longer vacuum.

Your help is greatly appreciated!

 

[abrewmaster]

Ok, so you can calculate the change in pressure that would cause the mercury to move from 75cm to 59cm by using the equation you showed P=hρg. After finding that you can calculate how much air would be needed to go on top of it by using that same amount of pressure. The odd thing with how this question is worded is that it sounds like they want you to not pressurize the air but have it fill that fixed volume (because of the 9cm of vacuum above it) which at least initially seems impossible since air has such a smaller density than mercury but who knows. Is this the way the question was asked?

Edit: For clarity on my concern I mean that you have two fixed variables for the air that's being added. It has to fit in a defined volume yet also stay at a constant pressure (atmospheric) and you have to come up with how much volume would be needed? The question doesn't seem to make much sense.