Finding the Length of mercry

[Frostfire]

Homework Statement

Au shaped tube has a total length of 1 m, it is initially filled with air at 20* C and 1 atm, mercury is poured in without letting air escape, compressing the air. This continues until the mercury is filled to a level L, how long is L

Homework Equations

Im guessing PV=NRT,
It seems like it should involve the density of HG but its not given, nor is the volume

The Attempt at a Solution

I don't even know where to start, It seems like the final pressure is needed, Any suggestions?

 

[ideasrule]

As more mercury is piled on, the length of the air column goes down. This continues until mercury and the compressed air fills the entire tube.

 

[Frostfire]

As more mercury is piled on, the length of the air column goes down. This continues until mercury and the compressed air fills the entire tube.

I'm still missing something, what does that lead to? Is there a formula Im just not seeing, W/E or ....

 

[ideasrule]

Well, it leads to the formula La+Lm=Ltot, where La and Lm are the lengths of mercury and air. You need one more equation to solve the problem; this equation has to relate La with Lm.

 

[Frostfire]

Well, it leads to the formula La+Lm=Ltot, where La and Lm are the lengths of mercury and air. You need one more equation to solve the problem; this equation has to relate La with Lm.

I don't want to appear dense( no pun intended) but I still don't get it. None of the equations I see are in terms of L, only pressure, velocity or area. I can't see how the youngs modulus would have anything to do with it

 

[Frostfire]

I don't want to appear dense( no pun intended) but I still don't get it. None of the equations I see are in terms of L, only pressure, velocity or area. I can't see how the youngs modulus would have anything to do with it

Does it involve the pressure of mercury as 1 atm is 760 mm HG?