Mercury Displacement in a Sealed Tube: Isothermal vs. Adiabatic Processes

[zygisyyy]

Homework Statement

A thin tube, sealed at both ends, is 1 m long. It lies horizontally, the middle 10 cm containing mercury at the two equal ends containing air at standard atmospheric pressure. If the tube is now turned to a vertical position, by what amount will the mercury be displaced? Assume that the process is (a) isothermal and (b) adiabatic. Which assumption is more reasonable?

Homework Equations

F=p*A

The Attempt at a Solution

I figured maybe I could calculate the displacement by finding the difference between the two pressures ( or vector sum ) and by using F=p*A and other intermediate equations like that of volume find the displacement.
I got 0.072m of displacement in isothermal case. I think the answer can actually be near the logical one, but i still want to make sure whether I'm using the correct approach.
and maybe there is simpler way to do this?

 

[WhoWee]

It lies horizontally, the middle 10 cm containing mercury at the two equal ends containing air at standard atmospheric pressure.

Can you clarify this please?

 

[Borek]

Tube is thin enough so that mercury closes it, separating air on both sides.