NavList:

The problem you describe has a non-obvious answer.  For the entire class of fluids, gasses and chambers, you need to know the thermal coefficient of expansion for each material in the set.  Further, you need to understand how the chamber will expand or contract, given its shape, using the chamber vessel structure and material stiffness.

Finally then, for a stable temperature, you would model the chamber volume and the volumes of gas and fluids.  Internally, the chamber, the fluid and gas pressures must balance as they expand and contract.  The inside chamber pressure and outside atmospheric pressure will provide an additional deformation of the chamber, leading to yet another iteration of modeling.  Eventually, stability will be found and the size of the bubble determined.

Under this set of circumstances, I do not believe that the bubble is precisely the same size, given the combinations possible.  As a practical matter, the bubble may appear to be about the same size, when in fact, it is not.

As you have found with your compass, when it is cold, the fluid contracts and atmospheric gasses leak in.  When it is warmer, the fluid expands and forces the gasses right back out.  This same expansion occurs in a sealed chamber as well, however, there isn't any leakage.

I hope some of this made sense.  There isn't some basic method of controlling the bubble size.  It really isn't stable, I think it changes all the time, just not perceptively so in real time.  Given the proper metrology, periodic, precise measurements would show variation in size.

So how did manufacturers do it prior to computer driven thermodynamic modeling packages that are computationally expensive?   Trial and error... 

Brad