Ideal Gas & Piston Homework: Calculate Distance Moved

[Asla]

Homework Statement

Asshown in the figure below, an enclosed cylindrical container(cross-sectional area : S) is divided into two sections (A,B) by piston P.The length of each section is 10cm.Each section contains a monoatomic gas at temperature 0°C and pressure 1.0×10^5 Pa.(both contain the same type of gas)The gas in B is in contact with the thermostatic bath and does not change temperature.The piston and the container do not conduct heat.The area of contact between the piston and the container is tightly sealed and frictionless
The gas in A is heated to 57°C using a heater.What distance does the piston P move?

The Attempt at a Solution

I am still trying to connect the work done and distance moved.
I have a instinct that one of the gases is undergoing an isobaric change while the other undergoes an adiabatic change but I am not sure about that.

 

[mfb]

You don't have to care about work done, or details of the changes. Just consider the system before (what is the relative amount of gas?) and afterwards (how does the new equilibrium position look like?).

 

[Chestermiller]

Use the ideal gas law on each of the chambers. You know the initial temperatures, pressures, and volumes, and you know the final temperatures, but not the final pressures and volumes. However, you do know that the final pressures in the two chambers are equal, and you also know that the total volume of the two chambers does not change.