I don't know what turbo expander is? Is it a turbine, a compressor or something different? But I understand that I can use the state variables to solve the question. Do you mean it? For example for the piston case, the initial and final pressures are the same. If I can find one more same state variable, than all the others will be same.?
Evacuated chamber can be a good approach, system can be selected as the all volume, it can be easier.
But I didn't understand it totally I think. Maybe I have to research more. Is it about only the first Law of thermodynamics, will I use the entropy balance equation or, is it only about the conservation of energy?