## Thermodynamics: water in a piston-cylinder device

1. The problem statement, all variables and given/known data
A piston–cylinder device initially contains steam at
3.5 MPa, superheated by 5°C. Now, steam loses heat to the
surroundings and the piston moves down hitting a set of stops
at which point the cylinder contains saturated liquid water.
The cooling continues until the cylinder contains water at
200°C. Determine (a) the initial temperature, (b) the enthalpy
change per unit mass of the steam by the time the piston first
hits the stops, and (c) the final pressure and the quality (if
mixture).

2. The attempt at a solution

a. is easy... I lookup Tsat@3.5MPA in a table and add 5°C to it.

b) we are looking for h2-h1 where h2 is hf@3.5MPA,Tsat and h1 is hg@3.5MPA,Tsat+5

c) This is where Im stuck. I only have one intensive property, which is temperature=200°C. I need to find another one to find the state of the final water. Since it is impossible to tell whether or not we have a mixture with the temperature and the pressure only, I am guessing the other intensive property I need to find is the specifc volume. However I have no idea how to do that.

After the piston hits the stops, the volume is constant and the pressure changes. Thus, if at 200°C we still have some gas, then obviously the final pressure is Psat@200°C. However, I can't tell if we still have some gas.