Ok the problem I have been set has a frictionless piston containing steam at 200kpa at 200 degrees c and it is originally at 0.5m^3. It has a linear spring above it just touching and exerting no force. Heat is added and the gas expands pushing the cylinder up and causing the spring to exert a force that seeing as it is linear is proportional to the distance it is pushed up. Finally it stops at 0.6m^3, 500kpa and I have to work out work, temp and heat input.
Ok so its neither isobaric, isochoric or isothermal and we have not been told that it's ideal so im assuming you could use that. (However just using ideal gas law to find temp yields wrong answer) Also I know W=P dv but that again gives the wrong answer as P is not constant.
The Attempt at a Solution
To find work i plotted it on a P-v diagram and found the area: [(200kpa+500Kpa)/2]*(0.6-0.5) = 35Kj which i know is the correct answer.
I have tried using ideal gas law at both pressures to find T but it's wrong, actual answer is 1132 degrees c. Also I tried saying Qin = Wout + delta U and then reading U from the steam tables and rearranging to find Qin and therefore final temp maybe but it also didnt work. Please could someone help me with this, we are not given area or spring constant of the piston or spring just what I have stated.