Water is contained in a cylinder fitted with a frictionless piston (figure shows that atmospheric pressure acts on piston from above). The mass of the water is 0.45 kg, and the piston area is 0.186 m2. Initially, the water conditions are 110oC and 90% dryness fraction, and the spring just touches the piston but exerts no forces on it. Now, heat is added to the water and the piston begins to rise. During this process, the spring resisting force is proportional to the distance moved with a coefficient of 88 N/cm. Calculate the pressure in the cylinder when the temperature reaches 160oC.
1)Fs = kΔx
Fs: spring force, k = coefficient, x = distance moved by piston
2)PA = PοA + Fs + mg
P = Water pressure
Water is not and ideal gas but just in case :
3)P1V1/T1 = P2V2/T2
4) Q + W = m (cvΔT+gΔx)
W is the boundary work
The Attempt at a Solution
I can get P1 by letting x=0 in eq2 --> P1=18855.5 Pa
Now I'm stuck and I hope someone can help.