Thermodynamics-heating water in piston help

JGreen48

1. The problem statement, all variables and given/known data
A cylinder/piston arrangement contains water at 105 C, 85% quality with a volume of 1L.
The system is heated, causing the piston to rise and encounter a linear spring. At this
point, the volume is 1.5 L, piston diameter is 150 mm, and spring constant is 100 N/mm.
The heating continues, so the piston compresses the spring. What is the cylinder
temperature when the pressure reaches 200 kPa.


2. Relevant equations
F/A=pressure
F=K*d


3. The attempt at a solution
From what I stated with. I solved for the Force on the spring.
F/(pi/4)(.150^2)mm=200,000 Pa
F=3534.29N

Then I found out the displacement of the spring.
3534.39=100*d
d=35.3439mm

That is where I am stuck at. What I tough might work is to find the volume after the spring is compressed. That is just over 1.5L and comparing that to the saturation tables it is above the saturated vapor. So it would be a gas. But I don't think that is correct. If anyone can help straighten me out and point me in the right direction. Thanks.

Q_Goest

The expansion from 1 L to 1.5 L is done at constant pressure with heat input. So the final state (ie: quality) of the water/water vapor, can be found from the tables. Do you know how to do that?

Once the water/vapor mix begins pushing against the piston, it is doing work and follows a line of constant entropy. If you can find the state at 1.5L above, then you can find the entropy at that state from the tables. Follow the line of constant entropy up to the pressure specified to find the final state.