Water, piston-cylinder problem [Thermodynamics]

[leafjerky]

Homework Statement

Okay, so these are usually pretty easy for me to understand, but this one doesn't make sense.

10 kg of water in a piston cylinder arrangement exists as saturated liquid/vapor at 100 kPa, with a quality of 50%. It is now heated so the volume triples. The mass of the piston is such that a cylinder pressure of 200 kPa will float it. Find the final temperature and the heat transfer in the process.

Homework Equations

v = V/m
v - specific volume
V - volume
m - mass

y = y_f +xy_fg

The Attempt at a Solution

State 1:[/B]
m₁ = m₂ = m = 10kg
x₁ = .5 ---> 2-phase mixture
P₁ = 100 kPa = 1 bar
v₁ = .0010432 m³/kg + (.5)(1.694 - .0010432)
v₁ = .8475 m³/kg

State 2:
v₂ = 3*v1 = 2.5425 m³/kg
P₂ = 200 kPa --> pressure is constant from this point on

Solutions I have found online say that the final temp is in the 800's. How is that possible? I went into my steam tables (Fundamentals of Engineering Thermodynamics, Moran) and I couldn't figure out the state. I assume it is a superheated vapour. Is this right? If so, I go to the tables and the temp could probably be interpolated between 1.5 bar and 3 bar, but even then it's not close to 800. I believe the answer is 827 or 829 degrees C. Thanks for any help.

 

[Chestermiller]

What temperature does the ideal gas law give you? (This is a pretty low pressure).

 

[leafjerky]

Thank you! I've always been under the assumption to never use ideal gas for non ideal gases though? This is a first for me. Is there a way to know? Thanks again

 

[Chestermiller]

Thank you! I've always been under the assumption to never use ideal gas for non ideal gases though? This is a first for me. Is there a way to know? Thanks again

Calculate the reduced pressure and the reduced temperature. Then, see the chart in Moran et al for the Z factor. Or better yet, calculate the pseudo-reduced volume and the reduced pressure and use the Z chart in Moran.

Chet