A piston-and-cylinder device contains 50 kg of water at 250 kPa and 25°C.
The cross-sectional area of the piston is 0.1 m2. Heat is now transferred to
the water, causing part of it to evaporate and expand. When the volume reaches 0.2 m3, the piston reaches a linear spring whose spring constant is 100 kN/m. More heat is transferred to the water until the piston rises 20 cm more. Determine...
a.) The final pressure and temperature
b.) The work done during this process
c.) Show the process on a P-V diagram
10 comments:
I don't quite understand what I am doing wrong with this problem. I assumed that W(13) = W(12) + W(23).
To find W(12) I used an integral from the inital to final volume at a constant P. For W(23) I found an equation for P as a function of x (distance moved by the spring) and then an equation for dv as a function of dx. In the end I get 337KJ and not 44. What step am I doing wrong? Thanks
First I the final pressure by adding the pressure plus the force due to the spring, then I used this in combination with NIST to find the final temp. Then I divided into 2 stages, the first with constant pressure, for which the work is pdeltaV, and obtained a value of about 37kj. For the second stage, the pressure changes with distance, so I need to actually use an integral from initial to final volume. I'm not sure how to get the equation for how the pressure changes though. I used 250kPa + (k*deltax)/area. But deltaX is just deltaV/area, so area is deltaV/deltax, so my equation becomes 250kPa + k(deltaV/area^2). This isn't getting me the right answer however, whats up?
Katie 8:34 PM
You are correct: W(13) = W(12) + W(23)
Your method for determining W12 is correct as well. The integral is particularly easy because step 1-2 is an isobaric process.
I think you are doing step 2-3 correctly as well. Is this a units problem ? The linear spring means F is linear with respect to position, x. It also means P is linear with respect to V: P = a V + b (just like in P1).
W13 ~ 44 kJ
If this doesn't help, please give me some more details and/or values+units from your work.
Washburn 9:21 PM
You were doing great up to the last part. The linear spring means F is linear with respect to position, x. It also means P is linear with respect to V: P = a V + b (just like in P1). Determine a and b and then integrate.
in this PV diagram i have a question. At no time does the substance become superheated, so that should mean that all steps in the diagram lay below the saturation curve. is that correct?
I have a question regarding the final temperature. a)we know the final pressure equals the pressure from the spring plus the pressure of the water (250 kPa), right? b) We can also determine the specific volume at the final state Vfinal/kg of water which is 0.0044 m^3/kg...which is a value for a saturated liquid.
Can we use V^ to determine its final state given the pressure? And if not...how do we come about the conclusion that its a superheated vapor as the correct temperature states?
I have question about solving for final temperature. How do we get V1? What are the processes of 1-2 and 2-3. I am totally confused about this problem here.
Anon 8:09 PM
That is correct.
Jolene 11:35 AM
P3 = P2 + Fspring / Apiston
But I think that is what you meant, right ?
You are correct that V3^ = 0.0044 m^3/kg, but this is not a saturated liquid. If you determine P3 using the eqn in the previous paragraph, you can use P3 to determine Vsatliq and Vsatvap at P3. You will find that Vsatliq < 0.0044 < Vsatvap. Fron this you can conclude that state 3 lies within the 2-phase envelope and is a saturated mixture.
Kaifu 10:48 PM
You can determine V1^ from the given T and P. It is a subcooled liquid.
In step 2-3 the fluid expands isobarically as heat is added.
In step 3-4, the fluid expands as heat is added, but the pressure increases linearly with respect to volume because this is a "linear" spring. This makes it relatively easy to evaluate Wb as long as we can assume the expansion is a quasi-equilibrium process.
I hope this is helpful. Read the other comments here if you need more help because I am going to sleep !
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