Solving Piston & Spring Homework Problem - Work, Temp & Heat Input

[Carlo09]

Homework Statement

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.

Homework Equations

Ok so its neither isobaric, isochoric or isothermal and we have not been told that it's ideal so I am 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.

 

[kuruman]

(However just using ideal gas law to find temp yields wrong answer)

How do you know? How did you get the answer that you got for the temperature?

 

[Carlo09]

How do you know? How did you get the answer that you got for the temperature?

The problem sheet we have been given has the answers on it, we need to show our working as it is that which is important.

 

[kuruman]

OK then, show your work. What value for the final temperature did you get and how exactly did you get it?

 

[Carlo09]

OK then, show your work. What value for the final temperature did you get and how exactly did you get it?

My work is wrong, it gives me the wrong answer.

P1V1=nRT1 / P2V2=nRT2

P1V1/P2V2 =T1/T2 T2 = T1P2V2 / P1V1 and I get T2= 1146 degrees C which is Slightly too high.

 

[kuruman]

The formula that you are using is correct. Maybe you put in the numbers in the wrong place, maybe you did the calculation incorrectly. If you don't show exactly what you did and how you got the numbers, I cannot find where the problem is.

 

[Carlo09]

The formula that you are using is correct. Maybe you put in the numbers in the wrong place, maybe you did the calculation incorrectly. If you don't show exactly what you did and how you got the numbers, I cannot find where the problem is.

I solved it, this is what I did:

From the temperature we know it's superhated steam so looking at the steam tables we can find it's specific volume, 1/Specific volume = Density, density * volume = mass

So now we have the mass of the steam in the system.

Now mass / final volume = density ... 1/density = specific volume at the final state and now looking at the steam tables and interpolating you can find final temperature :)