How Is Work Calculated in a Piston-Cylinder Device with a Linear Spring?

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In a piston-cylinder device containing steam, the initial state is at 200 kPa and 200°C with a volume of 0.5 m³. As heat is added, the pressure and volume increase to 500 kPa and 0.6 m³, respectively, with the work done calculated as -113.5 kJ. To find the final temperature and total heat transferred, the relationship between pressure, volume, and temperature must be utilized, although steam is not an ideal gas, necessitating the use of thermodynamic tables. The specific volume of steam should be calculated to determine the mass, which will aid in finding the final state and corresponding temperature. The work done against the external spring is essential for applying the first law of thermodynamics to calculate heat transfer.
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A frictionless piston-cylinder device initially contains steam at 200 kPa, 200oC and 0.5 m3. At this state, a linear spring (F ∝ x) is touching the piston but exerts no force on it. Heat is now slowly transferred to the steam, causing the pressure and the volume to rise to 500 kPa and 0.6 m3, respectively.

Calculate the work done, final temperature and the total heat transferred.

I've been given a superheated water table.I've calculated work done to be -113.5kJ

But I'm not sure how to calculate the final temperature and total heat transferred.

For the total heat transferred I know that q = du + w. That would require me to know the change in internal energy but I can't calculate that without knowing the final temperature (i think?).

OR

is this is an isothermal process which means that the final temperature is 200oC and heat transferred is -113.5kJ?

Thanks for your help...
 
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bruceflea said:
That would require me to know the change in internal energy but I can't calculate that without knowing the final temperature (i think?).

You know P1,V1,T1,P2 and V2. You need to find T2. Do you know an equation relating these variables?
 
P1*v1/t1 = P2*v2/t2?
 
bruceflea said:
P1*v1/t1 = P2*v2/t2?

Yes, that's the one. Now you can find T2 and hence change in Internal Energy.
 
siddharth said:
Yes, that's the one. Now you can find T2 and hence change in Internal Energy.

That equation is only applicable for perfectly ideal gas case , and steam in this case is not perfect gas , so you need to use the thermodynamic-tables to find out the solution.

The given process is nether isothermal nor adiabatic.Calculate the specific volume of steam initially , from there you get the mass of steam which would also be the mass in final conditions, get the specific volume from final conditions because you know the mass and voulme, now find out the state of water using tables, and corresponding temperature.

Work done will be to expand against the extrenal spring.Once work done is calculated, use the first law to calculate the heat transferred.

BJ
 

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