Thermodynamics of an Insulated Box: Water-Steam Question

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The discussion revolves around calculating the maximum heat that can be added to a sealed, insulated tank containing water and steam without exceeding a safe pressure of 4 bar. The user outlines their method, which includes determining the initial masses of liquid and vapor, calculating the dryness fraction, and using the ideal gas law. However, they encounter an issue where the calculated dryness fraction exceeds 1, indicating a flaw in their approach. Other participants suggest utilizing steam tables to obtain specific volumes for better accuracy in the final state calculations. The conversation emphasizes the importance of accurate thermodynamic properties in solving such problems.
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Homework Statement


A sealed, thermally insulated tank of volume 2 m^3 has a safe working pressure of 4 bar. At 20 degrees Celcius, 10% of the volume is occupied by water, the remainder by water vapour. Calculate how much heat can be added without exceeding the safe working pressure.

This question is from "Basic Engineering Thermodynamics' - P. B. Whalley - p. 63, q6.6

Homework Equations


1st law of Thermodynamics: Q - W = \Delta U
Other equations in the photo

The Attempt at a Solution


The attached photo is my attempt (apologies, was trying to find out how to make it just an attachment). Hopefully, it is legible, was initially working in draft...
IMG_6178.JPG


My method outline:
1. work out the initial masses of liquid and vapour
2. work out the dryness fraction
3. work out the initial (specific) internal energy
4. using ideal gas law to calculate specific volume that would give pressure of 4 bar
5. calculate final dryness fraction
6. calculate final (specific) internal energy
7. find the difference between the U values (after including mass in the calculation)

However, in step 5, I am getting a dryness fraction > 1, which doesn't make sense. I would appreciate any help regarding any flaws in my method or working.

Thanks in advance
 

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In the final state, you still have liquid and vapor present. Why didn't you use the steam tables to get the specific volumes of the liquid and vapor in the final state?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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