# Thermodynamics of an Insulated Box: Water-Steam Question

#### Master1022

1. The problem statement, all variables and given/known data
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

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

3. 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...

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.

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#### PF_Help_Bot

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.

#### Chestermiller

Mentor
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?

"Thermodynamics of an Insulated Box: Water-Steam Question"

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