In a sample of wet steam at 11 bar, 75% of the total internal energy is contained in the vapour portion. Calculate the dryness fraction of the steam to 3 decimal places.
u(kJ/kg) = (1-x)uf + x*ug
x - dryness fraction
f - saturated liquid state
g - saturated vapour state
The Attempt at a Solution
I have done the following to no avail:
At 11 bar using steam tables uf = 780 kJ/kg and ug = 2568 kj/kg
Assuming u = 75% of ug.
u = (1-x)uf + x*ug
0.75*ug = (1-x)uf + x*ug
0.75*2568 = (1-x)*(780) + x*(2568)
x = 0.642
Therefore, dryness fraction is equal to 0.642.
However this is incorrect and I'm unsure what I'm doing wrong. Possibly interpreting the 75% of total internal energy wrong.
Could it be that I need to use u = 0.25*uf + 0.75*ug?
Thanks for your help, it's appreciated.