Thermodynamics closed system - first law

[meanmachine]

Homework Statement

1kg of water that is initially at 90 degrees celsius with a quality of 10% occupies a spring loaded piston cylinder device. The device is now heated until the pressure rises to 800kPa and the temperature is 250 degrees c
Determine the total work done during this process, in KJ

Homework Equations

The first law for closed systems
Q - W = ΔU
(h₂-h₁ - u₂ - u₁) = ΔU

The Attempt at a Solution

State 1

Saturated mixture (90 degrees)
x = 0.1
H1 = 605.29 KJ/kg
U1 = 588.67 KJ/kg

State 2 - super heated vapour

h2 = 2950.4 KJ/kg
u2 = 2715.9 KJ/kg

therefore,

ΔU = (2950.4 - 605.29) - (2715.9 - 588.67) = 217.88 KJ

which is incorrect, can you assist me with this question?

 

[rock.freak667]

You would actually just need to apply

W = m(h₂-h₁)

remember that enthalpy h includes internal energy u.