Answer
$\Delta u_{overall}=1299.27\frac{kJ}{kg}$
Image shows the T-v diagram sketch.
Work Step by Step
1) As $T_{1}\gt T_{sat}$ is a superheated vapor
From table A-6:
$u_{1}=2808.8\frac{kJ}{kg}$
2) From table A-5"
$\upsilon_{2}=0.88578\frac{m^3}{kg}$
3)$\upsilon_{3}=\upsilon_{2}$
As $0.001043\frac{m^3}{kg}\lt u_{3}\lt 1.6941\frac{kJ}{kg}$ is a saturated mixture.
$x_{3}=\frac{\upsilon_{3}-\upsilon_{f,3}}{\upsilon_{g,3}-\upsilon_{f,3}}=\frac{0.88578\frac{m^3}{kg}-0.001043\frac{m^3}{kg}}{1.6941\frac{m^3}{kg}-0.001043\frac{m^3}{kg}}=0.523$
$u_{3}=u_{3,f}+xu_{3,fg}=417.4\frac{kJ}{kg}+0.523*2088.2\frac{kJ}{kg}=1509.53\frac{kJ}{kg}$
Finally:
$\Delta u_{overall} = u_{1}-u_{3}=2808.8\frac{kJ}{kg}-1509.53\frac{kJ}{kg}=1299.27\frac{kJ}{kg}$
