Answer
$\dot{W}_s=17.8\ MW$
Work Step by Step
From tables A-5 and A-6:
Inlet ($P_1=8\ MPa, T_1=600°C$): $h_1=3642.4\ kJ/kg$
First outlet ($P_2=0.3\ MPa$, sat. vapor): $h_2=2724.9\ kJ/kg$
Second outlet ($P_3=10\ kPa, x_3=0.85$): $h_3=2225.1\ kJ/kg$
From the energy balance, for both turbines as the system:
$\dot{m}_1h_1=\dot{m}_2h_2+\dot{m}_3h_3+\dot{W}_s$
With $\dot{m}_2=0.1\dot{m}_1,\ \dot{m}_3=0.9\dot{m}_1,\ \dot{m}_1=13\ kg/s$
$\dot{W}_s=\dot{m}_1(h_1-0.1h_2-0.9h_3)$
$\dot{W}_s=17.8\ MW$
