Answer
$\dot{W}_{net}=20,448\ kW$
Work Step by Step
From tables A-4 to A-6, at the turbine:
Inlet ($P_3=12.5\ MPa, T_3=500°C$): $h_3=3343.6\ kJ/kg$
Outlet ($P_4=10\ kPa, x_4=0.92$): $h_4=2392.5\ kJ/kg$
From table A-17, at the compressor:
Inlet ($T_1=295\ K$): $h_1=295.17\ kJ/kg$
Outlet ($T_2=620\ K$): $h_2=628.07\ kJ/kg$
$\dot{m}_ah_1+\dot{m}_sh_3=\dot{m}_ah_2+\dot{m}_sh_4+\dot{W}_{net}$
Given $\dot{m}_a=10\ kg/s,\ \dot{m}_s=25\ kg/s$
$\dot{W}_{net}=20,448\ kW$
