9 Steam expands steadily in a turbine at a rate of 11 kgs St

9. Steam expands steadily in a turbine at a rate of 11 kg/s. Steam enters the turbine at 7 MPa, 500 °C and exits as saturated vapor at 50 kPa. If the turbine produces 8,000 kW shaft power, determine the entropy generation rate (kW/K). Use a boundary temperature of 25 °C. Note that the turbine may not be adiabatic (20 points).

Solution

at 7MPa, 500 °C, entropy = 6.8 kJ/kg K, Enthalpy h1 = 3411.4 kJ/kg

at 50 kPa, entropy of saturated vapour = 7.5931 kJ/kg K. h2=2645.2 kJ/kg

W = m( h1- h2) = 11*(3411.4-2645.2)= 8428.2 kW

But shaft power = 8000 kW (given) .

so, heat lost =(8428.2-8000) = 428.8 kW

so, entropy generation S_gen = (S₂-S₁) + dQ/T₀ =(7.5931-6.8) + 428.8/(25+273) = 2.232 kJ/kg K