HW-30 (See HW-17 and HW-28) A power cycle operating steadily is shown below. The boiler (a heat exchanger to boil liquid water) produces steam at an absolute pressure of 10 MPa and a temperature of 480C (State 1). Steam leaving the boiler enters a high-pressure turbine (HPT) and expands to an absolute pressure of 0.7 MPa and a quality of 98.5% (State 2). A fraction of the steam (y) is extracted at State 2 and the remaining fraction of the steam (1 - y) at State 2 expands in a low-pressure turbine (LPT) to an absolute pressure of 6 kPa and quality of 82% (State 3). Steam leaving the LPT is cooled in a condenser and exits as saturated liquid at an absolute pressure of 6 kPa (State 4). Saturated liquid water leaving from the condenser is pumped to an absolute pressure of 10 MPa and a temperature of 36.8C (State 5) in a pump. Liquid leaving the pump (State 5) is heated using the extracted steam (State 2) in a rigid and well-insulated heat exchanger to an absolute pressure of 10 MPa and a temperature of 164.95C (State 6) and is supplied to the boiler. Extracted steam (State 2) exits the heat exchanger as saturated liquid at an absolute pressure of 0.7 MPa (State 7) and is throttled to an absolute pressure of 6 kPa (State 8) feeding into the condenser. Assume that both turbines and pump are adiabatic. (a) Find the isentropic efficiency of the high-pressure turbine, in %. (b) Calculate the isentropic efficiency of the low-pressure turbine, in %. (c) Determine the isentropic efficiency of the pump, in %. (d) Show the turbine and pump processes on T-s diagram and the appropriate lines of constant pressure. Label actual and isentropic states and identify process directions with arrows. For water: Pcritical = 221 bar and Tcritical = 374C. P = 10 MPa T = 480C steam Boiler 1P2 = 0.7 MPa x2 = 0.985 Remaining Steam -(1-y)mate steam HPT LPT P3 = 6 kPa x3 = 0.82 Extracted Steamym steam Heat Exchanger Ps P = 10 MPa T = 164.95C Extracted Steamym steam P7 = 0.7 MPa sat. liquid 10 MPa Ts = 36.8C Pump P = 6 kPa sat. liquid PB = 6 kPa Condenser