Thermodynamics

582 | Thermodynamicscycle and thus the pumps and the turbines are isentropic; there are no pressuredrops in the boiler, process heater, and condenser; and steam leavesthe condenser and the process heater as saturated liquid.The work inputs to the pumps and the enthalpies at various states are asfollows:w pump I,in v 8 1P 9 P 8 2 10.001005 m 3 1 kJ>kg2317000 52kPa4a1 kPa # b m3(a) The maximum rate of process heat is achieved when all the steam leavingthe boiler is throttled and sent to the process heater and none is sent to theturbine (that is, m . 4 m. 7 m. 1 15 kg/s and m. 3 m. 5 m. 6 0). Thus,Q # p,max m # 1 1h 4 h 7 2 115 kg>s2313411.4 640.092 kJ>kg4 41,570 kWThe utilization factor is 100 percent in this case since no heat is rejected inthe condenser, heat losses from the piping and other components areassumed to be negligible, and combustion losses are not considered.(b) When no process heat is supplied, all the steam leaving the boiler passesthrough the turbine and expands to the condenser pressure of 5 kPa (that is,m . 3 m. 6 m. 1 15 kg/s and m. 2 m. 5 0). Maximum power is producedin this mode, which is determined to beW # turb,out m # 1h 3 h 6 2 115 kg>s2313411.4 2073.02 kJ>kg4 20,076 kWW # pump,in 115 kg>s217.03 kJ>kg2 105 kWW # net,out W # turb,out W # pump,in 120,076 1052 kW 19,971 kW 20.0 MWThus, 7.03 kJ>kg1 kJw pump II,in v 7 1P 10 P 7 2 10.001093 m 3 >kg2317000 5002 kPa4 a1 kPa # b m3 7.10 kJ>kgh 1 h 2 h 3 h 4 3411.4 kJ>kgh 5 2739.3 kJ>kgh 6 2073.0 kJ>kgh 7 h f @ 500 kPa 640.09 kJ>kgh 8 h f @ 5 kPa 137.75 kJ>kgh 9 h 8 w pump I,in 1137.75 7.032 kJ>kg 144.78 kJ>kgh 10 h 7 w pump II,in 1640.09 7.102 kJ>kg 647.19 kJ>kgQ # in m # 1 1h 1 h 11 2 115 kg>s2313411.4 144.782 kJ>kg4 48,999 kW u W# net Q # pQ # in119,971 02 kW 0.408 or 40.8%48,999 kWThat is, 40.8 percent of the energy is utilized for a useful purpose. Noticethat the utilization factor is equivalent to the thermal efficiency in this case.(c) Neglecting any kinetic and potential energy changes, an energy balanceon the process heater yields