ME $405$: Thermal Systems Design

Homework $\backslash$#$5$

$(1)$ Steam enters the turbine of a cogeneration plant at $4$ MPa and $\backslash (500^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ One$-$fourth of the steam is extracted from the turbine at $\backslash (1200-\backslash$mathrm$\{$kPa$\}\backslash )$ pressure for process heating. The remaining steam continues to expand to $10$ kPa $.$ The extracted steam is then condensed and mixed with feedwater at constant pressure and the mixture is pumped to the boiler pressure of $4$ MPa $.$ The mass flow rate of steam through the boiler is $\backslash (55\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$s$\}\backslash ).$ Disregarding any pressure drops and heat losses in the piping, and assuming the turbine and the pump to be isentropic$,$ determine the net power produced and the utilization factor of the plant.