$3$: Consider a coal$-$fired steam power plant that produces $275$ MW of electric power. The power plant operates on a simple ideal Rankine cycle with turbine inlet conditions of $10$ MPa and $\backslash (550^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and a condenser pressure of $15$ kPa $.$ The coal has a heating value $($energy released when the fuel is burned$)$ of $\backslash (29,300\backslash$mathrm$\{$~kJ$\}/\backslash$mathrm$\{$kg$\}\backslash ).$ Assuming that $85$ percent of this energy is transferred to the steam in the boiler and that the electric generator has an efficiency of $96$ percent, determine $($a$)$ the overall plant efficiency $($the ratio of net electric power output to the energy input as fuel$)$ and $($b$)$ the required rate of coal supply.