$(2)$ Consider a coal$-$fired steam power plant that produces $175$ MW of electric power. The

power plant operates on a simple ideal Rankine cycle with turbine inlet conditions of

$7$ MPa and $550C$ and a condenser pressure of $15$ kPa $.$ The coal has a heating value

$($energy released when the fuel is burned$)$ of $29,300k\frac{J}{k}g.$ 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.