Problem $1$

Steam circulating in a Rankine$-$cycle power plant discharges heat in the condenser to cooling water at a rate of $500$ MW $.$ At steady state, the cooling water leaves the condenser at $45C$ and enters a cooling tower. Cooled water at $23C$ is returned to the condenser. Inside the cooling tower, moist air enters at $25C,100$kPa and $30\%$ relative humidity. Moist air exits at $36C,100$kPa and $90\%$ relative humidity. Makeup water is supplied at $18C.$ Note: you may assume that the numeric value of the dry bulb temperature $($in K$)$ closely approximates the enthalpy of dry air $($in $k\frac{J}{k}g).$

Calculate:

$($a$)$ the mass flow rate of the atmospheric air entering the tower;

$($b$)$ the mass flow of the make$-$up water.