A 200-MW power plant generates electricity with an efficiency of 40%, with 87% of this waste heat removed via cooling water. The average flow in the river to which this cooling water will be discharged is 45 m^3/s, and the plant wishes to discharge its cooling water at a temperature of 80 degrees celsius. If the river temperature is 18 degrees celsius, what is the maximum rate (m^3/s) at which cooling water could be discharged under average river flow conditions such that the river's downstream temperature will not exceed 22 degrees celsius?
Pontentially useful constants: specific heat of liquid water = 4184 J/kg
Heat of vaporization (occurs at 100c) = 2257 kJ/kg; density of liquid water = 1000 kg/m^3