A stream of air at 500°C and 835torr with a dew point of 30°C flowing at a rate of 1515 L/s is to be cooled in a spray cooler. A fine mist of liquid water at 25°C is sprayed into the hot air at a rate of 110.0 g/s and evaporates completely. The cooled air emerges at 1 atm.

(a) Calculate the final temperature of the emerging air stream, assuming that the process is adiabatic. (Suggestion: Derive expressions for the enthalpies of dry air and water at the outlet air temperature. substitute them into the energy balance, and use a spreadsheet to solve the resulting fourth-order polynomial equation.)

(b) At what rate (kW) is heat transferred from the hot air feed stream in the spray cooler? What becomes of this heat?

(c) In a few sentences, explain how this process works in terms that a high school senior could understand. Incorporate the results of parts (a) and (b) in your explanation.