The enthalpy of vaporization for water is 40.65 kJ mol^-1. As a design engineer for a project in a desert climate, you are exploring the option of using evaporative cooling.

(a) If the air has an average volumetric heat capacity of 0.00130 J cm^-3 K^-1, what is the minimum mass of water that would need to evaporate in order to cool a 5 m × 5 m room with a 3 m ceiling by 5°F using this method?

(b) Is this a spontaneous or nonspontaneous process?