$12\mathrm{.}84$ An air$-$conditioning system consists of a spray section followed by a reheater. Moist air at $32C$ and $=77\%$ enters the system and passes through a water spray, leaving the spray section cooled and saturated with water. The moist air is then heated to $25C$ and $=45\%$ with no change in the amount of water vapor present. For operation at steady state, determine

$($a$)$ the temperature of the moist air leaving the spray section, in $C.$

$($b$)$ the change i the amount of water vapor contained in the moist air passing through the system, in kg per kg of dry air. Locate the principal states on a psychrometric chart.