A central air conditioning system operates as shown below $($Figure $1).$ The mass flow rate of moist air into the system is $8\mathrm{.}6k\frac{g}{m}in.$ Atmospheric Pressure is equal to $1$ atm $.$ Using the psychrometric chart as much as possible to:

$($a$)$ Sketch the process on the psychrometric chart. $($Draw heavy lines and label state points.$)$

$($b$)$ Calculate the required cooling capacity of the cooling coils in $k\frac{J}{m}in.$

$($c$)$ Calculate the rate of heat transfer for the heating coils in $k\frac{J}{m}in.$

$($d$)$ Determine the amount of condensate produced in one hour of operation.