On a summer day at Muscat area, the typical average outdoor temperature is $35$ degrees Celsius. For the indoor temperature of a house to be kept constant a temperature of $24$ degrees Celsius, the rate of heat removal from the house by an air conditioning unit has to be $68\mathrm{.}5\frac{kJ}{s}.$

$($a$)$ Determine the minimum work input to the unit in kW$?$

$($b$)$ The maximum efficiency of the unit.