An air conditioner using R$-134$a as the working fluid maintains a room at $23C$ while rejecting heat to the atmosphere at $37C.$ Heat enters the room at a rate of $250k\frac{J}{m}in$ through walls and windows, and the computer, TV$,$ and lights in the room generate $900$ W of heat. R$-134$a enters the compressor as saturated vapor at $400$ kPa with a mass flow rate of $1k\frac{g}{s}$ and exits at $1200$ kPa and $70C.$

$($a$)$ Determine the actual cooling efficiency of the air conditioner.

$($b$)$ Determine the theoretical maximum cooling efficiency of this air conditioner.

$2$