A heat pump with R$-134$a refrigerant as the working fluid is used to maintain a space at $77$F by absorbing heat from geothermal water that enters the evaporator at $122$F at a unit rate and exits at $104$F$.$ The refrigerant enters the evaporator at $68$F with a quality of $25$ percent and exits at the inlet pressure as saturated vapor. The refrigerant loses $350$ W of heat to the surroundings as it flows through the compressor and the refrigerant leaves the compressor at $210$psia at the same entropy as the inlet. Determine: a$)$ The maximum operating power in the compressor for the same heating load $($BTU$/$hr$)$ b$)$ The mass flow of the refrigerant $($lb$/$s$).$