Problem $11-44$:

Refrigerant$-134$a enters the condenser of a residential heat pump at $800$ kPa and $50C$ at a rate of $0\mathrm{.}022k\frac{g}{s}$ and leaves at $750$ kPa subcooled by $3C.$ The refrigerant enters the compressor at $200$ kPa superheated by $4C.$ Determine $($a$)$ the isentropic efficiency of the compressor, $($b$)$ the rate of heat supplied to the heated room, and $(c)$ the COP of the heat pump. Also, determine $($d$)$ the COP and the rate of heat supplied to the heated room if this heat pump operated on the ideal vapor$-$ compression cycle between the pressure limits of $200$ and $800$ kPa

$($Please solve the quastion by your hand $,$ and use this P$-$h digram$)$