Problem $1(25$ points$)$

Refrigerant$-134$a enters the condenser of a residential heat pump at $800$ kPa and $50C$ at a rate of $0\mathrm{.}03k\frac{g}{s}$ and leaves at $750$ kPa subcooled by $3C.$ The refrigerant enters the compressor at $200$ kPa superheated by $4C.$ Do the following:

a$)$ Draw this cycle on a T$-$s diagram.

b$)$ Determine the isentropic efficiency of the compressor.

c$)$ Determine the rate of heat supplied to the heated room.

d$)$ Determine the COP of the heat pump.

e$)$ Determine 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 $200$ kPa and $800$ kPa $.$