$3.$ There is a heat pump using R$-134$a that provides $32$ kJ$/$s of heat to a house when it is below freezing outside. Saturated vapor goes into the compressor at $1\mathrm{.}4$ bar and saturated liquid comes out of the condenser which has a pressure of $7\mathrm{.}5$ bar. The compressor operates isentropically$.$ Please determine:

a$)$ The mass flow rate $($kg$/$s$)$

b$)$ The power into the compressor $($kW$)$

c$)$ The coefficient of performance $($no units$)$

d$)$ The amount of heat removed from the cool region $($kJ$/$s$)$

e$)$ The highest possible temperature of the house $($C$)$

f$)$ Recalculate parts b and c for an isentropic efficiency of $75\%$