Please solve and show work.

An ideal vapor$-$compression heat pump cycle uses R$-134$a to heat a home. The mass flow rate of the refrigerant is $30\mathrm{.}59l\frac{b}{m}in.$ Sketch the cycle on a T$-$s diagram and determine:

a$)$ The compressor power, in hp$.$

b$)$ The rate of heat transfer to the interior of the home, in Btu$/$min$.$

c$)$ The coefficient of performance

d$)$ If the heat pump operated between $15C$ and $80C,$ what is the theoretical max coefficient of performance?

$\backslash$table$[[$State$,$Pressure $($psi$),$Temp $(($:$F$