Problem $2.$ A heat pump used to heat a home operates on an ideal vapor$-$compression cycle. In this ideal cycle, assume that the compressor is isentropic and adiabatic, the compressor inlet state is a saturated vapor, and the condenser outlet state is a saturated liquid. Refrigerant $134$a is the working fluid. The mass flow rate is $\backslash (0\mathrm{.}32\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$s$\}\backslash ).$ The condenser pressure is $900$ kPa and the evaporator pressure is $200$ kPa $.$

a$.$ Sketch the cycle on a T$-$s diagram with respect to the vapor dome.

b$.$ Determine the rate of heat supplied to the house $($kW$).$

c$.$ What is the compressor pressure ratio?

d$.$ Determine the coefficient of performance of the heat pump.