Problem $2(18$ points$)$:

A vapor$-$compression cycle used as a refrigerator uses R$-134$a as the working fluid. The condenser operates at $700$ kPa and the fluid is kept to $20C$ at the inlet of the evaporator. The compressor is isentropic and the fluid entering the compressor is superheated by $10C.$ The fluid at the condenser outlet is at a temperature of $24C.$ The cycle is designed for a mass flow rate of $0\mathrm{.}3k\frac{g}{s}$ refrigerant.

a$.$ Show the cycle on the T$-$s diagram and include the saturation lines. Label all work and heat interactions $($inputs and outputs$).$

b$.$ What is the amount of subcooling in the cycle?

c$.$ Determine the work input to the compressor per unit mass of refrigerant $($Answer: $36\mathrm{.}38k\frac{J}{k}g)$

d$.$ Determine the power input to the compressor and the heat removal from the cool space, in kW

e$.$ Determine the COP of the system $($Answer: $4\mathrm{.}44)$

f$.$ Find the exergy destroyed by the throttling valve, if the ambient temperature is $22C.($Answer: $1\mathrm{.}77$ kW $)$