A vapour compression refrigeration system operates between condenser and evaporator

temperatures of $30C$ and $-10C,$ respectively. The system employs a regenerative liquid

to vapour heat exchanger, which sub$-$cools saturated liquid from the condenser with

vapour from the evaporator at $-10C.$ Given that the refrigerant enthalpy drop in sub$-$

cooling is $6\mathrm{.}602k\frac{J}{k}g$ and the compressor displacement is $1\mathrm{.}1\frac{m^3}{m}in.$ Assuming

compression to be isentropic and specinc vorume at the suction of compressor to be equal

to specific volume of saturated vapour, calculate:

i$.$ The mass flow rate of refrigerant in $k\frac{g}{m}in,$ given Volumetric efficiency $vv=0\mathrm{.}92.$

ii$.$ The refrigeration capacity in TR$.$

iii. The COP for cooling and

iv$.$ The theoretical $h\frac{p}{T}R$ needed to run the compressor.