Problem $12\mathrm{.}059$ E $-$ Two$-$Stage compression refrigeration with vapor$-$liquid separation

A two$-$stage compression refrigeration system with an adiabatic liquid$-$vapor separation unit like that in the figure uses refrigerant$134$ a as the working fluid. The system operates the evaporator at $100\mathrm{.}0$ psia the condenser at $300\mathrm{.}0$ psia, and the separator at $200\mathrm{.}0$ psia. The compressors use $29\mathrm{.}00$ kW of power. Determine the rate of cooling provided by the evaporator and the COP of this cycle. The refrigerant is a saturated liquid at the inlet of each expansion valve and a saturated vapor at the inlet of each compressor, and the compressors are isentropic$.($Round the final answers to three decimal places.$)$

$($Take the required values from saturated refrigerant$-134$a tables.$)$

The rate of cooling provided by the evaporator is $$ Btu$/$h$,$ and the COP of the refrigerator is $$