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.$)$

In the two$-$stage compression refrigeration system, the refrigerant passes through a compressor into a condenser, m $2.$ From the condenser, the product passes to a separator via a pipeline into an evaporator m $6.$ In the last stage, the product passes to the compressor into a separator.

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