Cascaded refrigation system can maintain relatively good performance when cooling to low

temperatures is required. Here, a two$-$stage system operates between $12$ bar and $0\mathrm{.}6$ bar as the

overall pressure limits$.$ Between the upper and lower cycle there is a insulated counterflow heat

exchanger with pressures of $3\mathrm{.}6$ bar and $4$ bar on the upper cycle and lower cycle sides, respectively.

Coming out of the condenser, the R$134$a exactly reaches the saturated liquid state in both cases, and

at the compressor inlets, the state is saturated vapour. The compressors have an isentropic efficiency

of $85\%.$ The refrigerant flow rate in the lower cycle is $200$ g$/$s$.$ Calculate:

$($a$)$ the R$134$a mass flow rate in the upper cycle

$($b$)$ the refrigeration capacity

$($c$)$ the COP of the overall system.