A two$-$stage compression refrigeration system operates with refrigerant $134$a between

the pressure limits of $0\mathrm{.}16$ and $1\mathrm{.}4$ MPa. The refrigerant leaves the condenser as a saturated

liquid and is throttled to a flash tank operating at $0\mathrm{.}5$ MPa. Heat rejection from the lower to the

upper cycle takes place in an adiabatic counterflow heat exchanger where the pressure in the

upper and lower cycles are $0\mathrm{.}4$ and $0\mathrm{.}5$ MPa, respectively. In both cycles, the refrigerant is a

saturated liquid at the condenser exit and a saturated vapor at the compressor inlet, and the

isentropic efficiencies of the compressors are $80\%.$ If the mass flow rate through the lower cycle

is $0\mathrm{.}25$ kg$/$s$,$ determine a$)$ the mass flowrate of the of the refrigerant through the upper cycle, b$)$

the rate of heat removal from the refrigerated space, and c$)$ the refrigerator$$s COP.