Problem $2$ A two$-$stage compression refrigeration system operates with refrigerant $134$a between the pressure limits of $\backslash (\backslash$mathbf$\{0.16\}\backslash )$ and $\backslash (\backslash$mathbf$\{1.4\}\backslash$mathbf$\{$M P a$\}\backslash ).$ 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 $\backslash (\backslash$mathbf$\{80\backslash \%\}\backslash ).$ If the mass flow rate through the lower cycle is $\backslash (0\mathrm{.}25\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$s$\}\backslash ),$ 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.