$4.$ Consider a two$-$stage cascade refrigeration system operating between the pressure limits of $0\mathrm{.}8$ and $0\mathrm{.}14$ MPa $.$ Each stage operates on the ideal vaporcompression refrigeration cycle with refrigerant$-134$a as the working fluid. Heat rejection from the lower cycle to the upper cycle takes place in an adiabatic counterflow heat exchanger where both streams enter at about $0\mathrm{.}4$ MPa $.$ If the mass flow rate of the refrigerant through the upper cycle is $\backslash (0\mathrm{.}24\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$s$\}\backslash ),$ determine $($a$)$ the mass flow rate of the refrigerant through the lower cycle, $($b$)$ the rate of heat removal from the refrigerated space and the power input to the compressor, and $($c$)$ the coefficient of performance of this cascade refrigerator.