Design Problem

Two$-$stage compression refrigeration system operating between the pressure limits of $1\mathrm{.}4$ and $0\mathrm{.}1$ MPa $.$ The working fluid is refrigerant$-134$a$.$ The refrigerant leaves the condenser as a saturated liquid and is throttled to a flash chamber operating at $0\mathrm{.}4$ MPa $.$ Part of the refrigerant evaporates during this flashing process, and this vapor is mixed with the refrigerant leaving the low$-$pressure compressor. The mixture is then compressed to the condenser pressure by the high$-$pressure compressor. The liquid in the flash chamber is throttled to the evaporator pressure and cools the refrigerated space as it vaporizes in the evaporator. Assuming the refrigerant leaves the evaporator as a saturated vapor and both compressors are isentropic$.$ Determine $($a$)$ the cooling load of the system if the mass flow rate through the condenser is $\backslash (0\mathrm{.}25\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$s$\}\backslash ),$ and $($b$)$ the COP of the system. Also, $($c$)$ conduct a parametric study to determine the effect of flash chamber pressure on the system performance, and $($d$)$ optimize the COP of the system and determine the optimal design parameters.