Problem $4-1.$ A refrigerator operates on the ideal vapor$-$compression refrigeration cycle and uses Refrigerant$-134$a as the working fluid. The condenser operates at a pressure of $\backslash (400\backslash$mathrm$\{$lbf$\}/\backslash$mathrm$\{$in$\}^\{2\}\backslash )$ and the evaporator at a temperature of $\backslash (25^\{\backslash$circ$\}\backslash$mathrm$\{$F$\}\backslash ).$ The compressor isentropic efficiency is $\backslash (88\backslash \%\backslash ).$ Calculate:

a$)$ The refrigeration capacity in $\backslash (\backslash$mathrm$\{$Btu$\}/\backslash$mathrm$\{$lb$\}\backslash )$ of refrigerant

b$)$ The coefficient of performance,

c$)$ If$,$ instead of the standard throttling process used to expand the liquid leaving the condenser to the evaporator pressure, an adiabatic and reversible $($isentropic$)$ expansion device is proposed, determine the percent improvement in coefficient of performance, COP, by using this device, and

d$)$ Discuss briefly why the process described in c$)$ cannot be implemented in an actual cycle.