H$5\mathrm{.}3($Ch$5)$ Consider a household refrigerator. Refrigerant$-134$a enters the evaporator at the back of the freezer section at $120$ kPa with a quality of $\backslash (20\backslash \%\backslash )$ and leaves as saturated vapor at $120$ kPa $.$ If the compressor consumes $600$ W of power and the coefficient of performance for the refrigerator is $1\mathrm{.}5,$ determine:

a$.$ the mass flow rate of the refrigerant $\backslash ([\backslash$mathrm$\{$kg$\}/\backslash$mathrm$\{$s$\}]\backslash )$

b$.$ the rate of heat rejected at condenser to the kitchen air $[$W$]$

c$.$ for the same rate of cooling at the evaporator, what is the minimum power input $[$W$]$ required by the refrigerator. Assume a freezer section temperature of $\backslash (-20^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and kitchen air temperature of $\backslash (27^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$