$6.(20$ points$)$ A heat pump operating on the ideal vapor compression cycle uses R$-134$a as the working fluid. The evaporator and condenser temperatures are $\backslash (-10^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and $\backslash (45^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ respectively.

$($a$)(5$ points$)$ Determine the coefficient of performance $($COP$)$

$($b$)(5$ points$)$ Calculate the compressor work input per kg of refrigerant

$($c$)(5$ points$)$ Find the heat rejection rate in the condenser for a mass flow rate of $\backslash (0\mathrm{.}05\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$s$\}\backslash )$

$($d$)(5$ points$)$ Calculate the evaporator capacity