Q$2[10$ points$]$ Consider a Carnot$-$cycle heat pump with $($Ammonia$)$ as the refrigerant. Heat is rejected from the refrigerant at $\backslash (30^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ),$ during which process the refrigerant changes from saturated vapor to saturated liquid. The heat is transferred to the refrigerant at $\backslash (0^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$

$($a$)$ Show the cycle on the $\backslash ($ T$-$s $\backslash )$ diagram.

$($b$)$ Find the quality of the refrigerant at the beginning and end of the isothermal heat addition process at $\backslash (0^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$

$($c$)$ Determine the COP for the cycle.

$[$Answer$]($b$)0\mathrm{.}10588$ and $0\mathrm{.}9227$; $($c$)10\mathrm{.}17$