$6.$ In the real vapour$-$compression refrigeration cycle shown below, R$-134$a exits the evaporator as a saturated vapour at $180$ kPa $($Stream $1).$ The R$-134$a is compressed in an adiabatic compressor to $1\mathrm{.}2$ MPa and $\backslash (70^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )($Stream $2).$ The R$-134$a leaves the condenser as a saturated liquid at $1\mathrm{.}2$ MPa $($Stream $3).$ The R$-134$a is throttled back to the evaporator pressure of $180$ kPa $($Stream $4).$ The warm surroundings are at $\backslash (30^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$

$($Changes in kinetic and potential energies can be neglected.$)$

$[9]($a$)$ Find the isentropic efficiency of the compressor.

$[10]($b$)$ Find the total specific entropy generation by the condenser, $\backslash ($ s$\_\{\backslash$text $\{$gen $\}\}\backslash )$ in $\backslash (\backslash$mathrm$\{$kJ$\}/(\backslash$mathrm$\{$kg$\}\backslash$mathrm$\{$K$\})\backslash ).$

$[6]($c$)$ Find the quality of Stream $\backslash (4,$ x$\_\{4\}\backslash ).$

$[7]($d$)$ Find the coefficient of performance of the real refrigeration cycle.

$[10]($e$)$ Draw the refrigeration cycle on a $\backslash ($ T $\backslash )-$s diagram with respect to saturation lines. Label all streams with numbers; indicate the direction of all streams with arrows. Label both the actual and the isentropic exit streams of the compressor.

$[5]($f$)$ If the maximum possible coefficient of performance that any refrigerator could have when operating between the same two temperature reservoirs $($the warm surroundings at $\backslash (30^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and the refrigerated space$)$ is $10\mathrm{.}66,$ what is the temperature at which the refrigerated space is kept?