Refrigerant R$134$a enters the compressor as a superheated vapor at $0\mathrm{.}14$ MPa and $-10$C with a mass flow rate of $0\mathrm{.}05$ kg$/$s$.$ It is compressed to $0\mathrm{.}8$ MPa and $50$C$.$ The refrigerant is then condensed to a saturated liquid state at $0\mathrm{.}7$ MPa and $26\mathrm{.}72$C and passes through a throttling valve to $0\mathrm{.}15$ MPa. Answer the following questions:

$($a$)$ Draw a schematic diagram. $(5$ points$)$

$($b$)$ Draw a T$-$s diagram. $(5$ points$)$

$($c$)$ Calculate the heat transfer in the cooling space $($kW$).(5$ points$)$

$($d$)$ Calculate the work supplied to the compressor $($kW$).(5$ points$)$

$($e$)$ Evaluate the coefficient of performance $($COP$)$ of the refrigeration system. $(10$ points$)$