$5.(20$ points$)$ You're an engineer tasked with designing a novel refrigeration system for a high$-$tech food storage facility. The facility needs to keep perishable products at low temperatures around the clock, requiring a reliable and efficient refrigeration system. After evaluating several refrigerants, you decide on Refrigerant$-134$adue to its performance and environmental properties. During the design phase, you specify a compressor for the system. The compressor must handle refrigerant$-134$a entering as a saturated vapo at $0\mathrm{.}14$ MPa ahd leaving as a superheated vapdr at $0\mathrm{.}8$ MPa and

$\backslash ($ T$\_\{2\}\backslash )\backslash (60^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ Given the size of the facility, you estimate that the mass flow rate of the refrigerant through the compressor needs to be $\backslash (0\mathrm{.}06\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$s$\}\backslash ).)$ to ensure that the system's energy requirements align with the facility's sustainability goals, you need to calculate the energy transfers by mass into and out of the compressor.

Using the thermodynamic properties for refrigerant$-134$a$,$ you find:

$-$ The inlet enthalpy for the saturated vapor at $0\mathrm{.}14$ MPa is approximately $\backslash (247\mathrm{.}27\backslash$mathrm$\{$~kJ$\}/\backslash$mathrm$\{$kg$\}\backslash ).$

$-$ The outlet enthalpy for the superheated vapor at $0\mathrm{.}8$ MPa and $\backslash (60^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ is approximately $\backslash (283\mathrm{.}23\backslash$mathrm$\{$~kJ$\}/\backslash$mathrm$\{$kg$\}\backslash ).$

a$.$ Plot the initial and final states of the system on a pressure$-$specific volume diagram that includes the saturated liquid and saturated vapor lines. $(5$ points$)\backslash (\backslash$quad C$^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash \{\backslash )$ PCMPA$)$