$($a$)$ Expansion valve$/$capillary tube obstructs flow to trigger phase transition. It is adiabatic and does not involve work, and the enthalpy remains constant throughout the process. What is the state of R $-134$a entering the evaporator? State the quality if it is binary mixture. $[2$ Pts$]$

$($b$)$ What is the coefficient of performance for cooling $\backslash ((\backslash$beta$)\backslash )?[6$ Pts$]$

$($c$)$ What is the mass flux rate needed for R$-134$a if this cycle is to cool $10$ kg of air $($not flowing$)$ from $\backslash (30^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ to $\backslash (25^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ in $10$ minutes? Use the ideal gas properties of air. $[4$ Pts$]$