$1)$ An engineer has proposed that a simple ideal Rankine cycle that uses refrigerant$-134$a be used to produce work with heat from a low$-$temperature thermal energy reservoir. The boiler operates at $1\mathrm{.}6$ MPa $,$ the condenser at $0\mathrm{.}4$ MPa $,$ and the turbine inlet at $\backslash (80^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ Determine the R$-134$a mass flow rate needed for this cycle to produce $750$ kW of power and the thermal efficiency of the cycle. $(35$ points$)$