$(1)$ A portion of a two$-$stage compression refrigeration circuit operating with R$-134$a refrigerant is illustrated in the figure. Part of the refrigerant at $1000$ kPa and $35\backslash$deg C$,$ state $1,$ is sent to tank A through valve V$1.$ The other $($larger$)$ portion is sent to the evaporator through valve V$2.$ In the evaporator, the refrigerant removes heat at a rate of $100$ kW and its pressure is equal to $85\mathrm{.}1$ kPa, leaving in the saturated vapor state, $4.$ It is then compressed adiabatically and reversibly to state $5,$ where it is introduced into tank A$.$ Saturated vapor, state $6,$ leaves tank A$.$ The pressure in tank A$,$ whose walls can be assumed to be adiabatic, is equal to: $350$ kPa. Assume Steady State and neglect variations in kinetic and potential energy in all processes. Determine:

$($a$)$ The refrigerant flow rate that circulates through the evaporator $[$kg$/$s$].$

$($b$)$ The liquid flow rate in state $1$ that is diverted to tank A $[$kg$/$s$].$

$($c$)$ The compression power of the vapor that leaves the evaporator to state $5[$kW$].$

$($d$)$ Determine the rate of entropy generation in the evaporator $[$kW$/$K$]$ if the heat exchange is with an environment at $-30\backslash$deg C$.$

$($e$)$ Locate the different states on a diagram $($T versus s$).$