$2.(30$ pts$)$ Steam enters a turbine with a velocity of $\backslash (120\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ at $\backslash (600^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and $6000$ kPa $.$ The steam leaves the turbine as saturated vapor at $200$ kPa with a velocity of $\backslash (180\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).$ Heat is transferred from the turbine to the surroundings in the amount of $30$ kJ for every kilogram of steam flowing through the turbine. The mass flow rate of steam through the turbine is $\backslash (20\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$s$\}\backslash ).$

a$.$ Determine the rate of work done by the steam in the turbine, in kW$.$

b$.$ Determine the flow area at the entrance to the turbine, in $\backslash (\backslash$mathrm$\{$m$\}^\{2\}\backslash ).$