Steam at $\frac{120}{b}ar,560C,$ and a velocity of $0\mathrm{.}6\frac{m}{s}$ enters a turbine operating at steady state with a rate of $500k\frac{g}{s}.$ As shown in the Figure below, some steam at a rate of $100k\frac{g}{s}$ is extracted at state $2$ at $\frac{1\mathrm{.}5}{b}ar,240C,$ with a velocity of $3\frac{m}{s}.$ The rest of the steam exits at state $3$ as a two$-$phase liquid$-$vapor mixture at $8$ kPa $,$ with a quality of $95\%$ and a velocity of $45\frac{m}{s}.$ Consider heat transfer from the turbine at a rate of $10$ MW $.$ Neglecting the potential energy effects, determine:

$($i$)$ The specific enthalpy at states $1,2,3($in $k\frac{J}{k}g),$

$($ii$)$ The turbine power output $($in MW$),$

$(3$ points$)$

$($iii$)$ The area of the extraction $($state$2)$ duct $($in $m^2).$

$(6$ points$)$

$(3$ points$)$