Problem $05\mathrm{.}060-$ Turbine flow

A portion of the steam passing through a steam turbine is sometimes removed for the purposes of feedwater heating as shown in the

figure. Consider an adiabatic steam turbine with $12\mathrm{.}5$ MPa and $550\backslash$deg C steam entering at a rate of $20$k$($g$)/($s$).$ Steam is bled from this

turbine at $1000$ kPa and $200\backslash$deg C with a mass flow rate of $1\mathrm{.}100$k$($g$)/($s$).$ The remaining steam leaves the turbine at $100$ kPa and $100\backslash$deg C$.$

Determine the power produced by this turbine. The enthalpies at the given temperature and pressures are

h$\_(1)=3476\mathrm{.}5$k$($J$)/($k$)$g$,$h$\_(2)=2828\mathrm{.}3$k$($J$)/($k$)$g$,$ and h$\_(3)=2675\mathrm{.}8$k$($J$)/($k$)$g