Preblem $2(25$ points$)$

As a measure to increase the efficiency of a steam$-$based power cycle, a portion of water vapor is routed from the turbine to an open feedwater heater to preheat liquid water prior to entering a boiler. Liquid water enters the heater at a peessure of $p_1=\frac{15}{b}ar$ and $T_1=30C$ Steam enters the heater at the same pressure and at $T_2=400C$ and mixes with the water. A saturated liquidvapor mixture leaves the heater at a quality $x_3=0\mathrm{.}20.$

a$)$ Find the temperature of the exiting mixturc, $T_3.$

b$)$ What is the ratio of mass flow rate of steam to the total mass flow rate through the open feciwater heater $\frac{f{l}_2}{mi{n}_2}?$

c$)$ Plot states $1,2,$ and $3$ on the $P-$v and $T-$v diagrams below