Challenge Problem $m_1^{}=10k\frac{g}{s}$

$p_1=1$MPa

$T_1=250C$

$p_2=1$MPa

$x_2=0$

$(1)$

$(3)p_3=1$MPa

$(2)$

$x_3=1$

A $10k\frac{g}{s}$ stream of super$-$heated steam at $250C$ and a stream of saturated liquid water are combined in a mixing heat exchanger and a stream of saturated vapor exits, with all

three streams at $p=1$MPa as shown in the diagram below. It can be assumed that the heat exchanger is adiabatic, the changes in kinetic and potential energy are negligible,

and the environment is at $T_0=25C.$

$($a$)$ What is the mass flow rate at $2,m_2^{}?$

$($b$)$ What is the mass flow rate at $3,m_3^{}?$

$($c$)$ How much entropy is generated during the process, $S_{\text{g}\text{e}\text{n}}^{}?$

$($d$)$ What is the cause of the irreversibility?

$($e$)$ What is the rate of exergy destruction for the process, $x_d^{}?$

$($f$)$ What is the second law efficiency of the process, ${}_{II}?$

$($g$)$ Draw and label a $T-s$ diagram for the process.