Question $7$: $(20\backslash \%)$

Liquid water at $\backslash (15^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ is heated in a chamber by mixing it with saturated steam. Liquid water enters the chamber at the steam pressure at a rate of $\backslash (4\mathrm{.}6\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$s$\}\backslash )$ and the saturated steam enters at a rate of $\backslash (0\mathrm{.}23\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$s$\}\backslash ).$ The mixture leaves the mixing chamber as a liquid at $\backslash (45^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ If the surroundings are at $\backslash (15^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ),$ determine $($a$)$ the temperature of saturated steam entering the chamber, $($b$)$ the exergy destruction during this mixing process, and $($c$)$ the second$-$law efficiency of the mixing chamber.

Hint: Assume $1$ Steady operating conditions exist. $2$ Kinetic and potential energy changes are negligible. $3$ Heat loss from the chamber is negligible.