Problem # $2$

Consider an ordinary shower where hot water at $T_1=60C$ is mixed with cold water at $T_2=10C.$ It is desired to steadily supply warm water at $T_3$ for the daily use. Compute the outlet temperature $T_3$ of the exit water from the mixing point if the ratio of the mass flow rates of the hot to cold water varies from $0\mathrm{.}4$ to $5$ with an increment of $0\mathrm{.}2.$ Plot the outlet temperature as a function of the mass ratio $($of hot to cold water$).$ Determine the most suitable mass ratio or range of the mass ratios, provide your justification.

Hint: Assume the heat losses from the mixing chamber to be negligible and the mixing to take place at a constant pressure of $200$ kPa SOLVE MANULAY BY HAND