A $50-$kg copper block initially at $160$C is dropped into an insulated tank that contains $90$ L of liquid water at $15$C$.$ Assume that the specific heats of copper and water are $0\mathrm{.}42$ kJ$/$kg K and $4\mathrm{.}18$ kJ$/$kg K$,$ respectively. $($a$)(3$ points$)$ Determine the final equilibrium temperature. $($Hint: Write the energy equation for a system consisting of the copper and the water. Treat liquid water as an incompressible substance. Answer: $22\mathrm{.}7$C$)($b$)(3$ points$)$ Determine the total change in the entropy of system for this process. $($Answer: $1\mathrm{.}887$ kJ$/$K$)$