A $2\mathrm{.}54-$kg copper part, initially at $450$ K$,$ is plunged into a tank containing $4$ kg of liquid water, initially at $350$ K$.$ The copper part and water can be modeled as incompressible with specific heats $0\mathrm{.}385$ kJ$/$kg $$ K and $4\mathrm{.}2$ kJ$/$kg$$K$,$ respectively. For the copper part and water as the system, determine $$

$($a$)$ the final equilibrium temperature, in K$,$

$($b$)$ the amount of entropy produced within the tank, in kJ$/$K$.$

$$Ignore heat transfer between the system and its surroundings.