Question $5(20$ points$)$

A $2.F4-kg$ copper part, initially at $4$ F $0$ K $,$ is plunged into a tank containing $4$ kg of liquid water, initially at $3F0K.$ The copper part and water can be modeled as incompressible with specific heats $0\mathrm{.}385k\frac{J}{k}g.K$ and $4\mathrm{.}2k\frac{J}{k}g.K,$ 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 $k\frac{J}{K}.$

Ignore heat transfer between the system and its surroundings.