A $2\mathrm{.}34-kg$ copper part, initially at $430$ K $,$ is plunged into a tank containing $4$ kg of liquid water, initially at $330$ K $.$ 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.