Problem $2(50$ points$)$

In a heat$-$treating process, a $1-kg$ metal part, initially at $1075$ K $,$ is quenched in a tank containing $100$ kg of water, initially at $295$ K $.$ There is negligible heat transfer between the contents of the tank and their surroundings. The metal part and water can be modeled as incompressible with specific heats of $0\mathrm{.}5k\frac{J}{kg*K}$ and $4\mathrm{.}2k\frac{J}{kg*K},$ respectively.

Determine:

$($a$)$ the final equilibrium temperature after quenching, in $[$K$],$ and

$($b$)$ the amount of entropy produced within the tank, in $k\frac{J}{K}.$