In a heat$-$treating process, a $10-$kg metal part, initially at $1100$ K $,$ is quenched in a closed tank containing $100$ kg of water, initially at $295$ K $.$ There is negligible heat transfer between the contents of the tank and their surroundings.

Modeling the metal part and water as incompressible with constant specific heats $0\mathrm{.}5k\frac{J}{k}g*K$ and $4\mathrm{.}4k\frac{J}{k}g*K,$ respectively, determine the final equilibrium temperature after quenching, in $K.$

$T_f=$ K