$17\mathrm{.}84$ :: $$You cool an mFe $=100\mathrm{.}0$ g slug of red$-$hot iron $($temperature T$0,$Fe $=745$C$)$ by dropping it into an insulated cup of negligible mass containing mw $=85\mathrm{.}0$ g of water at T$0,$w $=20\mathrm{.}0$C$.$ Assume no heat is exchanged with the surroundings. $($a$)$ Thoroughly explain the final temperature of the water. Be sure to include a couple of calculations proving why the water reaches this temperature. $($b$)$ What is the final mass of the iron and the remaining water? Since we did some of the preliminary calculations to prove the equilibrium temperature of the system, we can now algebraically solve for the masses. Here are the specific heats and latent heat of vaporization for your calculations $($you$\text{'}$re welcome :$))$: cFe$=470$ J$/($kg K$),$ cH$20=4190$ J$/($kg K$),$ and LvH$20=2256103$ J$/$kg$.$