$($a$)$

You have a styrofoam container with $743$ g of tomato juice $($specific heat of $3,980$ J$/($kg $$C$))$ at $31\mathrm{.}0$ and you add a $75$ g chunk of ice at $0$C$.$ Assume the liquid and water mix uniformly as the ice melts and determine the final temperature of the mixture $($in $$C$).$

$20\mathrm{.}37$C

$($b$)$

What If$?$ What is the minimum mass of the ice cube $($in g$)$ that will result in a final mixture at exactly $0$C$?$

$274\mathrm{.}4$ g