Problem $24$

A $200\mathrm{.}0$ g aluminum calorimeter cup contains $600\mathrm{.}0$ g of water at $20\mathrm{.}0$C$.$ A $100\mathrm{.}0$ g

piece of ice is cooled to $20\mathrm{.}0$C and then placed in the cup. Once thermal equilibrium

is reached, all of the ice melts. Use the following specific heats: cAl $=904$ J Kg$1$C$1,$

cwater $=4186$ J Kg$1$C$1,$ and cice $=2108$ J Kg$1$C$1.$ The latent heat of fusion of water is

LF $=333,500$ J Kg$1.$

$($a$)$ Find the final temperature, assuming the calorimeter is perfectly insulated

$($i$.$e$.,$ no heat flows in or out of the water $+$ ice $+$ aluminum system$).$

$($b$)$ A second piece of ice at $20\mathrm{.}0$C with a mass of $100\mathrm{.}0$ g is added to the

calorimeter. After the system reaches thermal equilibrium, there is a mixture

of liquid water and solid ice in the calorimeter. How much solid ice remains

once equilibrium is reached?