Learning Goal:

To practice Problem$-$Solving Strategy $12\mathrm{.}1$ Calorimetry problems.

On a hot summer day, you decide to make some iced tea. First, you brew $1\mathrm{.}50$ L of hot tea and leave it to steep until it has reached a temperature of Ttea $=75\mathrm{.}0$C$.$ You then add $0\mathrm{.}975$ kg of ice taken from the freezer at a temperature of Tice $=0$C$.$ By the time the mix reaches equilibrium, all of the ice has melted. What is the final temperature Tf of the mixture?

For the purposes of this problem, assume that the tea has the same thermodynamic properties as plain water.

The specific heat of water is c $=4190$ J$/$kg$$C$.$

The heat of fusion of ice is Lf $=3\mathrm{.}33105$ J$/$kg $.$

The density of the tea is tea $=1\mathrm{.}00$ kg$/$L $.$

Determine which quantities are known and which are unknown.

initial mass of tea: mtea

initial mass of ice: mice

initial volume of tea: Vtea

initial volume of ice: Vice

initial temperature of tea: Ttea

initial temperature of ice: Tice

final temperature of system: Tf