Calorimetry involving temperature and phase changes in making iced tea

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Calorimetry involving temperature and phase changes in making iced tea.

PSS 17.2: Making the Iced Tea
Learning Goal: To practice Problem-Solving Strategy 17.2 for calorimetry problems involving temperature and phase changes.
On a hot summer day, you decide to make some iced tea. First, you brew a volume of 0.750 of hot tea at a temperature of 85.0 . You then add some ice taken from the freezer at a temperature of -15.0 . By the time the mix reaches equilibrium at , exactly one-half of the ice has melted. What is the original mass of ice added to the tea?
For the purposes of this problem, you can assume that the tea has the same thermodynamic properties as plain water. The specific heat of ice is 2090 , the specific heat of water is 4190 , the heat of fusion of ice is 3.33×105 , and the density of water is 1.00 .
MODEL: Identify the interacting systems. Assume that they are isolated from the larger environment.
VISUALIZE: List known information and identify what you need to find. Convert all quantities to SI units.
SOLVE: The mathematical representation, which is a statement of energy conservation, is
.
 For systems that undergo a temperature change, . Be sure to have temperatures and in the correct order.
 For systems that undergo a phase change, . Supply the correct sign by observing whether energy enters or leaves the system during the transition.
 Some systems may undergo both a temperature change and a phase change. Treat the changes separately. The heat energy is .
ASSESS: Is the final temperature in the middle? A that is higher or lower than all initial temperatures indicates that something is wrong, usually a sign error.
Model
Start by making simplifying assumptions appropriate for the situation.
A. What are the interacting systems in this problem?
the ice and the tea
the ice; the tea; and the freezer
the ice; the tea; and the teapot
the ice; the tea; the teapot; and the freezer
B. In this process, the systems undergo which of the following changes?
phase changes only
temperature changes only
both phase and temperature changes
neither phase nor temperature changes
Visualize
List all known and unknown quantities. Use your list to answer the following question.
A. Choose the letters corresponding to the known quantities in this problem.
A. initial mass of tea
B. initial mass of ice
C. initial volume of tea
D. initial volume of ice
E. initial temperature of tea
F. initial temperature of ice
G. final temperature of tea
H. final temperature of ice

List the letters of all the correct answers in alphabetical order. Do not use commas. For instance, if you think that C, F, and G represent known quantities, enter CFG.
CEFGH

Solve
Use the information and the insights that you have accumulated to construct the necessary mathematical expressions and to derive the solution.
A. Find the initial mass of the ice that was added to the tea.

Express your answer numerically in kilograms.