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How Many Grams of Ice at -17°C Must Be Added 70C70 ^ { \circ } \mathrm { C }

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How many grams of ice at -17°C must be added to 741 grams of water that is initially at a temperature of 70C70 ^ { \circ } \mathrm { C } to produce water at a final temperature of 12C?12 ^ { \circ } \mathrm { C } ? Assume that no heat is lost to the surroundings and that the container has negligible mass. The specific heat of liquid water is 4190 J/kg ? C° and of ice is 2000 J/kg ? C°. For water the normal melting point is 0°C and the heat of fusion is 334 × 103 J/kg. The normal boiling point is 100°C and the heat of vaporization is 2.256 × 106 J/kg.

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