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How Many Grams of Ice At 17C- 17 ^ { \circ } \mathrm { C }

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How many grams of ice at 17C- 17 ^ { \circ } \mathrm { 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 } \text { ? } 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/kgC4190 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { C } ^ { \circ } and of ice is 2000 J/kgC2000 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { C } ^ { \circ } For water the normal melting
point is 0C0 ^ { \circ } \mathrm { C } and the heat of fusion is 334×103 J/kg334 \times 10 ^ { 3 } \mathrm {~J} / \mathrm { kg } The normal boiling point is 100C100 ^ { \circ } \mathrm { C } and the heat of vaporization is 2.256×106 J/kg2.256 \times 10 ^ { 6 } \mathrm {~J} / \mathrm { kg }


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