Calculate Tf When 77g Ice & 300g Water at 0°C & 50°C Mix

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To find the final temperature (Tf) when mixing 77 grams of ice at 0 °C with 300 grams of water at 50 °C, apply the principle of conservation of thermal energy. The heat lost by the water must equal the heat gained by the ice, which involves calculating the energy needed to melt the ice and then raise the temperature of the resulting water. The specific heat of water and the heat of fusion for ice are crucial for these calculations. Solving the equation requires careful consideration of energy transfers during the phase change and temperature adjustments. This approach will yield the final temperature of the mixture.
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Determine the final temperature Tf, that results when 77 grams of ice at 0 °C are mixed with 300 grams of liquid water at 50 °C.
Specific heat of water: c = 1.00 cal/(gram*°C).
Heat of fusion for the ice - liquid water transition: cF = 79.7 cal/gram

I have tried this several times and several different ways and cannot solve the answer.
 
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dmolson said:
Determine the final temperature Tf, that results when 77 grams of ice at 0 °C are mixed with 300 grams of liquid water at 50 °C.
Specific heat of water: c = 1.00 cal/(gram*°C).
Heat of fusion for the ice - liquid water transition: cF = 79.7 cal/gram

I have tried this several times and several different ways and cannot solve the answer.

Tell us how you think it should be done, even if you did get the wrong answer. Then we can help you.
 
What are your thoughts on this?

Apply conservation of thermal energy. Take in the before and after situation and equate the increase of wnergy with the loss of energy.
 
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