Physics
posted by Dawna .
3. The quantity 0.850kg of ice at 20 degrees Celsius is added to 1.100kg of water in an aluminum Calorimetry cup at 7 degrees Celsius. The mass of the Calorimetry cup is 0.250kg. Use your knowledge of specific heats and latent heats to determine the temperature for the ice/water/cup system after it has come to thermal equilibrium. If that thermal equilibrium is zero degrees Celsius, determine how much of the ice in the cup has melted, and how much remains frozen. Another scenario for the zero degrees Celsius equilibrium is that where none of the ice melts, and instead some of the cooled water actually freezes, adding to the amount of ice in the system.
Note: This problem requires a careful analysis of both positive and negative quantities of heat.

Nuts to the note.
The sum of heats gained is zero. (some of the heats gained will be negative).
Heat gained by ice to zeroC+heatgained by melted ice at 0C +heat gained by water in cup+ heatgained by aluminum=0
Now the algebra:
.850*Cice*(0  (20)) + M*Hf+1.1cwater*(07)+.250Calum*(07)=0
where M is the mass of ice melting. Now if it comes out negative, that means ice was made from the water.
Hf is the latent heat of fusion of water/ice. It should be a heat gained.
My gut feel and head thinking...ignore the aluminum...is that ice is formed from the water, M will be negative, but it is close in my head. Happy computing 
So am i supposed to know the latent heat of fusion of water and ice or is that something i look up/figure out? sorry physics is not my best subject...
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