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**The following experiment was performed to determine the latent heat of fusion of ice. A 50.0-g aluminum cup was filled with 100 g of warm water. The temperature of the cup and water stabilized at 35C. A 15-g piece of ice at 0C was placed in the water and quickly melted. The final temperature of the system was 21.4C. What value was obtained for the heat of fusion of ice?**

**Energy (heat) = mcΔT**

m= mass

c= specific heat

ΔT = change in temperature

Energy (heat) = mHf

m = mass

Hf = heat of fusion

Specific Heat of Water: 4200 J/kgC

Specific Heat of Ice: 2100 J/KgC

Specific Heat of Aluminum: 900 J/KgC

Latent Heat of Fusion for Water: 335,000 J/Kg

Latent Heat of Vaporization for Water: 2,260,000 J/Kg

m= mass

c= specific heat

ΔT = change in temperature

Energy (heat) = mHf

m = mass

Hf = heat of fusion

Specific Heat of Water: 4200 J/kgC

Specific Heat of Ice: 2100 J/KgC

Specific Heat of Aluminum: 900 J/KgC

Latent Heat of Fusion for Water: 335,000 J/Kg

Latent Heat of Vaporization for Water: 2,260,000 J/Kg

Okay, so I'm sure the aluminum cup and the water play a role when solving for this problem, but I'm not quite sure what to do. My physics teacher hasn't taught us this yet. In fact he started our entire thermal energy unit 3 days before Christmas break, expects us to learn this on our own over the break, and we're being given a test this tuesday after 2 1/2 weeks off. Anyways, this is what I have so far:

**Eh (ice) = mcΔT**

= (0.015kg)(2100 J/KgC)(21.4C)

= 674.1 J

Eh = mHf

Hf = Eh/m

=674.1 J/0.015Kg

= 44940 J/Kg

= (0.015kg)(2100 J/KgC)(21.4C)

= 674.1 J

Eh = mHf

Hf = Eh/m

=674.1 J/0.015Kg

= 44940 J/Kg

Thanks for anyone who could help me with this!

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