Can Aluminum at 90 Degrees Celsius Melt 10 Grams of Ice?

[BlueSkyy]

Melting Ice With Aluminum??

Homework Statement

How many grams of aluminum at 90 degrees C would have to be dropped into a hole in a block of ice at 0.0 degrees C to melt 10 g of ice?

Homework Equations

Q = (m)(c)(deltaT)
c of aluminum = 0.9
c of ice = 2.1
c of water = 4.186
333.7 kJ is needed to get past the ice/water boundary

The Attempt at a Solution

I've tried setting up a few different equations, like:
(.01 kg)(2.1)(+45) + (x kg)(0.9)(-45) = 0
(.01 kg)(2.1)(+45) + 333.7 + (x kg)(0.9)(-45) = 0
and a few others I don't have on hand, but I can't seem to get the correct answer. What do I use for delta T? Am I even doing this right at all?

Thanks for your help.

 

[marcusl]

No, I think you are missing it. First calculate the heat energy Q needed to melt 10 g of ice. Your latent heat of fusion should read 333.7 kJ/kg. Then solve for the mass of aluminum having this value of Q, using deltaT=90C (since the final temp of the Al is 0C once it's done its job).