How to Calculate Mass of Aluminum Needed to Melt 20 g of Ice with Heat of Fusion

[dmolson]

Homework Statement

How many grams of aluminum at 90 C would have to be dropped into a hole in a block of ice at 0 C to melt 20 g of ice.

Homework Equations

Q = mcdelta T and Q = mLf
c(H2O) = 1 cal/g.C
c(Al) = 0.215 cal/g.C

The Attempt at a Solution

I can find the heat of fusion Q = (20 g)(79.7 cal/g) = 1594 cal.
The next step I thought would be to set that equal to mcdeltaT of the aluminum, but there is no final temp for the aluminum. I don't know if I am supposed to find the final temp first or how I would do that to find the mass of the aluminum.

 

[Doc Al]

...but there is no final temp for the aluminum.

Only a small portion of the block of ice melts. So what must be the final temperature?

 

[sicjeff]

Do you know anything about equillibrium? It could be easily shown that this system would reach steady state right?