Water and Ice heat transfer equilibrium

[merbear]

Homework Statement

A 300 cm3 glass is filled with 120 g of ice at 0°C and 210 g of water at 25°C.

(a) Characterize the content of the glass after equilibrium has been reached. Neglect heat transfer to and from the environment.

Find:
mass of water?
mass of ice?
equilibrium temperature?

Homework Equations

Q=mL

delta Q1 + delta Q2 + delta Q3 = 0

delta q= 0 (for the system)

The Attempt at a Solution

I don't know how to solve for the latent heat of fusion, so I tried to set up a series of equations from which I would be able to substitute to solve for the unknowns. I ended up with too many variables and not able to isolate them to solve for values. Since the latent heat of fusion is the heat flow necessary to bring about a phase change, I assumed that Q=mL would be a necessary equation, but I can't figure out how to implement the equation to get values. Any help on starting this problem would be appreciated!

Thank-you!

 

[Shooting Star]

First find out whether there is enough heat in the water to melt all of the ice.

Heat reqd to melt ice = m1*L. Heat given up by water to come down to 0 C = m2*c*(25 -0).

Case 1.
If the whole ice cannot melt, find how much would melt. The resulting temp is obvious.

Case 2.
If the whole ice does melt, then the water from the ice is at 0 C will heat up to temp t, say. Then it becomes a straight forward heat exchange problem.