What Is the Final Temperature When Ice Melts in Water?

[cugirl]

Homework Statement

An insulated cup contains 1kg of water initially at 20 C. 0.50 kg of ice, initially at
0 C is added to the cup of water. The water and ice are allowed to come to thermal equilibrium. The specific heat of ice is 2000 J/kg oC, the specific heat of water 4186 J/kg oC, the latent heat of fusion of water is 33.5x104J/kg. What is the final temperature of the water?

(A) 0 C
(B) 1.2 C
(C) 4.6 C
(D) 9.2 C
(E) 15.2 C

Homework Equations

Q_gain(ice) = Q_lost(water)
mc(Ti-Tf) = mLf + mc(Tf-0)

The Attempt at a Solution

Q_gain(ice) = Q_lost(water)
mc(Ti-Tf) = mLf + mc(Tf-0)
(1.0)(4186)(20 - Tf) = (.5)( 33.5x104 ) + (.5)(4186)(Tf)
83,720 – 4186Tf = 167,500 + 2093 Tf
-83780= 6279 Tf
-13.3 = Tf

 

[mgb_phys]

Correct method
But what is the total energy needed to melt the ice?
How much energy can you get from the initial water before it cools to 0c?