Thermodynamics question regarding latent heat of fusion of ice.

[Bigdutchman]

Homework Statement

(a) An insulated copper container of mass 0.250 kg contains 0.350 kg water. Both the container and the water are initially at 25.0 0C. Then 0.012 kg of ice at 0.0 0C is added to the container. Eventually the container and contents reach thermal equilibrium at 21.7 0C.

(i) What is the total heat released (in J) by the copper container and the 0.350 kg water as they cool down from 25.0 0C to 21.7 0C?

I got 5154.104J (Correct answer)


(ii) Determine the latent heat of fusion of ice. <---- Can't do this mofo. Keep getting different answer. They have 3.39x10^5 J/kg. Can someone pls show me how they got that? THANKS!

Homework Equations

Q=mc delta T
Q=mL

The Attempt at a Solution

One of my failed attempts:
5154/0.012 = 4.29x10^5 J/kg

 

[Andrew Mason]

You are not taking into account the heat lost by the copper and the water.

AM

 

[Bigdutchman]

how do i do that? lol

 

[Andrew Mason]

how do i do that? lol

If the copper changes temperature by \Delta T how much heat does it lose? Do the same for water.

AM

 

[tcw46]

Q = mL for state changes. (mass, L being the heat needed, which is what you're trying to find)

and for heating of liquids, Q = mC * change in temp

heat lost by copper = -heat lost by water (i.e. heat is gained by water)
mC * change in temp for copper = - (mL + mC * change in temp for water)

rearrange to find L