Finding the Mass of an Aluminum Cup Based on Heat Transfer in a System

[jincy34]

Homework Statement

A 105.05 g ice cube at -15°C is placed in an aluminum cup whose initial temperature is 73°C. The system comes to an equilibrium temperature of 24°C. What is the mass of the cup?

Homework Equations

Q=mc (delta T)

The Attempt at a Solution

the sum of total heat in the system is equal to zero.
Qice+Qaluminium cup=0
MiceCice(delta T)+MaluminiumCaluminium(delta T)=0
I solved for mass of aluminium cup, and got 0.1951 kg. But, it is wrong.
Please help.

 

[hage567]

Since the ice melts, I think you need to take into account the heat of fusion, Q=mL, where m is the mass of the ice and L is the latent heat of fusion.

Try that.

 

[jincy34]

I did, and got 0.8633 kg. But, that is wrong too.

 

[hage567]

You need to include terms for:
the heat required to bring the ice from -15 degrees to 0 degrees
the heat of fusion to melt the ice at 0 degrees to water at 0 degrees
the heat required to bring the water at 0 degrees to water at the final temperature of 24 degrees

This will be equal to the heat the aluminum cup loses.

 

[jincy34]

Thank you very much.