Thermodynamics Homework Help: Finding Final Temperature in a Water-Ice Mixture

[Corneo]

I have a question about my Thermodynamics homework.

In an insulated container, $0.50 kg$ of water at $80^\circ C$ is mixed with $0.050 kg$ of ice at $-5.0^\circ C$. After a while, all the ice melts, leaving only the water. Find the final temperature $T_f$ of the water. The freezing point of water is $0^\circ C$

I need to find all the $Q$'s and set their sum to equal 0.

I have the Q for the water, Q for the ice, Q from fusion. $T_f$ is the same for all the substances. But my answer is still off.

$Q_{H_2 0}= 0.5 kg c_{H_2 0} ( T_f-80^\circ C )$
$Q_{ice}= 0.05 kg c_{ice} (T_f+5^\circ C)$
$Q_{f}= 0.05 kg L_f$

Is there another Q I haven't accounted for?

 

[CartoonKid]

what are the specific heat capacity of ice and water in your question? Are they being stated to be the same or different? If different, then you have to recheck your $Q_{ice}$.

 

[Corneo]

They are different. What is wrong with my $Q_{ice}$?

 

[Doc Al]

$Q_{ice}= 0.05 kg c_{ice} (T_f+5^\circ C)$

Your error is treating the ice as if it remained ice. You need to treat it in three parts:
(1) heating of 0.05 kg of ice from -5 to 0
(2) melting of ice (you have that piece already)
(3) heating of 0.05 kg of water from 0 to T_f

 

[Corneo]

Ah... thank you very much.