Thermodynamics quick Question

1. Nov 12, 2004

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?

2. Nov 12, 2004

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 $Q_{ice}$.

3. Nov 13, 2004

Corneo

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

4. Nov 13, 2004

Staff: Mentor

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

5. Nov 13, 2004

Corneo

Ah... thank you very much.