# Ice Cubes & Liquid Water - Thermodynamics

1. Jun 14, 2012

### ahaanomegas

1. The problem statement, all variables and given/known data

Four ice cubes at exactly $0 \ { }^{\circ} \text{C}$ with a total mass of $53.5 \ \text{g}$ are combined with $115 \ \text{g}$ of water at $75 \ { }^{\circ} \text{C}$ in an insulated container. If no heat is lost to the surroundings, what will be the final temperature of the mixture?

2. Relevant equations

No specific formulas. Just basic thermodynamics, as explained in the solution.

3. The attempt at a solution

Magnitude of heat gained by Ice cubes = Magnitude of heat lost by Water
$4m_{\text{one ice cube}}c_{\text{ice}}(T'-T_{\text{0-ice}})=m_{\text{water}}c_{\text{water}}(T_{\text{0-water}}-T')$
From here, I used the numbers in my book and got the wrong answer [below]. :(
21 Degrees Celsius

Last edited: Jun 14, 2012
2. Jun 14, 2012

### Staff: Mentor

You mean you end with water and ice at 21°C?

3. Jun 14, 2012

### ahaanomegas

Yes, Sir, but that's my answer, not the correct one.

4. Jun 14, 2012

### Staff: Mentor

Sigh.

Have you ever seen ice at 21°C?

5. Jun 14, 2012

### ahaanomegas

Ah! I guess I forgot the latent heat. That was obliviously silly. Thanks for helping me through my silliness! I'll re-try the problem once I can and, hopefully, I'll get it right this time around. :) Sorry and thank you, again.