How Do You Calculate the Final Temperature of a Mixture of Ice and Hot Water?

[Forceofmatter]

1. Homework Statement [/b]

A 20.0 g sample of ice at -10.0 degrees Celsius is mixed with 100.0 g of water at 80.0 degrees Celsius. Calculate the final temperature of the mixture assuming no heat loss to the surroundings. The heat capacities of H20 (solid) and H20 (liquid) are 2.08 J/g deg. Celsius and 4.18 J/g deg. Celsius respectively, and the enthalpy of fusion of ice is 6.01 kJ/mol.

The answer is 52.4 deg. Celsius. But I am unsure of how to get the answer. Please help asap. No heat loss means no heat (J) is lost to the environment, so you can basically ignore that part of the question.

2. Homework Equations
q=mc delta T
phase change formulas: there are none. Have to use a heating curve to change from solid to liquid and so on.

c=specific heat
q=heat in Joules
T=temperature in this case celsius

 

[Mapes]

How about an equation associated with phase changes?
What's the implication of the assumption of "no heat loss"?

 

[Borek]

phase change formulas: there are none.

Latent heat.