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

AI Thread Summary
To calculate the final temperature of a mixture of ice and hot water, the heat gained by the ice must equal the heat lost by the water, assuming no heat loss to the surroundings. The specific heat capacities of ice and water, along with the enthalpy of fusion, are essential for determining the energy transfer during the phase change. The equation q=mcΔT is used to calculate the heat exchange, where q is the heat in Joules, m is mass, c is specific heat, and ΔT is the change in temperature. The final temperature of the mixture is determined to be 52.4 degrees Celsius. Understanding the implications of no heat loss is crucial for accurate calculations.
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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
 
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How about an equation associated with phase changes?
What's the implication of the assumption of "no heat loss"?
 
Forceofmatter said:
phase change formulas: there are none.

Latent heat.
 
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