A 0.0475 kg ice cube at −30.0°C is placed in 0.577 kg of 35.0°C water in a very well insulated container. The latent heat of fusion of water is 334 kJ/kg, the specific heat of ice is 2092 J/(kg · K), and the specific heat of water is 4184 J/(kg · K). The system comes to equilibrium after all of the ice has melted. What is the final temperature of the system?

HINTS: This problem must be broken into pieces. Think about it chronologically: The ice can't melt until it warms up to its melting point. The ice will then melt, but will still be at zero degrees. You will need to then consider the melted ice warming to the equilibrium temperature, and the original water cooling to the equilibrium temperature.

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  1. Nuts to the hint. The sum of the heats gained in the system is zero (some gain, some lose)

    Heatwarmingice+Heatfusion+heatwarming melted ice+heat warming orig water=0
    let mi be the massice, mw mass of the orginal water.

    mi*Ci*(0+30+ mi*Li+ mi(cw(tf-30)+mw*cw*(Tf-35)=0
    solve for Tf

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