You mix mI = 1.2 kg of ice at TI = -19°C with mW = 3.4 kg of water at TW = 86°C in an insulated container. The specific heats of ice and water are cI = 2.10×103 J/(kg⋅°C) and cW = 4.19×103 J/(kg⋅°C), respectively, and the latent heat of fusion for water is Lf = 3.34 × 105 J/kg.
Enter an expression for the final equilibrium temperature of the mixture in terms of the defined quantities.
Hints :
Heat problems involving phase changes generally need to be dealt with step by step, taking into account that when there is no temperature difference, there will be no
-In an isolated system all the heat lost by any components of the system is gained by the system’s other components.
-Use the relation among heat, mass, specific heat, and temperature change.
-First, the ice reaches 0°C. Then it starts melting while the warmer water continues cooling. Now consider whether the ice melts completely before the warmer water cools to 0°C.
-Use the relation among heat, mass, and latent heat that holds for phase changes.
-The ice melts completely. The cooling, originally warm water then warms the water resulting from the melted ice until the mixture reaches equilibrium temperature.
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