The Melting Ice Cube Race · AI Generator #GEN-6ED11B43

Physics · thermodynamics

Problem

Two identical ice cubes are removed from a freezer at −10°C-10°\text{C} and placed in different environments to melt. Ice cube A is placed in a room at 25°C25°\text{C}, while ice cube B is placed in a room at 50°C50°\text{C}. Both rooms have the same air circulation, so the heat transfer coefficient is identical for both cubes. Assuming that heat transfer to each ice cube is proportional to the temperature difference between the cube and its surroundings, calculate the ratio of the time it takes ice cube A to completely melt to the time it takes ice cube B to completely melt. Given data: - Specific heat of ice: cice=2100  J/(kg⋅K)c_{ice} = 2100\;\text{J/(kg·K)} - Latent heat of fusion: Lf=334,000  J/kgL_f = 334,000\;\text{J/kg} - Each ice cube has mass m=20  gm = 20\;\text{g}

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