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A scientist adds 421 g of water at 26°C to ice at 0°C. If the final temperature of this closed system is 0°C, determine how much ice melted.

User Dav Evans
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Final answer:

By using the conservation of energy principle and the specific heat capacity and latent heat of fusion for water, it is calculated that approximately 136.58 g of ice would have melted when 421 g of water at 26°C is added to ice at 0°C.

Step-by-step explanation:

To determine how much ice melted when 421 g of water at 26°C is added to ice at 0°C, resulting in a final temperature of 0°C, we use the concept of conservation of energy. The heat lost by the water (cooling from 26°C to 0°C) will be used to melt a portion of the ice.

  1. Calculate the heat lost by the water: Q = mcΔT, where m is the mass of the water, c is the specific heat capacity, and ΔT is the change in temperature.
  2. Calculate the mass of ice melted: Use the heat of fusion for ice, Q = mL, where L is the latent heat of fusion and solve for m.

Given that the specific heat capacity of water is approximately 4.18 J/g°C and the latent heat of fusion of ice is about 334 J/g, we proceed with the calculations.

Heat lost by water: Q = (421 g)(4.18 J/g°C)(26°C) = 45615.56 J

Mass of ice melted: Q = (m)(334 J/g), solving for m we get m = 45615.56 J / 334 J/g = 136.58 g.

Hence, approximately 136.58 g of ice melted.

User Delp
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