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Ice at 0 °C is added to 1.0 kg of water at 20 °C, cooling it down to 10 °C. Determine how much ice was added.

User Tibs
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Final answer:

Approximately 0.125 g of ice was added to cool the water from 20 °C to 10 °C.

Step-by-step explanation:

First, we need to calculate how much heat is needed to cool the water from 20 °C to 10 °C. We can use the formula:
Q = mcΔT

where Q is the heat transfer, m is the mass of water, c is the specific heat capacity of water, and ΔT is the change in temperature.

Assuming the specific heat capacity of water is approximately 4.18 J/g°C, the mass of water is 1.0 kg, and the change in temperature is 20 °C - 10 °C = 10 °C, we can calculate the heat transfer as:

Q = (1.0 kg)(4.18 J/g°C)(10 °C) = 41.8 J

Now, we need to calculate the amount of heat released by the ice to cool the water. We can use the formula:
Q = mL

where Q is the heat transfer, m is the mass of ice, and L is the latent heat of fusion of ice.

Assuming the latent heat of fusion of ice is approximately 334 J/g, we can calculate the mass of ice as:

m = Q / L = 41.8 J / 334 J/g ≈ 0.125 g

Therefore, approximately 0.125 g of ice was added to cool the water from 20 °C to 10 °C.

User Alberto C
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