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4. An ice cube at 0.00 °C is placed in your dog's dish which contains 2500.0 grams of water at 27.0°C on a warm day. After the ice melts in your dog's extremely well insulated dog bowl, you note that the temperature of the water in the bowl has dropped to 18.0 °C. What was the mass of

the ice cube?

User Iamdeit
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1 Answer

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Answer:

289.8 grams.

Step-by-step explanation:

When the ice cube melts, it absorbs heat from the water in the dog's dish and undergoes a phase change from solid to liquid at 0.00 °C. The heat absorbed by the ice cube can be calculated using the formula:

Q = m * L

where Q is the heat absorbed, m is the mass of the ice cube, and L is the heat of fusion of water (which is 334 J/g). The heat absorbed by the ice cube is then equal to the heat released by the water, which can be calculated using the formula:

Q = m * c * ΔT

where m is the mass of the water, c is the specific heat capacity of water (which is 4.184 J/g·°C), and ΔT is the change in temperature of the water.

Setting the two formulas equal to each other, we get:

m * L = m * c * ΔT

Solving for m, we get:

m = (c * ΔT * m_water) / L

where m_water is the mass of the water in the dog's dish.

Substituting the given values, we get:

m = (4.184 J/g·°C * (27.0 °C - 18.0 °C) * 2500.0 g) / (334 J/g)

m ≈ 289.8 g

Therefore, the mass of the ice cube was approximately 289.8 grams.

User Dagronlund
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