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A copper cube with a mass of 100 grams is heated in a boiling water bath to 100.0 Celsius. The cube is removed from the bath and placed on a very large block of ice which is at a temperature of 0.00 Celsius. What is the maximum mass of ice that could conceivably be melted by the heat exchange, assuming all the thermal energy is used to melt the ice? The specific heat of copper is 0.39 J/g-C and the enthalpy of fusion for water is 334 J/g.

User Tomino
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2 Answers

4 votes

Final answer:

The maximum mass of ice that could be melted by the heat exchange is approximately 11.68 grams.

Step-by-step explanation:

To find the maximum mass of ice that could be melted by the heat exchange, we need to calculate the amount of thermal energy transferred from the copper cube to the ice. We can use the equation Q = m * c * ΔT, where Q is the thermal energy, m is the mass, c is the specific heat, and ΔT is the change in temperature.

First, let's calculate the thermal energy transferred by the copper cube in the boiling water bath. The cube's mass is 100 grams, the specific heat of copper is 0.39 J/g-C, and the temperature change is 100.0 - 0.0 = 100.0 Celsius. Therefore, Q1 = (100g) * (0.39 J/g-C) * (100.0 C) = 3900 J.

Next, let's calculate the thermal energy required to melt the ice. The enthalpy of fusion for water is 334 J/g. Assuming that all the thermal energy is used to melt the ice, we can calculate the maximum mass of ice that could be melted using the equation Q2 = m * ΔHf, where Q2 is the thermal energy, m is the mass, and ΔHf is the enthalpy of fusion. Rearranging the equation, we have m = Q2 / ΔHf.

Since the thermal energy transferred by the copper cube is equal to the thermal energy required to melt the ice, we can equate Q1 and Q2: 3900 J = m * (334 J/g). Solving for m, we get m = 3900 J / 334 J/g = 11.68 g.

Therefore, the maximum mass of ice that could be melted by the heat exchange is approximately 11.68 grams.

User Workflow
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5 votes

Answer:

The copper cube has a mass of 11.68 grams

Step-by-step explanation:

Step 1: Data given

Mass of the copper cube = 100 grams

Temperature of water = 100°C

Temperature of ice = 0°C

Specific heat of copper = 0.39J/g°C

Enthalpy of fusion of water = 334 J/g

Step 2: Calculate the energy for cooling the copper

energy in the copper as it cools from 100º to 0º = 0.39 J/g°C * 100g *100°C = 3900 J

Step 3: Calculate the mass of the copper cube

3900 J / 334 J/g = 11.68 grams

The copper cube has a mass of 11.68 grams

M = 3900/334 = 11.68 g

change is 3900 J

User Fluter
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