Question

A 10.000g ice cube is added to 100.000g of water at 80.0 oC in a calorimeter. The final temperature of the water in the calorimeter is 65.5 oC. How much heat in kilojoules was needed to melt the ice cube?

Answer 1

The amount of heat needed to melt the ice cube is 16.7 kJ.

Step-by-step explanation:

To calculate the amount of heat needed to melt the ice cube, we can use the principle of energy conservation. The heat gained by the water is equal to the heat lost by the ice cube.

We know that the specific heat capacity of water is 4.184 J/(g·°C) and the heat of fusion of ice is 334 kJ/kg. Assuming the final temperature is 0°C after melting, we can calculate the heat needed:

Heat gained by water = Heat lost by ice cube

Mass of water × specific heat capacity of water × temperature change = Mass of ice cube × heat of fusion of ice

(100,000 g water) × (4.184 J/(g·°C)) × (65.5°C - 80.0°C) = (10,000 g ice cube) × (334,000 J/g)

Solving this equation, we find that the heat needed to melt the ice cube is 16.7 kJ.