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Use the specific heat capacity of ice when you are raising the temperature of ice. Because the ice is already at 0C, you don't need to use the specific heat capacity of ice because the ice doesn't get warmer than 0C. Instead, use the heat of fusion to calculate the energy needed to melt the ice, then use specific heat of liquid water to calculate the energy needed to raise the temperature.
for these types of problems, I would highly encourage drawing a diagram---this helps you keep track of the state of the substance at hand so you now the correspond specific heat capacity. since ice melts into water before the water raises temperature, you need to use the specific heat capacity of water.
DamianW wrote:In this problem do you have to account for fusion as well ?
Yes! Since there is a difference in temperature between the ice cube and the water, the ice cube would first melt (enthapy of fusion) and then have a temperature change.
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