Thermal Energy problem - Ice placed in water

[Bobazoide]

Homework Statement

An ice cube at its freezing point is placed in nested Styrofoam cups which contain 240g of water at 21.5 degrees C. If the final equilibrium temperature when the last trace of ice melts is 15 degrees C, what was the mass of the ice cube?

Homework Equations

mCΔt = -mCΔt

The Attempt at a Solution

My problem here is the logistics of the question itself. As the ice melts, it turns into water, which has a different heat capacity than that of ice. I'm not sure if I have to take this constantly changing heat capacity into account, since I'm only in grade 11 of high school and my class hasn't been taught complex mathematics, so our teacher expects us to solve this with basic arithmetic. I'm not sure if he wants us to just use a constant specific heat capacity or not, but logically it would have to change.

 

[ehild]

Homework Statement

An ice cube at its freezing point is placed in nested Styrofoam cups which contain 240g of water at 21.5 degrees C. If the final equilibrium temperature when the last trace of ice melts is 15 degrees C, what was the mass of the ice cube?

Homework Equations

mCΔt = -mCΔt That line has no sense.

The Attempt at a Solution

My problem here is the logistics of the question itself. As the ice melts, it turns into water, which has a different heat capacity than that of ice. I'm not sure if I have to take this constantly changing heat capacity into account, since I'm only in grade 11 of high school and my class hasn't been taught complex mathematics, so our teacher expects us to solve this with basic arithmetic. I'm not sure if he wants us to just use a constant specific heat capacity or not, but logically it would have to change.

The ice cube is placed into the water at its freezing point. The temperature of ice will not change until it melts, so you do not need to calculate with the heat capacity of the ice. You need to know the latent heat of fusion of ice, and the specific heat capacity of water.

What is the equation you need to use?

ehild