hi! what is the specific heat capacity (heat fusion) of ice?

this is just one part of a greater problem I would really appreciate an explanation for ..
here goes ...

water and ice co-exist (or something like that ...) at 0 degrees celsius. So, i have water and ice at 0 degrees celsius in a calorimeter, and the ice weighs 50 grams. I know that when a 35 gram metal ball, at 100 degrees celsius with a specific heat capacity of .442J/gXdegrees celsius is placed in this ice/water solution, the heat released from the metal ball will only go into the ice to heat the ice (heat does not effect the water, it just goes to the ice and melts the ice ..). So, in the end, we have our ice that was first 50 grams, now melted to 48 grams. And the metal ball has gone from 100 degrees to 0 degrees.

How can I measure the specific heat capacity of this ice. I know that the ball released 1547 juoles of energy (q=m X C X change in temp). But, im stuck on calculating the heat capacity needed to raise 1g of ice by 1 degree celsius.

all help is appreciated ... thank you

note:the ice has not increased or decreased in temperature, which means I would be dividing by zero,

c=q/(mass X change in temp)

the change in temp of the ice is zero and i dont know whether to use the beginning mass of the ice or the end mass of the ice because the ice melted from 50 grams to 48 grams .... the temp is still 0 degrees celsius ..

One of those seemingly simple problems...

You are correct that your ice water system
has not changed temperature. The heat from the metal ball has been used to make a phase change from ice to water. you've measured the heat of fusion for your 2 grams of Ice.

Your original question is what is the "heat capacity of ice?" Your system was already at equilibrium temperature. To measure the heat capcity of Ice I would start again with a measured mass of water. A measured mass of ice that is colder than 0C. When you place the ice into the water the system will change to zero degrees C equilibrium. With your new found information for the heat of fusion of the ice you can correct for the mass of ice that was melted by the water and figure only the temperature change of the mass of ice.. (50 grams of Ice warmed from -40C to 0 C).

Your Instructor has made a very good thought provoking experiment that is about as safe as can be.