I am doing a AP Chemistry lab in which we determine the heat capacity of a calorimeter (a concept that seems like it should depend on a lot more than just the calorimeter.) We have to calorimeters with water of different temperatures (which is tracked the whole time) but equal mass. We then mix them. We then track temperature again. We then extrapolate to the time of mixing (with a linear regression for some reason.) We look at how much energy was lost by the hot water and gained by the cold water based on all 3 lines (each calorimeter before, and the mixed calorimeter after.) Next we take the difference of the energy gained and energy lost at a single instant divide by the temperature change of the cold calorimeter (I have no idea why the cold one) and this is the calorimeters heat capacity.
I am having trouble understanding this, since at a single instance, the energy gained by the hot water and lost by the cold should be equal, and any difference would be error. It also seems completely random to divide by the temperature of the cold water and not the hot. What is going on here?
P.S. Later in the lab, extrapolating to the time of mixing is used to find the energy change due to a reaction, which makes more sense.
P.S.S One Calorimeter was fully mixed into the other (I forget which one, but either way does not make sense, and calorimeters themselves (like the material it was made from) had negligible heat capacity.))
P.S.S.S It is the teacher's first year doing this lab I think.