20 ml of 80°c water is mixed with 20 ml of 0°c water in a perfect calorimeter. what is the final temperature?

To calculate for the final temperature, we need to remember that the heat rejected should be equal to the absorbed by the other system. We calculate as follows:

Q1 = Q2
(mCΔT)1 = (mCΔT)2

We can cancel m assuming the two systems are equal in mass. Also, we cancel C since they are the same system. This leaves us,

 (ΔT)1 = (ΔT)2
(T - 80) = (0 - T)
T = 40°C