The values should be equal in magnitude, but opposite in sign if all the energy is transferred from the hot water to the cold water. The values are opposite in sign but the magnitude of the values is not the same. Since the magnitudes of the heat transfers are different, some of the heat must be transferred to something else. The missing heat is the heat that is transferred to the calorimeter or the surroundings. So, the heat that is released by the hot water is absorbed by the cold water and the calorimeter.
All equation eq.
13 says is that the amount of heat absorbed by the water, q cw , plus the amount of heat absorbed by the calorimeter, q cal , is equal in magnitude but opposite in sign to the amount of heat released by the hot water, q hw . Since q cal will be different for different temperature changes knowing q cal for the mixing of these two samples of water will not be helpful for determining the q of other reactions. The heat capacity of the calorimeter needs to be found. If the heat capacity of the calorimeter is known, then the amount of heat that the calorimeter absorbs can be determined for almost any temperature change. T cal eq.