Two methods to represent calorimetry equations

In chemistry, the energy change of a system in a calorimeter can be modeled in more than one way. The common method is to label it -q_metal=q_water where the both the heat variables are q=constant x (T_final-T_initial). This leads to a consistent use of q in equations as long as it is remembered that one item side is negative.

Another method is to use q_metal=q_water where one side is q=constant x (T_final-T_initial) and the other is q=constant x (T_initial-T_final). This method relies on the side that is lower in temperature and increasing in temperature to be be (T_final-T_initial). The side higher in temperature and decreasing is the opposite with (T_initial-T_final).

It doesn’t matter which method is used as they are mathematically equivalent to each other.