The law of conservation of energy is used to explain how a calorimeter works.
A physical change or chemical reaction takes place causing a change in potential energy. This causes a change in kinetic energy (temperature) of the water.
Calorimetry problems can be solved in three steps.
Step 1: Finding qrxn (system) or qwater based on the information given. The equations qsystem = nΔH or qwater = mcΔT will have to be used.
Step 2: Stating that qsystem = - qcalorimeter (water). If qsystem was calculated, then qcalorimeter is also known.
Step 3: Finding the requested information with the q value.