In order to determine the heat absorbed or given by a metal it is important to determine the heat loss or gained by calorimeter
If we dip a hot metal piece in a calorimeter, it will lose energy which will be absorbed by calorimeter
The heat absorbed by calorimeter = heat loss by metal
the heat absorbed by calorimeter = heat capacity of calorimter X change in temperature
so we should have the value of heat absorbed by calorimeter which will be equal to the heat loss by metal
heat loss by metal = mass of metal X specific heat of metal X change in temperature
thus we can calculate the specific heat of metal.