First thing to do, you need the specific heats of the substances in the system and the heat of fusion of ice. From literature, they are as follows:
Copper = 0.385 kJ/kg.°C
Lead = 0.127 kJ/kg.°C
Water = 4.181 kJ/kg.°C
heat of fusion of ice = 333.6 kJ/kg
Next, we let the final temperature be T in units of °C.
The ice and water are in equilibrium thermally, so the temperature should be 0°C. By the law of conservation of energy,
Heat lost = Heat gained
Heat lost by lead = [ 0.75 (0.127 ) (255-T) ]kJ
Heat from the melting ice = [(0.018 ) 333.6 ]kJ
Heat gained from 0 to T = [(4.181) (T) (0.16 + 0.018)] kJ
Heat to raise the calorimeter to T = 0.0385T] kJ
Equating heat lost and heat gain, we can calculate for T. Therefore,
(0.75) (0.127) (255-T) = 6.0048 + 0.7442T + 0.0385T
T = 20.83 C
