Ice-Water Calorimetry and Final State
100 g of ice at 0 °C is added to 300 g of water at 60 °C contained in a 200 g aluminium calorimeter. The specific heat capacity of water is 4.2 J g⁻¹ °C⁻¹, that of aluminium is 0.90 J g⁻¹ °C⁻¹, and the latent heat of fusion of ice is 336 J g⁻¹. A student predicts that the final temperature will be 0 °C because the ice will cool the water until some ice remains. Another student says all the ice will melt and the final temperature will be above 0 °C. The calorimeter is assumed to be well insulated and no heat is lost to the surroundings. The class is asked to settle the disagreement by calculation, and then to find how much ice at 0 °C would have to be added for some ice to remain at the end.
1. Determine whether all the ice melts. Support your answer with heat calculations.
Read the worked answer
Heat released by water cooling to 0 °C: 300×4.2×60 = 75,600 J. Heat released by aluminium calorimeter cooling to 0 °C: 200×0.90×60 = 10,800 J. Total available = 86,400 J. Heat needed to melt 100 g ice = 100×336 = 33,600 J. Since 86,400 J > 33,600 J, all the ice melts and much heat remains.
2. Calculate the final temperature if all the ice melts.
Read the worked answer
After melting, the remaining heat is 86,400−33,600 = 52,800 J. The final water mass is 300+100 = 400 g. Heat capacity of water = 400×4.2 = 1680 J °C⁻¹; calorimeter = 200×0.90 = 180 J °C⁻¹; total = 1860 J °C⁻¹. Rise in temperature = 52,800/1860 ≈ 28.4 °C. Since the mixture started at 0 °C after melting, final temperature ≈ 28.4 °C.
3. Find the minimum mass of ice at 0 °C that would leave some ice unmelted in this calorimeter. Explain why the final temperature would then be 0 °C.
Read the worked answer
For some ice to remain, the heat available must be less than that needed to melt all added ice. The minimum mass is m = 86,400/336 ≈ 257 g. If more than about 257 g of ice at 0 °C is added, not all of it melts. The final temperature then stays at 0 °C because any heat transferred to the mixture is used as latent heat to melt ice at 0 °C rather than to raise the temperature.