Final answer:
The mass of the ice cube can be found by equating the heat gained by the ice while warming, melting, and heating to the final temperature with the heat lost by the water and aluminum calorimeter cooling to the final temperature.
Step-by-step explanation:
To determine the mass of the ice cube, we must first understand that energy will be exchanged between the ice, the aluminum calorimeter, and the water until thermal equilibrium is reached. The ice must first warm up to 0 °C, melt, and then raise in temperature to the final temperature of 17.0 °C. The calorimeter and water will cool down to this same temperature. The heat gained by the ice will equal the heat lost by the water and calorimeter combined.
Let's denote the mass of the ice as m, in kilograms. The amount of heat required to warm the ice from -5.5 °C to 0 °C is given by q1 = m × c_ice × ΔT, where c_ice is the specific heat of ice. To melt the ice at 0 °C, we use q2 = m × L_fusion, where L_fusion is the heat of fusion of ice. Finally, to warm the melted ice from 0 °C to 17.0 °C, we need q3 = m × c_water × ΔT, where c_water is the specific heat of water.
The heat lost by the water is q4 = m_water × c_water × ΔT, and the heat lost by the calorimeter is q5 = m_cal × c_al × ΔT. The sum of the heat lost by water and the calorimeter must equal the sum of the heats gained by the ice in all its transformations, so q1 + q2 + q3 = q4 + q5. By substituting the given values and solving for m, we get the mass of the ice.