Question

A student sets up four cups with 40 mL of water in each and adds different amounts of ice to each cup. The student measures the temperature of the water before and after the ice melts in each cup.
Which statement describes how the student can determine the connection between the temperature change and the transfer of kinetic energy?

Answer 1

Answer: Measure the temperature change in each cup and use calorimetry (Q = mcΔT and Q = mL for melting) to calculate the heat transferred. The temperature change of the water is a direct measure of the change in the average kinetic energy of its molecules, so:

- For each cup record mwater, Tinitial and Tfinal. Compute heat lost by water: Qlost = mwater · cw · (Tinitial − Tfinal).
- For the ice, compute the heat gained: Qgained = mice · Lf + mice · cw · (Tfinal − 0°C) (include warming of melted ice if needed; include warming of ice if it started below 0°C).
- In an insulated system Qlost ≈ Qgained. Comparing Qlost (or ΔT) for different amounts of ice shows how increasing ice mass increases energy transferred out of the water and therefore increases the decrease in kinetic energy (bigger |ΔT|).

You can also plot ΔT versus mass of ice to show the relationship. Control variables (same initial water temperature and volume, same ice temperature, minimal heat loss to surroundings) for valid results.