How much heat is required to change the temperature of a 15 g aluminum can with 100 g of water from 24.5°c to 55°c?

Heat capacity of aluminium = 0.900 J/g°C
While heat capacity of water = 4.186 J/g°C
Heat = heat gained by water + heat gained by aluminium 
Heat gained by water = 100 × 4.186 × 30.5 
                                   = 12767.3 Joules
Heat gained by aluminium = 15 × 0.9 × 30.5 
                                          = 411.75 Joules
Heat required = 13179.05 Joules or 13.179 kJoules

Because a model would make the investigation easier to understand

Solubility would be your answer.