Final answer:
The temperature of the hot alloy decreases primarily due to heat transfer to the water, conserving energy until reaching thermal equilibrium.
Step-by-step explanation:
When a 58.8-gram piece of hot alloy is placed in 125 grams of cold water in a calorimeter, the temperature of the alloy decreases by 106.1 degrees Celsius predominantly because of heat transfer to the water. This is in accordance with the principle of conservation of energy. In a calorimeter, the system is designed to prevent heat loss to the surroundings, thus, the heat lost by the hot alloy is gained by the colder water until thermal equilibrium is reached, meaning both the alloy and the water will attain the same temperature. There is no indication of a chemical reaction or significant expansion of the alloy contributing to the temperature change.