Answer:
In a perfect world, where the calorimeter does not exchange any heat with its contents, the amount of heat lost by the hot water will be equal to the amount of heat gained by the cool metal pieces. This is due to the principle of conservation of energy, which states that energy cannot be created or destroyed, only transferred from one form to another. Therefore, the number of calories gained by the metal pieces will be equal to the number of calories lost by the hot water, which is 75 calories.
Step-by-step explanation:
In summary, according to the principle of conservation of energy, in a perfect world where a calorimeter does not exchange any heat with its contents, the number of calories gained by the cool metal pieces will be equal to the number of calories lost by the hot water, which is 75 calories.