Final answer:
The final temperatures of copper and gold spheres with the same mass differ when the same amount of heat is added due to their different specific heat capacities, which is a measure of the energy needed per unit mass to change the temperature by one degree Celsius.
Step-by-step explanation:
The reason for the different final temperatures when the same amount of heat is added to copper and gold spheres with the same mass and initial temperature is best explained by the specific heat capacities of the two spheres being different. Specific heat capacity is a property that indicates how much heat energy is needed to raise the temperature of a unit mass of a substance by one degree Celsius. Different materials require different amounts of energy to change their temperature. Since copper and gold have different specific heat capacities, the energy added causes different temperature changes in each material. For example, if copper has a lower specific heat capacity than gold, it would take less heat to raise the temperature of the copper sphere by a given number of degrees compared to the gold sphere.