Final answer:
If one gold dollar increases the water's temperature by 3.0°C, ideally, five gold dollars would increase it by 15.0°C, assuming linear scaling and no significant external heat loss.
Step-by-step explanation:
The change in temperature of water when gold dollars are moved from boiling water into it, is an example of calorimetry, a part of thermodynamics within the field of physics. If one gold dollar increased the water's temperature by 3.0°C, the temperature increase with five gold dollars depends on the assumption that all other conditions remain same and that there is no significant loss of heat to the surroundings. Considering that each gold dollar transfers a certain amount of heat, it can be predictable that five gold dollars will transfer five times more heat to the water, assuming the capacity of the cold water to absorb heat is not exceeded.
Therefore, if one coin causes a 3.0°C increase, five coins would cause a 15.0°C increase in temperature, under ideal conditions. It's important to note that this answer assumes linear scaling, which in real-world conditions may not be accurate due to other factors like heat loss to the environment, the initial temperature of the water, if it is able to absorb all the heat, etc.