Final answer:
The ratio of the mass of copper to water when identical amounts of heat transfer occur causing identical changes in temperature is 1:1.00.
Step-by-step explanation:
In this scenario, identical amounts of heat transfer into different masses of copper and water, causing identical changes in temperature. The ratio of the mass of copper to water can be determined based on the principle that the amount of heat transferred depends on the mass of the system. The amount of heat transferred to cause a temperature change is directly proportional to the mass of the substance. Therefore, if it takes a certain amount of heat to cause a temperature change in a given mass of copper, it will take the same amount of heat to cause the equivalent temperature change in the same mass of water. The ratio of the mass of copper to water is 1:1.00.