Final answer:
The question involves finding the temperature of the heating element for a copper-bottomed pot given that a similar aluminum-bottomed pot has a heating element at 156.0°C and both are boiling water at the same rate. Using principles of thermal conductivity and heat transfer, the temperature of the copper heating element would be lower due to copper's higher thermal efficiency.
Step-by-step explanation:
The question is related to the concept of heat conduction in Physics, specifically how it applies to different materials with different thermal conductivities dealing with the transfer of heat at the same rate. When two pots, one with an aluminum bottom and the other with a copper bottom, are boiling water at the same rate, and the aluminum pot maintains a temperature difference of 156.0°C on the heating element, we can use this information to find the temperature of the heating element for the copper bottom.
The heat conduction through the materials can be described by the equation for the rate of heat transfer, which takes into account the material's thermal conductivity, the cross-sectional area, the temperature difference, and the thickness of the material.
Knowing that copper has a higher thermal conductivity than aluminum, and assuming all other factors (such as the thickness and cross-sectional area of the pot's bottom and the rate at which water is boiling away) remain constant, the temperature difference across the copper bottom will be smaller because copper transfers heat more efficiently. Therefore, the temperature of the heating element on which the copper bottom rests must be lower than 156.0°C, the temperature for the aluminum pot.