Question
A chef takes four pans from different parts of her kitchen and puts them in two stacks. The diagram above shows the pans before they touch each other. Use the information in the diagram to answer the question.
After the pans have been touching for a while, which of the two bottom pans will be cooler, and why?
Responses
a
The smaller bottom pan will be cooler than the larger bottom pan, because less energy has to transfer for the molecules to reach the same temperature as the molecules of the top pan.
The smaller bottom pan will be cooler than the larger bottom pan, because less energy has to transfer for the molecules to reach the same temperature as the molecules of the top pan.
b
The larger bottom pan will be cooler than the smaller bottom pan. It started with more total energy, so less energy had to transfer for both pans to reach the same total energy.
The larger bottom pan will be cooler than the smaller bottom pan. It started with more total energy, so less energy had to transfer for both pans to reach the same total energy.
c
The larger bottom pan will be cooler than the smaller bottom pan, because the energy that transferred to it will have spread out over more molecules.
The larger bottom pan will be cooler than the smaller bottom pan, because the energy that transferred to it will have spread out over more molecules.
d
Both pans will be the same temperature because both of the top pans had the same amount of energy to transfer and the molecules in the bottom pans start with the same energy.
After the pans have been touching for a while, which of the two bottom pans will be cooler, and why?
Responses
a
The smaller bottom pan will be cooler than the larger bottom pan, because less energy has to transfer for the molecules to reach the same temperature as the molecules of the top pan.
The smaller bottom pan will be cooler than the larger bottom pan, because less energy has to transfer for the molecules to reach the same temperature as the molecules of the top pan.
b
The larger bottom pan will be cooler than the smaller bottom pan. It started with more total energy, so less energy had to transfer for both pans to reach the same total energy.
The larger bottom pan will be cooler than the smaller bottom pan. It started with more total energy, so less energy had to transfer for both pans to reach the same total energy.
c
The larger bottom pan will be cooler than the smaller bottom pan, because the energy that transferred to it will have spread out over more molecules.
The larger bottom pan will be cooler than the smaller bottom pan, because the energy that transferred to it will have spread out over more molecules.
d
Both pans will be the same temperature because both of the top pans had the same amount of energy to transfer and the molecules in the bottom pans start with the same energy.
Answers
GPT-4o mini
To determine which of the two bottom pans will be cooler after they have been touching, we should consider how heat transfer works when two surfaces are in contact.
When the top pans come into contact with the bottom pans, thermal energy will transfer from the hotter top pans to the bottom pans until equilibrium is reached. The factors that influence how the temperatures of the bottom pans will change depend on their sizes (and thus the amount of molecules) and their initial thermal energy.
Let's analyze the provided responses:
- **Response a** argues that the smaller bottom pan will be cooler because it requires less energy to reach the temperature of the top pan. However, this reasoning does not fully account for the fact that the larger pan may have received more energy overall due to its capacity to absorb heat.
- **Response b** suggests that the larger bottom pan will be cooler because it started with more total energy, implying that less energy would need to be transferred to maintain equilibrium. This logic is flawed as the total energy doesn’t necessarily dictate the temperature difference in this context.
- **Response c** states that the larger bottom pan will be cooler since the energy transferred to it will be spread over more molecules. This reasoning is grounded in the concept that a larger pan, with more mass, will have a lower temperature increase when the same amount of energy is distributed over more molecules, leading it to have a more significant heat capacity.
- **Response d** posits that both pans will end up at the same temperature because the top pans had equal energy and the bottom pans started at the same temperature. While touching pans will equilibrate, it doesn't address the size differences and how that affects the final temperatures.
Based on the explanation of heat transfer behavior, **Response c** is the most accurate:
**The larger bottom pan will be cooler than the smaller bottom pan, because the energy that transferred to it will have spread out over more molecules.**
This reflects the physical principle that larger objects can absorb heat without a significant rise in temperature compared to smaller objects.
When the top pans come into contact with the bottom pans, thermal energy will transfer from the hotter top pans to the bottom pans until equilibrium is reached. The factors that influence how the temperatures of the bottom pans will change depend on their sizes (and thus the amount of molecules) and their initial thermal energy.
Let's analyze the provided responses:
- **Response a** argues that the smaller bottom pan will be cooler because it requires less energy to reach the temperature of the top pan. However, this reasoning does not fully account for the fact that the larger pan may have received more energy overall due to its capacity to absorb heat.
- **Response b** suggests that the larger bottom pan will be cooler because it started with more total energy, implying that less energy would need to be transferred to maintain equilibrium. This logic is flawed as the total energy doesn’t necessarily dictate the temperature difference in this context.
- **Response c** states that the larger bottom pan will be cooler since the energy transferred to it will be spread over more molecules. This reasoning is grounded in the concept that a larger pan, with more mass, will have a lower temperature increase when the same amount of energy is distributed over more molecules, leading it to have a more significant heat capacity.
- **Response d** posits that both pans will end up at the same temperature because the top pans had equal energy and the bottom pans started at the same temperature. While touching pans will equilibrate, it doesn't address the size differences and how that affects the final temperatures.
Based on the explanation of heat transfer behavior, **Response c** is the most accurate:
**The larger bottom pan will be cooler than the smaller bottom pan, because the energy that transferred to it will have spread out over more molecules.**
This reflects the physical principle that larger objects can absorb heat without a significant rise in temperature compared to smaller objects.