Question
7. 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 in contact with the top pans, we need to consider how heat transfer works and the properties of the pans involved.
**Responses Analysis:**
- **Response a:** This response suggests that the smaller bottom pan will be cooler because it requires less energy transfer to match the temperature of the top pan. While it's true that smaller objects may reach thermal equilibrium sooner, it doesn't justify that the smaller pan will be cooler than the larger one after energy transfer takes place.
- **Response b:** This response argues that the larger bottom pan will be cooler because it started with more total energy. This is misleading since energy transfer depends not just on starting energy levels but also on how that energy is distributed among the molecules.
- **Response c:** This option states that the larger bottom pan will be cooler because the energy that transferred to it will have spread out over more molecules. This is the most scientifically sound option. When a larger pan (which has more mass) receives energy, that energy is distributed across more molecules, leading to a smaller increase in temperature compared to a smaller pan that receives the same amount of energy.
- **Response d:** This claim that both pans will be at the same temperature because of equal energy transfer from the top pans doesn't hold because the bottom pans may have different capacities to absorb heat due to their sizes and masses.
Given the information and the nature of heat transfer, the most accurate response would be:
**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.
**Responses Analysis:**
- **Response a:** This response suggests that the smaller bottom pan will be cooler because it requires less energy transfer to match the temperature of the top pan. While it's true that smaller objects may reach thermal equilibrium sooner, it doesn't justify that the smaller pan will be cooler than the larger one after energy transfer takes place.
- **Response b:** This response argues that the larger bottom pan will be cooler because it started with more total energy. This is misleading since energy transfer depends not just on starting energy levels but also on how that energy is distributed among the molecules.
- **Response c:** This option states that the larger bottom pan will be cooler because the energy that transferred to it will have spread out over more molecules. This is the most scientifically sound option. When a larger pan (which has more mass) receives energy, that energy is distributed across more molecules, leading to a smaller increase in temperature compared to a smaller pan that receives the same amount of energy.
- **Response d:** This claim that both pans will be at the same temperature because of equal energy transfer from the top pans doesn't hold because the bottom pans may have different capacities to absorb heat due to their sizes and masses.
Given the information and the nature of heat transfer, the most accurate response would be:
**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.