2 boxes sit below the header First Stack. A box labeled Top Pan contains 4 high energy molecules, each marked 100. Below is another box labeled Bottom Pan, containing 9 low energy molecules, each marked 20. 2 more boxes sit below the header Second Stack. The box labeled Top Pan contains 4 high energy molecules, each marked 100. Below is another box labeled Bottom Pan containing 4 low energy molecules, each marked 20.

Question

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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.

Answer 1

To answer the question about which of the two bottom pans will be cooler after they have been touching for a while, we need to consider the principles of thermal energy transfer and how temperature is related to energy distribution among molecules.

The Bottom Pan in the First Stack contains 9 low energy molecules, each marked 20, resulting in a total energy of \(9 \times 20 = 180\). The Bottom Pan in the Second Stack contains 4 low energy molecules, each marked 20, resulting in a total energy of \(4 \times 20 = 80\).

When the top pans (which have higher energy) touch the bottom pans, they will transfer energy to the bottom pans. The amount of energy absorbed by the bottom pans will cause their temperatures to rise.

Now let's evaluate the responses:

• Response A suggests that the smaller bottom pan will be cooler because less energy has to transfer. This reasoning is not entirely accurate, as the amount of energy transferred also depends on the initial total energy of the lower energy molecules.

• Response B states that the larger bottom pan will be cooler because it started with more total energy. This response seems misleading. While it's true that it started with more total energy, that doesn’t automatically mean it will be cooler after contact with the top pans.

• Response C asserts that the larger bottom pan will be cooler because the energy that transferred to it will have spread out over more molecules. This response correctly aligns with the concept that the total energy will be distributed across more molecules, leading to a lower average energy per molecule in the larger bottom pan compared to the smaller one.

• Response D claims both pans will be the same temperature, which is also inaccurate because they start with different amounts of energy and different numbers of molecules.

Based on the principles of thermal energy distribution, 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.