3. Louis has two sets of two gears (Set A and Set B) that he is using to build two different machines. He has all the gears laying out separately, as shown in the diagram above. Then he puts the gears into the machines so that the gears in Set A are touching each other and the gears in Set B are touching each other. Use the information in the diagram to answer the question.

Question

After the gears have been touching for a while, which of the two bottom gears will be cooler, and why?

Responses

a
The smaller bottom gear will be cooler than the larger bottom gear, because less energy has to transfer for the molecules to reach the same temperature as the molecules of the top gear.
The smaller bottom gear will be cooler than the larger bottom gear, because less energy has to transfer for the molecules to reach the same temperature as the molecules of the top gear.

b
The larger bottom gear will be cooler than the smaller bottom gear, because the energy that transferred to it was spread out over more molecules.
The larger bottom gear will be cooler than the smaller bottom gear, because the energy that transferred to it was spread out over more molecules.

c
The larger bottom gear will be cooler than the smaller bottom gear. It started with more total energy, so less energy had to transfer for both gears in Set B to reach the same total energy.
The larger bottom gear will be cooler than the smaller bottom gear. It started with more total energy, so less energy had to transfer for both gears in Set B to reach the same total energy.

d
Both gears will be the same temperature, because both of the top gears had the same amount of energy to transfer and the molecules in the bottom gears start with the same energy.
Both gears will be the same temperature, because both of the top gears had the same amount of energy to transfer and the molecules in the bottom gears start with the same energy.

Answer 1

To determine which of the two bottom gears will be cooler after a period of contact, we need to analyze the energy transfer and temperature distribution between the gears in Set A and Set B.

Assuming the top gears in both sets transfer energy evenly to the bottom gears, the key factor to consider is the relative sizes of the bottom gears (i.e., their surface areas and the number of molecules).

If we consider the mechanics of energy transfer, the bottom gear with a larger size (which generally has more mass and more molecules) will absorb the energy from the top gear over a greater number of molecules. This dispersal of energy means that the energy transfer results in a smaller increase in temperature for the larger gear.

Thus, based on these principles, the best response would be:

b: The larger bottom gear will be cooler than the smaller bottom gear, because the energy that transferred to it was spread out over more molecules.

This option explains that the larger gear can distribute the energy over more material, leading to a smaller increase in temperature compared to the smaller gear that has fewer molecules to absorb the same amount of energy.