To analyze the situation, we need to consider a few key points:
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Thermal Energy: Total thermal energy depends on both the temperature and the mass of the substance. The lake, being a large body of cold water, has a much greater total thermal energy due to its sheer volume, even if its temperature is lower than that of the coffee.
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Particle Movement: The temperature of a substance is a measure of the average kinetic energy of its particles. Therefore, the particles in the hot coffee, which has a higher temperature than the lake water, will be moving faster on average than the particles in the colder lake water.
Given this, the accurate comparison is:
The lake will have more total thermal energy, but the particles in the coffee will be moving faster.
This corresponds to the last option in your list.