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The major hang-up in this question is the mysterious phrase "uneven heat energy transfer".

As scientists and engineers, we're left scratching our beards when we read that one.

The quantity of heat energy that arrives at the cold water is the same quantity

that leaves the hot water. If there's any difference, then it means only that our

method of moving the energy from one place to another was leaky, and some of

the energy was allowed to escape into the surrounding air, or pipes, or containers, etc.

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Q: What happened to the extra energy in an uneven heat energy transfer between hot and cold water?
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