The amount of energy in uranium is not just more than coal, we are talking grams of uranium vs tons of coal for the same energy output.
Also, nuclear plant is a much bigger and more complicated investment than a coal plant, so the economics make more sense to be at a larger scale.
The size of a coal plant can vary by a lot, because they just need a furnace and turbines. You can have massive plants or smaller peaker plants that only spin up when needed during peak hours. So the avg nuclear will be larger than the avg coal plant. But the largest coal plants are similar size to Nuclear ones.
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