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There's been some research into high-temperature electrolysis.

The idea is that a lot of the energy to split the hydrogen and oxygen can be provided as heat; that means you need a lot less electrical energy. To a rough approximation, for every three units of heat energy produced by a nuclear plant, you get one unit of electricity, so the process could in theory considerably reduce the cost of zero-carbon hydrogen.

In practice, it seems like it's going to be very hard for a nuclear plant to beat an electrolyser that runs when near-free solar electricity is available.

As you say, if you get hot enough you can do away with electrolysis entirely. A little bit of casual reading suggests that the temperatures required by a naive approach are in excess of 2000 degrees Celsius, far, far beyond the point where any existing or near-term reactor design would turn into a puddle of very radioactive molten metal.




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