Number of joules that can be extracted from the atoms composing the molecules composing the steel wire it's made of.

...How can you not see this?

> joules that can be extracted from the atoms composing the molecules composing the steel wire it's made of

By this measure, the paper clips I have on my table have zero value to me. I cannot extract energy from them. Same for my phone and computer.

What's the physically intrinsic value of an energy extractor then?

The value of its atoms and the electrons orbiting those atoms (give or take labour costs for transforming those atoms) in joules or watts.

What if there's only one energy extractor in the world?

You screwed up the answer here in this classic Uber-commodity based economy (which no actual economist has ever proposed outside of thought experiments).

The traditional answer when people go down this path is “what ever the producer and consumer agree the price is based on a currency denominated in joules that can be extracted from an atom”.

By doing so you’ve eliminated all forms of value adding capabilities from your economic system. The paper clip is no more valuable than its unprocessed atomic components, which is clearly not how real value is derived (or your currency is completely divorced from value).