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I disagree on this, because biofuels are a viable substitute in almost every situation.

I'm fairly certain that our accumulated knowledge would make a second industrial happen even faster in spite of fossil-fuel-lack (but it might play out slightly differently, because of higher fuel costs...)

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Doubtful that there's enough biofuels to produce high quality steel in large quantities and that's a pre-requisite to a post-apocalyptic neo-Industrial Revolution. Only coal burns hot enough and was available the huge quantities necessary.

Sure, producing iron without coal sucks; but there is already enough scrap metal around to power several additional industrial revolutions, and an arc furnace is really simple, especially if already know how electricity works beforehand.

Long term, there are alternative routes that could be taken (capable of processing fresh ore) but using scrap metal just seems easier/more likely to me.

That is not true methane, propylene, hydrogen can be easily produced and they have temperature >2800C while burning of coal can produce combustion gases as hot as 2,500 °C (4,500 °F). https://www.thoughtco.com/flame-temperatures-table-607307

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