There’s three ways how a fire can generate higher temperatures:
1. Have a more energetic chemical reaction. Not all combustion is equal, some reactions just produce more heat than others. Not every fire has to be carbon combustion. Magnesium fires and Thermite are crazy hot.
2. Purifying the fuel. Stuff like coal has A LOT of junk. Wood is more junk than fuel. That junk either wastes heat by using it up in unwanted side reactions, or literally just wastes it by being heated. An example of the latter is water. When you burn wood or coal, a lot of heat is wasted on evaporating water. That’s why coke/charcoal burns hotter, it was preprocessed to remove as much junk as possible. Natural gas and other carbohydrates are even purer and better.
3. Have a more energy dense fuel and add more oxygen/oxidiser. If the chemical reaction itself doesn’t generate more energy (converting carbon to carbon dioxide has an upper limit) and the fuel is already as pure as it can be, you can always just have more of the reaction going on at once.
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