How do we gain energy out of fat?

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Physicsrapper
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"When your body runs out of glucose, it turns to fat for energy, which has 9 calories in every gram. This is a little more than double the amount in carbohydrates. Converting fat into energy takes longer than it does to convert glucose into energy, because fat must be first be broken down into its two component parts: fatty acid and glycerol. Each part follows a separate pathway to ultimately become available as energy. One common saturated fat, palmitic acid, makes 130 molecules of ATP for each molecule of fat."

This is all I found about this topic in the internet. Could you please explain it further (how fat is broken down exactly to convert it into energy) or find a source where I can read more about it?
 
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This is a topic that is covered in most Biochemistry textbooks (some of which are freely available online). For example, see:
https://www.ncbi.nlm.nih.gov/books/NBK21173/
https://www.ncbi.nlm.nih.gov/books/NBK22581/
 
Yes, this is an invitation to write several textbook chapters, which we often get - not efficient to do for one student!

That said, a little fact I like that seems often overlooked, is that the oxidation of fats is the source as well as of energy, of water. The camel's hump is fat, not water