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I'm trying to confirm the method by which the body physically loses weight during "long-term" weight loss. I'm specifying "long-term" here because obviously there are lots of ways to temporarily lose weight. Loss of water (jogging in the sun while wearing garbage bags to promote sweating?) can potentially lead to quick weight loss, but presumably the body just reclaims that water later. I'm referring to scenarios where a person, for instance, loses 100 pounds over a course of months via lifestyle changes like exercise and dieting. When this happens, how does the human body physically remove the weight?

It's long been my understanding that the answer is, effectively, "by breathing it out" (you breath in O2 and breath out CO2, with CO2 weighing more). This fact has always amused me (it's hard to imagine someone losing 100 pounds one breath at a time). I mentioned this "fact" to my wife recently and she looked at me very incredulously. I then realized two things: I had come to this conclusion myself but never actually verified it, and I wasn't sure how to explain the details enough to convince my very dubious wife.

I'm especially curious how much weight is actually lost (on average) per breath, and if there might be other physical processes which contribute to long-term weight loss. Obviously I'd be especially interested to find out that my expectation is completely wrong!

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How much weight is lost by each breath can be easily approximated. All you need to assume are the rate of weight loss and the average breath rate.

Your intuition is correct, weight loss is mostly happening through breathing. Weight loss is fat turning into mostly carbon dioxide - $CO_2$ and water - $H_2 O$. Fat contains mostly hydrogen - $H$ and carbon - $C$ so inhaling oxygen - $O$ and exhaling a mixture of oxygen, hydrogen and carbon in the form of carbon dioxide and water results in a mass loss from the body.

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Human metabolism generates about 100 watt. Approximating the chemical reaction as O$_2$ + fat -> CO$_2$ + H$_2$O, this yields about 0.5 MJ per mole carbon. So one mole carbon lasts about 5000 seconds (about 100 minutes). A breath takes about 5 seconds, so each breath would contain about a millimole of CO$_2$, about 50 mg.

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    $\begingroup$ Pretty good that your numerical result (50 mg/breath) agrees quite well with the other estimates above. The amount of water is not insignificant - if it is in equal proportion to the $CO_2$, there would also be about 20mg of water per breath. That would not all be breathed out - some would end up leaving via the kidneys in the usual way. $\endgroup$ – Oscar Bravo Aug 23 '18 at 15:45

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