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Where does most of the carbon we ingest go? I understand that a large amount is exhaled as carbon dioxide, but what percent is defecated (and theoretically deposited in the ground)?

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    $\begingroup$ not sure why the question got downvotes, but realised 'excretion' probably wasn't the right word, so changed it to 'defecation' to be more clear - pooping or breathing, where does most of the carbon we ingest go? $\endgroup$ – Amphibio May 12 at 21:57
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    $\begingroup$ You should use the term "bodily waste" or something else. The answer depends on the icountry, chaing the ratio by 100%, individual's diet and exercise habits in the sense of calories, and if you mean carbon which is converted to CO2 and methane after digestion. you can rephrase it as "do humans use more calories than they waste after digestion" .... rich countries eat nearly twice as many calories as they use, and other countries use 1 to 1.5 times as many... consider that average daily calories breathed out is about 2000: en.wikipedia.org/wiki/List_of_countries_by_food_energy_intake $\endgroup$ – aliential May 13 at 2:02
  • $\begingroup$ note that hot countries also have different characteristics. $\endgroup$ – aliential May 13 at 2:07
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The short answer

In a comparison between exhaled and faecal carbon, exhaled carbon wins.


The long answer

Warning: Assumptions, approximations and averages ahead.

Calculating faecal carbon excretion

The average human being produces about $29 \text{ g}$ faeces (dry weight) per day, the major component of which is bacteria [1]. For now, neglect variations with fibre and other dietary components. Also, assume that all of it is bacteria.

Now, carbon makes up about $50 \%$ of bacterial dry weight [2]. Thus daily carbon excretion in faeces is about $15 \text{ g}$.

Calculating carbon exhalation

An adult human being breathes about $20$ times a minute [3]. Each breath has a volume of about $500 \text{ mL}$ [4]. Thus the exhaled volume per day is $20 \times 60 \times 24 \times 500 \text{ mL} = 1.44 \times 10^7 \text{ mL}$.

Exhaled air is about $4 \%$ carbon dioxide [5]. The density of carbon dioxide at $37 \ ^{\circ} \text{C}$ and $1 \text{ bar}$ is $1.713 \text{ kg m}^{-3} = 1.713 \times 10 ^{-3} \text { g mL}^{-1}$ [6].

Hence, the mass of carbon dioxide exhaled per day is $0.04 \times \left(1.44 \times 10^7 \right) \times \left(1.713 \times 10^{-3} \right) \text{ g} \approx 987 \text{ g}$.

And since $\text{CO}_2$ is $\frac{12}{44}$ carbon, the mass of carbon exhaled per day comes out to be $\frac{12}{44} \times 987 \text{ g} = 269 \text{ g}$, which is at least an order of magnitude greater than the figure we got for faecal carbon.

References

  1. Rose C, Parker A, Jefferson B, Cartmell E. The characterization of feces and urine: a review of the literature to inform advanced treatment technology. Crit Rev Environ Sci Technol. 2015 Sep 2;45(17):1827-1879. https://doi.org/10.1080/10643389.2014.1000761.

  2. Lawford H, Rousseau J. Studies on nutrient requirements and cost-effective supplements for ethanol production by recombinant E. coli. Appl. Biochem. Biotechnol. 1996 Mar 1;57-58(1):307-326. https://doi.org/10.1007/BF02941710.

  3. Hooker EA, O'Brien DJ, Danzl DF, Barefoot JA, Brown JE. Respiratory rates in emergency department patients. J Emerg Med. 1989;7(2):129‐132. https://doi.org/10.1016/0736-4679(89)90257-6.

  4. https://en.m.wikipedia.org/wiki/Tidal_volume

  5. https://www.bbc.co.uk/bitesize/guides/z9hycdm/revision/3

  6. https://www.engineeringtoolbox.com/carbon-dioxide-density-specific-weight-temperature-pressure-d_2018.html

| improve this answer | |
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    $\begingroup$ I didn’t like the question — who cares? But the answer is exemplary. $\endgroup$ – David May 13 at 21:51
  • $\begingroup$ Sorry you didn't like the question, David. However, Adhish gave a very clear and simple answer, so the question can't have been that bad! Thankyou Adhish, that was great. $\endgroup$ – Amphibio May 14 at 18:56
  • $\begingroup$ I also had no idea that bacteria make up the majority of faecal dry weight, that is fascinating $\endgroup$ – Amphibio May 14 at 18:59

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