Implications of Charles law in a biological matrix: farts

See note 3 for source.

Maggie Koerth-Baker has a great piece up at the 538 blog: "How Big Is A Fart? Somewhere Between A Bottle Of Nail Polish And A Can Of Soda."  It's well researched, digging into the biomedical literature with verve.  And it's great that she gives the answer a context, it's easier to visualize a bottle of nail polish than a 17 ml blob for most people, me included.

I'm not at all surprised at what you can find in the primary literature (I tracked down papers on exploding people and deuterated dogs¹ for my introductory chemistry class last spring). The piece is the first in a series Science Question From A Toddler, though I suspect that people somewhat past the target age group (5 and under) would be interested in the answer to this question, too.

In a footnote Koerth-Baker suggests that farts in the body would be smaller because the gas would be compressed inside the body.  But the pressure inside the human colon is the same as atmospheric pressure.  Farts and burps keep it that way. What's different is the temperature, higher inside the body by about 30^oF (17^oC).  Gases expand at higher temperatures. You can use Charles' law to figure out by how much the volume changes with changes in temperature:  V2=(T2/T1)V2

The researchers measured the volume of the farts at room temperature (I read the paper!), so the volume of a fart should be slightly larger in the body than the reported numbers by a factor of (310/293) or about 6% larger.  So how big is a fart?  Just before exit, it's about the size of a 14 ounce ketchup bottle for the largest one in the 1997 study.

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The details of the experiments are fascinating.  The technique for quantitatively² capturing flatus in the bathtub is elegant, and while a significant improvement over the method used for the studies in the 1860s³ you have to wonder how they got volunteers for either experiment.  And speaking of volunteers, the assessment of the "flatus perception threshold" was done by delivering 100 ml of an odorant mixture "from a large 250ml syringe in about 1s, 1 meter beneath the nose of the panel members, mimicking a flatus emission."

And just in case you don't think this is serious stuff: "The common tendency to treat rectal gas as a humorous topic has obscured appreciation of the complex physiology that underlies the formation of this gas." Suarez et al. American Journal of Physiology  272, G1028-G1033 (1997).

1.  The physiological effects of drinking heavy water, D₂O, on dogs.  If you've ever wondered what would happen if your poured that little vial of D₂O into your coffee, the answer is not much.  It's not great for the dogs as a steady diet, but a sip or two won't hurt.
2.  The fancy chemistry term for "we got all of it!"
3.  See the figure, from Tangerman, "Measurement and biological significance of the volatile sulfur compounds hydrogen sulfide, methanethiol and dimethyl sulfide in various biological matrices" Journal of Chromatography B, 877,  3366-3377 (2009).