Some time ago I read/heard that when a person is cremated and the results of the combustion are released into the air, it eventually mixes and disperses into the atmosphere to the degree that if one were to take a breath, it’s likely that at least one molecule of that breath came from the cremation. Maybe an urban legend, but maybe plausible. Could this be essentially true? I don’t know how to attack such a question, but this is the place to find out. Dopers?
The numbers do tend to work out that way when dealing with crazy small and numerous things like individual molecules. Thorough mixing is a big assumption though and probably takes a long time.
Related thread topic:
There’s a volume of water such that the number of molecules in that volume is the same as the number of those volumes in the ocean. In other words, if you put that volume of “specially marked” water molecules into the ocean, mix it all up, and take that volume back out again, there should be about one of the original “specially marked” molecules in the volume.
That volume, I read, is a spoonful.
So when you drink a glass of water, if it’s all been thoroughly mixed in the environment, you’re drinking a huge number of Charlemagne pee molecules, just as an example.
I think there’s way more than fifteen pounds of water, on average, allotted to every square inch of Earth’s surface. But there’s fifteen pounds of air. So the atmosphere is less heavy than the water. I think the situation is therefore even more extreme in air.
This paper gives the ultimate analysis (elemental analysis) of human cadavers. Chemical and elemental analysis of humans in vivo using improved body composition models - PubMed
An average male, ~65 years of age (67.5 kg) and a BMI of 23.7 has 39.7kgs of Water, 17.51 kg of Carbon and 1.61kg of Nitrogen and the rest of the elements is in grams.
Lets just take the Carbon portion of the body. Assume the water is precipitated in rains and lets neglect the Nitrogen,
So a human releases 17.51 kg of Carbon when cremated. (17.51/12) k-moles of CO2.
Weight of Earth’s atmosphere is 5.15 × 10^18 kg Atmosphere of Earth - Wikipedia.
So Earth’s atmosphere is (5.15e18/29) k-moles (Average mol weight of earth’s atmosphere is 29)
So the Molar Fraction (Fraction of Molecules) of the human in atmosphere = 8e-8
One Breath of Air is about 0.5 liters Lung volumes and vital capacity - Cardio-respiratory system - Eduqas - GCSE Physical Education Revision - Eduqas - BBC Bitesize.
22.4 liters of air contain 6.023e23 molecules of air (1 mole definition)
So one breath (0.5 liters) contain 1.3e22 molecules, out of which a 8e-8 fraction works out to be 1e15
So roughly 1 Quadrillion molecules of that human’s atoms are in each of your breath.
Now CO2 in air has a half life of 120 years, so 120 years after the cremation, there will only be 1/2 Quadrillion molecules of that human in each breath.
What I’d like to know is how mobile water molecules are. Like if say… King George III peed in a cesspool at Buckingham Palace in 1776, would those water molecules have evaporated, rained/snowed, evaporated, and moved enough to have spread worldwide by now? Or would they maybe be in a cloud over western Europe and the North Atlantic?
It’s possible to sail from one continent to another, in reasonable human timespans, in a craft powered purely by ocean currents. This makes it seem very likely that worldwide mixing of water occurs on short timescales.
Looked it up, here is what I found
The dominant timescale for globalscale ocean circulation is 500–1,000 yr (as
determined by radiocarbon measurements; Page 5 of 24, Last but one paragraph : https://imedea.uib-csic.es/master/cambioglobal/Modulo_I_cod101601/tracers%20of%20ocean%20mixing%20TOG.pdf
Since for diffusion, the slowest step is the rate governing step this is the timescale you are looking at.
There are ocean surface currents, deep currents, and vast regions of negligble mixing.
The continents are similar. Surface loose dirt and dust is readily transported many miles by wind & water runoff. A blob of e.g. poop or dead body buried 6 ft down in hard soil may not move an inch in millennia.
And that’s before we consider stuff buried by crustal subduction or under a couple dozen feet of glacier or hardened lava. Some of that stuff may not resurface in the remaining existence of the Earth itself. It’ll re-enter ciculation as vapor or plasma as& when the Sun incinerates the whole planet.