I am writing a science fiction novel where dead humans are turned into diamonds by compacting cremated remains. What size of diamond would the amount of carbon in a human body form? I know that the size would vary somewhat depending on the weight of the person.
Specifically, would the diamond be small enough to be worn as an earring, or able to be worn as a necklace? Or would it be too large to practically be worn at all and be set as decoration?
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13$\begingroup$ Isn't there a company that actually does this now? I'm sure it's a con but still. $\endgroup$– oxide7Commented Nov 21, 2017 at 16:39
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5$\begingroup$ After cremation, the body of a human adult is reduced to 1.8 to 2.7 kg of ashes, mostly calcium phosphate; very very little carbon remains, most of it being lost as carbon dioxide during the cremation process. So I'd say that maybe there is enough carbon to make a diamond suitable to use as a ring stone. $\endgroup$– AlexPCommented Nov 21, 2017 at 16:44
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2$\begingroup$ The companies use a specified portion of ashes, and not all the ashes from a person. I am wondering about a futuristic society that is able to use all the carbon from a person in a diamond. $\endgroup$– CatloverCommented Nov 21, 2017 at 16:46
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3$\begingroup$ It's considered a good idea to wait at least 24 hours before accepting an answer that way people from every time zone get a chance to weigh in. $\endgroup$– sphenningsCommented Nov 21, 2017 at 19:56
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2$\begingroup$ @AlexP, is that a comment or an answer? Sure looks like an answer... $\endgroup$– RyanfaeScotlandCommented Nov 21, 2017 at 23:04
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3 Answers
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Before cremation
About 18.5% of the human body is carbon by composition.
One gram is five carats.
The average human being worldwide masses 62 kg. Note that people may be larger in some countries, e.g. in the United States is 88.3 kg.
$$ 62 \text{kg} \cdot 18.5\text{%} \cdot 1000 \text{ grams per kg} \cdot 5 \text{ carats per gram} \approx 57,000 \text{ carats}$$
So if we had some way of extracting all the carbon from a human body, you'd get an average of a fifty-seven thousand carat diamond. Or 5700 10-carat diamonds.
Post-cremation
But we're talking about post-cremation. There is much less carbon after cremation, as the carbon burns off as carbon dioxide in cremation.
- According to a funeral urns seller, a rule of thumb is that one pound of person will result in less than one cubic inch of ashes 99.5% of the time.
$$ 62 \text{ kg} \cdot 2.2 \text{ pounds/kg} \cdot 1 \text{ in}^3 \text{ per pound} / 14.4375 \text{ in}^3 \text{ per cup} = 9.4 \text{ cups}$$
- According to a cremation diamond seller, it takes two thirds of a cup of ashes to make a diamond. So that's 14 diamonds per average person. Each diamond is about .1 carats.
$$ 9.4 \text{cups} / (2/3 \text{ cup/diamond}) \cdot .1 \text{ carat per diamond} \approx 1.4 \text{ carats}$$
So the answer is that you could have a diamond as large as 1.4 carats using the current cremation diamond process' efficiency. If you harvested the hair prior to cremation, you could increase that. Hair is a better source of carbon than cremation ashes.
Note that we've been using the person's original mass to estimate the amount of ashes. It's worth noting that cremation will burn fat away. The amount of ashes is mostly based on the amount of bone in the body. So height would change that average more than weight.
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10$\begingroup$ A diamond is carbon with some impurities. For this kind of calculation, I think it is close enough to say that the diamond will weigh as much as the carbon in it. $\endgroup$– BrythanCommented Nov 21, 2017 at 21:28
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6$\begingroup$ @Brythan And the lower the impurities the higher the diamond will be rated. A perfect diamond is pure carbon. $\endgroup$ Commented Nov 21, 2017 at 22:24
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19$\begingroup$ How much silicon is in the body? 'Cause I'd rather be made into chips. $\endgroup$– davidbakCommented Nov 21, 2017 at 23:52
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57$\begingroup$ @davidbak I think most of my mass came from chips, actually... $\endgroup$– akaioiCommented Nov 22, 2017 at 5:28
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74$\begingroup$ "136.4 cubic inches = 9.4 cups"... USA, you need to stop this silliness already $\endgroup$– LopeCommented Nov 22, 2017 at 10:23
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Prior Art
First it's worth noting that there is at least one company that actually does this. LifeGem creates diamonds from carbon extracted from cremated remains.
Per wikipedia:
The company can extract enough purified carbon from a single cremated human body to synthesize up to 50 gems weighing one carat (200 mg) each, or up to 100 diamonds of smaller size, while sending remaining ashes to the family.
This is about ten grams of gem. I think that's too heavy for an earring, but I don't wear earrings. It probably wouldn't hurt in a necklace.
Is this the limit?
The question literally asks
What size of diamond would the amount of carbon in a human body form?
According to wikipedia the human body is about 18% carbon by mass. This means that a 70 kilo person contains about 12.6 kilos of carbon.
If we made a diamond from all the carbon in a human body, we'd have a 12.6 kilo gem which is frankly a bit excessive. This is 63000 carats, and would be a record-size diamond. I don't think anyone would wear that.
However, cremation removes a significant portion of this carbon (as carbon dioxide gas). Wikipedia states that a typical cremation leaves 1.8-2.7 kilograms of ash, mostly calcium salts from the bones.
From that same article:
Cremated remains are mostly dry calcium phosphates with some minor minerals, such as salts of sodium and potassium. Sulfur and most carbon are driven off as oxidized gases during the process, although a relatively small amount of carbon may remain as carbonate.
I assume that's why LifeGem doesn't produce 12 kilo monster gems.
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6$\begingroup$ The current largest synthetic diamond is only a little over 10 carats. $\endgroup$ Commented Nov 21, 2017 at 16:48
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2$\begingroup$ @sphennings that would be another good reason they don't produce 63000 carat monster gems! $\endgroup$– DeolaterCommented Nov 21, 2017 at 16:51
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2$\begingroup$ For more effective size measurements (since I have no idea what 63000 carats looks like), I used diamond's density of ~3.51 g/cm3 on the monster 12 kilogram gems... and came up with 3418.8 cubic centimeters; for an effective size comparison, that's roughly 10% smaller than a gallon of milk, or 10% larger than 3 liters. $\endgroup$– DeliothCommented Nov 21, 2017 at 19:51
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1$\begingroup$ @Delioth is that bigger than a breadbox? $\endgroup$ Commented Nov 22, 2017 at 21:37
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$\begingroup$ @A.C.A.C. depends, are we talking metric or imperial breadboxes? $\endgroup$– fgysinCommented Nov 28, 2017 at 10:10
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According to wikipedia, humans are 18% carbon by mass.
So a 70 kg human is made up of roughly 16 kg carbon.
The density of a diamond is roughly 3.5 g/cm^3
Assuming a lossless process where every atom of carbon is used in the resulting diamond this would result with a 4500 cm^3 diamond.
In the real world nothing is a lossless conversion. Memorial diamonds are being created by either using the cremated remains, or carbonized hair as the carbon source to create a lab grown diamond.
answered Nov 21, 2017 at 16:42
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1$\begingroup$ @AlexP I disagree, quote from OP: "The companies use a specified portion of ashes, and not all the ashes from a person. I am wondering about a futuristic society that is able to use all the carbon from a person in a diamond." $\endgroup$ Commented Nov 21, 2017 at 17:46
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1$\begingroup$ For comparison, since I can't visualize 4,500 cc very easily, is about 80% of a soccer ball. In other words a huge diamond. $\endgroup$ Commented Nov 21, 2017 at 18:34
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$\begingroup$ How'd you get to "16 kg carbon"?
70 * .18 = 12.6, according to my calculations... $\endgroup$ Commented Nov 21, 2017 at 19:05 -
$\begingroup$ @maxathousand I didn't independently calculate it. 16 kg came from the table on Wikipedia. $\endgroup$ Commented Nov 21, 2017 at 19:07