Which body is in the diamond?

Ok, folks. It is time to get back to some good, old-fashioned quantitative blogging. In her recent diamond blog, Jennifer mentioned Life Gem, which claims to sell diamonds made from the carbon extracted from a deceased loved one. A press release about this process floated through our work a few years ago. At the time, their technique was to capture exhaust fumes from cremation, extract the CO₂, reduce it, and make a diamond. A colleague of mine and I wondered about this. How much of that carbon would be from the body, and how much would be from the fuel used to combust it? We both suspected that such diamonds would contain mostly carbon from the fuel used to burn the body, with only a bit of loved one mixed in.

But why speculate when we can calculate? Let’s do the math, and then discuss how to test the prediction.

Assume a 70 kg body that is 20% carbon (various online sources give values between 18 and 23% carbon for a person).

70kg total x 0.2 C/total = 14kg C

How much fuel does it take to combust such a body? This website says 20 liters, but they don’t specify what the fuel type is. Let us assume it is fuel oil with a density of .85kg/l, and a carbon content of 85%.

20 l x .85kg/l = 17kg total x .85 C/total = 14.5 kg C

So if we are burning the body using fuel oil, the exhaust carbon will be about half body and half fuel.

Natural gas should give less carbon exhaust. According to Wikipedia, the energy density of diesel oil is about 46 MJ/kg, suggesting that 782 MJ are needed for cremation. Using natural gas, with an energy density of 54 MJ/kg, we need only 14.5 kg of gas. Furthermore, natural gas is only 75% carbon, so the total carbon mass from natural gas fuel is about 10.9 kg.

Of course, calculations are all well and good, but how can we test it? In the case of fuel oil, testing is difficult. However, natural gas tends to have a very light carbon isotopic composition, with a ¹³C/¹²C ratio 4-6 percent lighter than PDB (an arbitrary, but universal carbon isotopic standard). In contrast, a body will have a C isotopic content somewhere between 2.1 and 2.8 percent lighter, depending on how careful the person was about watching what they ate.

So if you really want to know how much of your diamond derives from your deceased beloved, and how much is burned natural gas (itself the remnant of long dead organisms), you can measure the carbon isotopic composition of the diamond. There’s just one problem.

Measuring carbon isotopes requires a destructive analysis. So some or all of the gemstone must be consumed. Otherwise, you’ll never really know which body is in the diamond.