0
$\begingroup$

I was reading an article about nuclear diamonds and they made an apples-to-oranges comparison of a 1 gram C14 nuclear diamond to a single AA battery. Here is the part I'm referencing:

"An alkaline AA battery weighs about 20 grams, has an energy density storage rating of 700 Joules/gram, and [uses] up this energy if operated continuously for about 24 hours." Meanwhile, "A diamond beta-battery containing 1 gram of C14 will deliver 15 Joules per day, and will continue to produce this level of output for 5,730 years — so its total energy storage rating is 2.7 TeraJ."

I'm far from a chemist or any other applicable type of scientist otherwise I'd take a crack at the answer myself. The question simply is this: according to the data provided how many Joules per gram would a C14 nuclear diamond produce if it weighed 20 grams (to compare it to the quoted AA battery that weighs 20 grams)?

To visualize the desired apples-to-apples answer:

Conventional 20 gram battery: 700 Joules/gram, for 24 hours.

Nuclear ?? gram battery: ??? Joules/gram, for 5,730 years.

|improve this question
$\endgroup$
  • $\begingroup$ Note that the period of 5730 years corresponds to the half-life of C-14. $\endgroup$ – Loong♦ Feb 13 '17 at 18:57
  • $\begingroup$ I'll point out that the battery output was normalized to 1 gram whereas the battery was noted as weighing 20 grams. $\endgroup$ – MaxW Feb 13 '17 at 19:05
  • 1
    $\begingroup$ And of course the output will be decreasing over time (implicit in the half-life, but perhaps better made explicitly). And this ignores the problem of converting the beta in to useful electrical output. Much less finding a gram of C14 (or 20g for that matter!). $\endgroup$ – Jon Custer Feb 13 '17 at 20:50
2
$\begingroup$

Let me address this part of your question first:

"[...] how many Joules per gram would a C14 nuclear diamond produce if it weighed 20 grams"

I think it's important to understand that the bolded/italicized phrase is redundant, because your are discussing (as did the article) the energy output per gram. So the per-gram output of a 20 gram battery is the same as that of a 1 gram battery. The 20 gram battery would have a total output of 14000 Joules in it's lifetime, where the one gram battery would have a total output of 700 Joules. The fact that the article, and your question, normalize to a per-gram basis is how they've maintained an apples-to-apples comparison.

The semantics get tricky when they talk about the mass of the diamond battery, and by my thinking this is where they may fail to give an apples-to-apples comparison. The diamond would not be pure $\ce{C^{14}}$, and at a minimum would contain a thin protective coating of non-radioactive $\ce{C^{12}}$ (protecting those on the outside from the radiation on the inside). So when they say "A diamond beta-battery containing 1 gram of $\ce{C^{14}}$", it is not made clear what the total mass of diamond would be (e.g. we aren't given the ratio of $\ce{C^{14}}$ to the $\ce{C^{12}}$ that would also be present).

That said, I think that the apples-to apples answer to your question, based on the information given in the article, is as follows:

Conventional 20 gram battery: 14000 Joules/day, for 1 day.
Nuclear 20 gram $\ce{C^{14}}$ battery: 300 Joules/day, for 5,730 years.

or, equivalently:

Conventional 1 gram battery: 700 Joules/day, for 1 day.
Nuclear 1 gram $\ce{C^{14}}$ battery: 15 Joules/day, for 5,730 years.

|improve this answer
$\endgroup$
  • $\begingroup$ I'm well aware of what half-life is as well as the fact that not all of the material is radioactive. It was more of the 15 versus 700 Joules of energy I was interested in. I suppose a secondary question would be, how large would those nuclear diamonds be in comparison? I imagine large enough to negate the size/energy efficiency of conventional batteries though the nuclear batteries certainly have a much longer shelf-life. Thank you. $\endgroup$ – John Feb 14 '17 at 9:19
  • 1
    $\begingroup$ I'm glad I was able to help. Thanks for the very interesting question! $\endgroup$ – airhuff Feb 14 '17 at 10:43

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.