OK, so for the coin cell contest, we want to know the maximum runtime. I have considered estimating this three different ways. As an example, I'll take the minimum pulse rate of the V3.0, 0.5 Hz (the light blinks once every 2 seconds). I measured the current drain to be around 1.15uA at this rate.
How long will this run on a CR2032?
First, you need to decide on the cell's capacity. I'll use 225mAh, which is on the Panasonic CR2032 Datasheet, since I'm using Panasonic cells. Other manufacturers quote other numbers.
Capacity / current
In this method, which you see most commonly used, you divide the capacity of the cell (in Ah) by the current drain of the device (in A), to yield a lifetime in hours. To get years, we divide by 24 hours/day, and 365 days/year (if you want to get technical, you can use 365.25). In this case, we get:
0.225 / 1.15e-6 / 24 / 365 = 22.3 years
Nice, but this exceeds the "shelf life" quoted as 10 years.
WTF is shelf life, anyway? It certainly doesn't mean the battery is dead at that point if left on the shelf. Instead, it's a measure of self-discharge. Elsewhere in their Lithium Handbook, Panasonic quotes a 1% self discharge rate per year. So, at the end of the 10 year shelf life, the cell should retain more than 90% of its initial capacity (depending on 1% of what: see below). Considering this, the 22.3 years calculated above doesn't seem correct anymore - at that point, the battery would have lost some of its initial capacity sitting on a shelf. It would be nice to take this into account.
To include the effects of self-discharge, I first assume the 1% per year means 1% of the remaining capacity. This means the capacity obeys the differential equation:
where s is the self-discharge rate, in this case 0.01/year. The solution of this equation is an exponential decay describing the capacity of a battery on the proverbial shelf, which is interesting, but doesn't answer the question. To figure the runtime, we also need to include the circuit's current drain. For the moment, assume the drain is a constant current of d amps. The equation now looks like:
In 2018, there's no need to be intimidated by (simple) differential equations like this: just throw them into Maxima.
I got maxima to solve the ODE, selected a specific solution by giving the initial conditions (fresh battery at t=0), and finally solved the result for the time when C=0. The result: 20.2 years. Two years shorter than the earlier estimate. (Note: earlier, I posted 19.4 years here due to a typo in the maxima code).
It's also possible that 1% discharge per year means 1% of the initial capacity per year. This would mean a linear decay of capacity obeying:
The solution to this one is trivial: we just add (0.225 Ah * 0.01 / 365 / 24) = 257nA to the device current. For the lifetime, we get 0.225 / (1.2e-6 + 257e-9) / 24 / 365 = 17.6 years. Two and a half years shorter still.
So, there you have it: the TritiLED V3.0 can run for somewhere between 17.6 and 20.2 years on a CR2032.
There's a subtle problem with each of these estimates. When the cell voltage falls over time, the circuit current also falls. This would extend the run-times, since the current is continually dropping. Ignoring this effect would tend to under-estimate the run-time, so the above estimates may be slightly conservative.