Have a little crank on the outside of the time capsule that turns a generator and charges a battery. Put a sign that reads "Please turn crank".
Someone ought to turn it within 100 years.
On a serious note, if you can sleep your processor and it uses 0.35 uA, it would require a 306.6 mAH battery. This assumes a zero internal discharge rate, and some form of battery chemistry that can last 100 years.
BulletMagnet83:
The one thing you won't run out of in the next hundred years is curious people.
Reminds me of when my brother was little, he made a small wooden box with a slot in the top. He wrote "Insert Coin Here". Of course when ever we had guests over, they all had to insert a coin to see what happens XD
The military uses some pretty exotic batteries that I think are supposed to have near-forever shelf-life (well, 20 years, anyway.) In missiles and fuzes and things. They're essentially solid and inert at room temperature and need to be activated by a pyrotechnic charge to melt the relevant parts. After which they produce plenty of power, for long enough for the device to reach the target. Molten-salt battery - Wikipedia
Come to think of it, there's a slightly similar class of water-activated batteries, and a near equivalent in the zinc-air batteries commonly used in hearing aids. I suspect that if you can build a storage container that will hold vacuum for 100 years, a circuit with OTS Zinc-air batteries might still work after 100 years once you let air (and moisture) in.
The time capsule is a metal box and it wil contain 100 objects. It will probably be stored in an attic. The circuit to be triggered after 100 years will be an audio circuit (maybe with a surface transducer sticked to the metal of the case).
Therefore I don't see a possibility with solar power.
Maybe it will be easier to use the services of a bailiff.
No doubt the power source is the stickiest problem here, but I'd also design some redundancy into the electronics. Source all parts based on reliability. That probably puts the flaps down on those cheap capacitors from eBay
Perhaps some sort of electromagnetic energy harvesting approach? Assuming an urban setting, the energy available might even increase over time. And if there is none in 100 years, it's probably because there's no one left to open the time capsule anyway.
A fuel cell could periodically charge a rechargeable battery or supercapacitor , therfore neutralising each other's shortcomings. I have a feeling you will end up needing a lot of power. Suppose the rechargeble could stay charged for 10 years, then the fuel cell should be able to work 11 times. This seems doable to me. Or you could use a wet battery and just replace the electrolyte with fresh one periodically.
Maybe temperature gradient exploitation using peltier devices?
I was going to suggest a radioisotope generator, but I doubt you can get one.
Or , someone mentioned a turtle. Don't they live 100 years? How much food could a turtle possibly eat in 100 years?
If there is no one to open the box in a hundred years, Who cares... But a water activated battery and some stored water and some instructions to "Pour Water Here to Activate" should work... All sealed in an inert gas? Nitrogen?, Neon, Argon to avoid corrosion. If the water contained a mild acid, Zinc and copper would serve well and I'm sure that there are better methods than what 2 minutes consideration gave me.
Assuming somebody is there to see what's in the box when it opens, why not put in a hand crank? They can use it to open the box manually.
The curiosity of passers-by will make sure the crank is turned once in a while. You can use that energy to charge a capacitor to run the Arduino for a while until the next person turns it.
The principle is basically the same as those water pumps that are connected to a children's playground. The infinite energy of children makes sure that no adult ever has to pump water manually.