[gji]

Those numbers aren't that bad, actually. A cell phone's peak power draw isn't much more than 5W, so you'd need 10g / efficiency. At 10% efficiency, that's 100g, which is 5 cm^3 for plutonium. A cell phone battery is about 3 times that size, assuming 3000 mAh and an energy density of 600 Wh/L. Of course you'd have to build in a heat engine, but perhaps even a peltier would work given the generous efficiency allowance.

[whoisthisdude]

At 10% efficiency you'd still be dumping out around 45 watts of heat in your pocket. We'll just need some aluminum pants for the heatsink!

[baybal2]

Saying along those lines used to be a popular joke among Soviet nuclear scientists.

[taneq]

Also you don't need peak power all the time, you just need more than your average power draw combined with a battery big enough to smooth out the gaps. I'd think the biggest problem would be your phone being dangerously hot all the time.

[Retric]

It's better than that. Normal iPhones have less than 8 watt hours of battery life, they simply don't need peak power much. 8/24 = 0.333w, you lose some to overhead but you also reduce power draw by 0.33w so that's a reasonable estimate. @ 20% efficient that's 1.65w of heat, but your also storing .3w so really only 1.35w of waste heat. That's a 30% heat production increase at peak which doesn't seem like a deal killer.

7 Plus has a ~30% larger battery, but can dump heat ever more area so not a big deal.