There is nowhere else for the heat to go.
Aren't you forgetting that the efficiency of a thermodynamic process is proportional the ratio of the differences in temperature and the ambient. If the Bitcoin mining chip is not as hot as the coils, then it will not be as efficient as the coils were. Also for example a hair dyer needs all the heat transfered within a short period of time, and if the heat transfer is slow not all of the heat may be extracted to the hair and instead wasted to the ambient. So somewhat less than free mining.
No. Work out the actual transfer equations if you like, but it ends up being an equivalence. Energy in = heat out. Or the device self destructs.
I am speaking about the efficiency of transfer on the time domain.
How is it that my hair dyer dries my hair after i turn it off but my mining chip is still hot? You've got have a large heat sink in order to move the heat efficiently in time.
Device doesn't self-destruct if the duty cycle is not greater than what the heat transfer sink can deliver.
Well work out the numbers if you like. The amount of energy stored in the mining chip will be negligible due to its small mass. Or you can use other tricks, like run the chip for a shorter period of time than the typical hair drying cycle (so the chip is usually idle and being cooled before the hair drier is turned off).
The heating chip will be kept relatively cool because first of all it is small and has a low mass, and second of all because it is being cooled by room air at the intake. The latter I can tell you from experience working with air cooled chips. A hair dryer has plenty of airflow to keep even a high power chip cool via air cooling. Worst case you downgrade the chip power if necessary to keep it cool (unlikely), so you get less output. Still (effectively) 100% efficiency, just less output, but that's not the play here.
These are engineering problems and I'm quite certain it won't be hard to dominate dedicated miners in terms of efficiency here. I'm far less confident in 21's investors getting a positive return on their investment, but that's a different story.
Heat sinks are often the most expensive part of the entire design. And there is a diminishing return. The heat of a mining chip is I believe very concentrated into a few mm2 versus coils which cheaply spread out their heat over a large surface area of air flow.
Just downgrade the chip power. You can air cool it easily without any kind of exotic heat sink, or maybe none at all.
