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Fully agree, the only small remark being that it's

η = 1 - Tcold/Thot

and to put in perspective: If your metal rod on one side of the peltier element (that's inside the device) is at 150°C = 302° = 423K and the cold side (water reservoir) is at 20°C = 68°F = 293K the maximum achievable efficiency is 30%.

In practice you'll waste a lot of energy (probably the flame outputs about a kilowatt of power, normally you'd comfortably use it to heat a kettle of water or canned spaghetty or...) for a meager 2W or 3W of power to your cellphone. That's because the energy transfer from a flame to a simple rod is very, very inefficient.



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