Following experimental setup.
We take copper coils which are small enough to be subject to brownian motion. We combine those coils with some other material to make them about as heavy as the liquid we submerge them in (same weight per volume) so they would neither all gather up at the top nor bottom of the liquid but rather spread out evenly.
Through permanent magnets we create a static magnetic field within the vicinity of the liquid.
When the coils are moved around randomly through brownian motion inside the liquid, wouldn't this induce some current? Wouldn't this basically resemble a magnetic brake which would result in cooling down the liquid? A refrigerator working without any outside source, other than the energy of particles moving around randomly and pushing the coils around randomly?
As a bonus, one could possibly imagine to use the current the coils are subject to when moving through the magnetic field in a way which would have them emit some electromagnetic waves in the spectrum of visible light. Possibly allowing us to see a glow in a dark room.
Since this would most likely violate the second law of Thermodynamics, and we cannot have that, my question is, what part of this experiment would not work as i imagine it?
Note that this experiment was proposed the other way around, where we would rather use nano magnets being moved through brownian motion, but those would clump together into a bigger magnet, so i was just thinking that instead of moving magnets, one could just move coils through a magnetic field if coils that small in the nano/micro size range could actually be built.
Answer
The state of the nano-circuits can be classified as one of the following three:
State A outputs large amounts of energy but is a low entropy state and therefore (due to the free energy being $F=U-TS$) will never arise.
State B consists of high orientational disorder which will generate light (or some other energy output). Due to the high entropy, this will be the favoured configuration at elevated temperatures. You correctly suggest that the energy will be extracted from the kinetic energy of the water, causing the temperature to decrease.
As the temperature decreases, the water will jiggle less, reducing the energy yield of the nano-circuits. As the temperature decreases more and more, one of two things could happen. The nano-circuits may retain their high entropy state, but the lack of brownian motion eliminates the energy output. Or (in an ideal case) the nano-circuits will align in a low-energy state (C).
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