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Can we use a rotating fan to generate electricity and then use that electricity to rotate that same fan forever? A rotating fan has kinetic energy. That can be converted into electricity using Magnetic fields like in a generator. And then we can use the same electricity to run the fan again, continuing the cycle. Assume no air resistance.

Will the fan keep rotating forever? I think the second law of thermodynamics is forbidding this ( because it's perpetual motion), but I'm not sure how. Energy is conserved in this process. So technically, the fundamental laws of physics shouldn't forbid this, or do they?

But it's still possible that the Second law of thermodynamics forbids this. But how exactly? How can the second law of thermodynamics forbid this but it doesn't forbid a simple harmonic oscillator (which also involves perpetual motion)?

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  • $\begingroup$ Let me say that kinetic energy of fan is not out of nowhere,- electric motor converted some electricity into rotational energy,- other goes into heat, etc, aka energy looses. Consequently only some of this rotational energy can be converted back to electricity,- there will be energetic looses too, like Eddy currents, etc. So due to energy leaks and other causes as well,- you'll never build a perpetual machine. Simple harmonic oscillator assumes no damping, i.e. no potential energy looses, better check damped harmonic oscillator, which includes that. Only this is compatible with 2nd law $\endgroup$ Commented Sep 18, 2022 at 8:46
  • $\begingroup$ @AgniusVasiliauskas Second law is merely the statement that there is always energy loss due to heat? How is this law non-trivial then? I read that second law was the statement that energy doesn't flow from cold body to hot body. $\endgroup$ Commented Sep 18, 2022 at 8:55
  • $\begingroup$ @LeopardMamba There are various equivalent ways of stating the second law of thermodynamics - see en.wikipedia.org/wiki/Second_law_of_thermodynamics. $\endgroup$
    – gandalf61
    Commented Sep 18, 2022 at 9:01
  • $\begingroup$ @LeopardMamba 2nd law has many interpretations/statements and all of them are equivalent. One of them states: "Not all heat energy can be converted into work in a cyclic process.". Energy flowing from hot to cold, means that it will always find a place to leak. $\endgroup$ Commented Sep 18, 2022 at 9:01

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A perfect fan, with no losses due to air resistance and friction in bearings and with perfect electrical conductors and a 100% efficient electric motor, could indeed run forever. You could use a battery to power the motor, the motor drives the fan, and the kinetic energy of the fan recharges the battery via a generator. If no energy is lost to the environment then all processes in the fan are reversible. This is in principle just like a simple harmonic oscillator with no losses - just much more complex.

The second law of thermodynamics does not forbid this - but it does say that you cannot extract additional work from such a system - all it can do is keep itself going. And we know that in practice there are always some losses due to friction etc. so a practical perpetual motion machine is impossible.

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  • $\begingroup$ Does the second law says that it's statistically very unlikely for this fan system to return to the exact same state after a cycle, because it has a very large number of particles? But since the Harmonic oscillator has only one particle, second laws doesn't apply there. $\endgroup$ Commented Sep 18, 2022 at 9:19
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Why not build the ultimate energy saving fan by harnessing the lost voltage on the output, minimising friction, while magnetically increasing turbine efficiency from the fan? Not a techie.

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