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I had a thought experiment.

Suppose you fill a conducting metal box with ions or other charged particles. Accelerating charges generate electromagnetic field, which induces a current in the presence of a conductor. Because the ions bump into the box walls all the time, get decelerated due to induction and then re-accelerated by other ions, this could effectively turn all the heat in the box into electricity. While the magnetic field in the box itself would cancel out and have no effect other than influencing other ions motion, near the wall the particles would have no other choice than to bump into the wall.

If the metal box conducts heat, this would turn heat from the outside slowly into electricity.

This seems to be violating the second law of thermodynamics, because you could turn the heat into electricity, use it nearby and turn the heat generated by the work into electricity again.

This seems to be wrong in some way but I don't know where my reasoning fails. What's the problem with the above thought experiment ?

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  • $\begingroup$ Your charged particles are not accelerating in the same direction. They move randomly, neglecting their mutual interaction. This random motion is due to thermal agitation. Hence there is no net electromagnetic effects. Also the conversion of outside temperature does not work that way. Any rise in temperature outside the box will make the metal hot and heat radiates into the box, which will increase the random motion of the ions. Random motion and directional motion are entirely different. $\endgroup$ – UKH Sep 17 '16 at 1:23
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The part where it gets wrong is assuming that the charges are accelerating in a particular way to generate usable magnetic field(that will later induce current). Thermal vibration is random in nature and the atoms vibrate randomly and hence their magnetic field would be changing instantaneously resulting in a time average of zero. Hence, you can't obtain any usable electricity from there.

But there are certain materials that on heating obtain a particular gradient which leads them to produce electricity. You can get a more detailed view from here ---> https://en.wikipedia.org/wiki/Pyroelectricity

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  • $\begingroup$ But only the magnetic field near the conducting material is important, because only that magnetic field induces a current. So any ion bumping into the wall will inherintly have a velocity/deceleration that points partially against the wall. If all 6 walls of the box are conductively isolated from each other, then there would be a current for each wall pointing in their respective directions. $\endgroup$ – HopefullyHelpful Sep 16 '16 at 14:53
  • $\begingroup$ Just to be clear I've understood your question, you're saying that if I have charged ions hitting a metal surface then the metal surface should get a current by induction. Is that right? $\endgroup$ – Sad_lab_rat Sep 16 '16 at 15:12
  • $\begingroup$ Yes, indeed. ^^^ $\endgroup$ – HopefullyHelpful Sep 16 '16 at 15:13
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    $\begingroup$ Let's assume the best case scenario in which the ions hit one wall normally. Then the vibrations they produce in the outermost lattice of the wall will be perperndicular to the surface as well. Now the direction of acceleration of the ions is normal to the surface. So it should behave like a current straight current carrying wire and will have a momentary circular magnetic field. This circle lies in the plane of the metal surface. But to induce current from there you'd need a flux change through a conductor. I don't think there's a flux change in this case. $\endgroup$ – Sad_lab_rat Sep 16 '16 at 15:25
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Perpetual-motion machines of the second kind converting ionic thermal energy into electricity do exist - see this:

http://scitation.aip.org/content/aip/journal/apl/103/16/10.1063/1.4825269 Electricity generated from ambient heat across a silicon surface, Guoan Tai, Zihan Xu, and Jinsong Liu, Appl. Phys. Lett. 103, 163902 (2013): "We report generation of electricity from the limitless thermal motion of ions across a two-dimensional (2D) silicon (Si) surface at room temperature. [...] ...limitless ambient heat, which is universally present in the form of kinetic energy from molecular, particle, and ion sources, has not yet been reported to generate electricity. [...] This study provides insights into the development of self-charging technologies to harvest energy from ambient heat, and the power output is comparable to several environmental energy harvesting techniques such as ZnO nanogenerator, liquid and gas flow-induced electricity generation across carbon nanotube thin films and graphene, although this remains a challenge to the second law of thermodynamics..."

http://arxiv.org/abs/1203.0161 Self-Charged Graphene Battery Harvests Electricity from Thermal Energy of the Environment, Zihan Xu et al: "Moreover, the thermal velocity of ions can be maintained by the external environment, which means it is unlimited. However, little study has been reported on converting the ionic thermal energy into electricity. Here we present a graphene device with asymmetric electrodes configuration to capture such ionic thermal energy and convert it into electricity. [...] To exclude the possibility of chemical reaction, we performed control experiments... [...] In conclusion, we could not find any evidences that support the opinion that the induced voltage came from chemical reaction. The mechanism for electricity generation by graphene in solution is a pure physical process..."

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