# Why this perpetuum mobile won't work?

Design of this perpetuum mobile is based on brownian motion. When you place a small particle ($$3\ \mathrm{\mu m}$$) in liquid, you can see it moving randomly, because it gets hit by moving molecules. These brownian particles receive energy from internal energy (heat).

Imagine a cup of oil with exactly one $$3\ \mathrm{\mu m}$$ particle, which has magnetic properties. This cup is placed inside a coil. Movement of this particle will generate (really small and chaotic) current in this coil.

From my point of view this mechanism violates 2nd law of thermodynamics, because it converts internal energy to electricity, which in a closed system will become heat which will then be converted to electricity again. What am I missing?

The electrical load, if it is not at 0 K, will also generate noise current through the coil, which will produce a magnetic field, which will do work on the magnetic particle, which will then transfer energy back to the particles of the fluid that it interacts with.

Ultimately, if the fluid is hotter than the load, energy will transfer from the fluid to the electrical load. If the load is hotter than the fluid, energy will transfer from the load to the fluid. Exactly as the second law of thermodynamics leads us to expect.

But let's simplify this example, we remove the coil and leave only oil and magnetic particle. This particle will be moving infinitely, getting its energy from heat motion. Isn't it a violation of a 2nd law?

In a lossless environment, it doesn't violate the 2nd law, and we don't consider it a perpetuum mobile, simply because an object remains in motion indefinitely. Indeed, any object that is perpetually stationary in one inertial reference frame is in perpetual motion in some other inertial reference frame.

The system is only considered a perpetuum mobile if we can extract energy from it indefinitely.

In your system, the velocity of the particle is non-zero, but it does not grow indefinitely as even if the particle obtains a high velocity it will soon lose that energy due to further collisions with the surrounding particles. If we were to somehow extract energy from the particle when it obtained high energy, then we would ultimately cool the surrounding medium and reduce the energy possible to be extracted in the future. Thus this is not a perpetuum mobile.

• Good point. But let's simplify this example, we remove the coil and leave only oil and magnetic particle. This particle will be moving infinitely, getting its energy from heat motion. Isn't it a violation of a 2nd law? Apr 4, 2021 at 6:33
• If the particle is not at 0 K, you should not expect it to be perfectly stationary. Apr 4, 2021 at 6:40
• An isolated particle at $T > 0K$ surrounded by a void has less entropy than a lower-temperature particle plus electromagnetic radiation. Apr 4, 2021 at 6:59
• "This particle will be moving infinitely, getting its energy from heat motion" also moving randomly, and randomly gaining and losing kinetic energy. As it has magnetic moment it will also, during accelerations and decelerations give off photons adding to the black body radiation of the system. Thus , with photons and interactions the number of microstates keeps increasing so entropy keeps increasing, is my view.. Apr 4, 2021 at 7:41
• If you ignore the effects of radiation with this isolated system,, then you are not removing work or energy from the system, and energy is conserved. What's the problem? Apr 4, 2021 at 18:59

From my point of view this mechanism violates 2nd law of thermodynamics, because it converts internal energy to electricity, which in a closed system will become heat which will then be converted to electricity again. What am I missing?

There is nothing that violates the 2nd law of thermodynamics about converting thermal energy into electricity. Indeed, most of our electrical energy is produced that way. You would only get a violation of the 2nd law if that energy were able to be produced at greater than the Carnot efficiency.

In this example it is not possible to exceed the Carnot efficiency, in fact, it is not remotely possible. The coil receiving the field also has thermal fluctuations, and these thermal fluctuations will produce thermal noise that will swamp any energy from a particle. And due to imperfect coupling there will be less influence from the magnetic particle than from the internal thermal motions.

In the end, energy will flow only if the receiver is colder than the particle. This is simply a heat engine. This may be surprising at first, but it turns out that solar panels are also heat engines, and their temperature affects their efficiency dramatically.