Can the Total Entropy Spontaneously Decrease?

One formulation of the second law of thermodynamics states that no process can solely convert heat to work. In other words, an irreversible process must cause an increase in entropy.

D’Abramo presents a model which seems to convert heat into electrical energy, while keeping temperature of the system constant. Since this is a spontaneous process, it seems as if heat is directly converted into electrical energy which could be used to do work. This decrease in heat implies a decrease in entropy, which seems to violate the second law of thermodynamics.

The system contains an uncharged spherical capacitor which is connected to a heat reservoir, such as a large room at room temperature. The inner sphere is a metal with a very low work function. This means relatively little energy is needed to emit electrons from the metal. The outer sphere has a very high work function, so it is assumed that over time, the inner sphere will thermally emit many more electrons than the outer sphere.

The spheres are also subject to blackbody radiation, which gives the emission of photons. Since the two spheres are at the same temperature, the two spheres will emit at the same rate. Perhaps the outer sphere emits more photons, as it has a larger surface area. In any case, photons from the outside will hit the inner sphere and also cause emission of electrons due to the photoelectric effect.

It is clear that the inner sphere will emit more photoelectrons and thermoelectrons than the outer sphere. It is then presumed that these emitted electrons will travel radially outward, as they have nowhere else to go. As a result, more electrons will hit the outer sphere than the electrons hitting the inner sphere. While the outer sphere has a high work function, some electrons will have enough kinetic energy to penetrate the outer sphere.

If any of the electrons get stuck on the outer sphere, an electric potential will build up in the spherical capacitor system. Of course, electrons would not build up forever. Eventually, the potential would reach some maximum where the electrons would no longer be accepted.

If this would occur experimentally, then a small amount of energy would be transferred into creating the electric potential. The energy would either come from black body radiation or thermal emission. Both of these are thermal processes, so the conservation of energy states that heat will be spontaneously converted into work!

Entropy is the amount of disorder. It seems as if this spontaneous process has caused a more ordered state, which gives a decrease in entropy in the forward direction of time.

What does this mean for the second law of thermodynamics? Is there somehow an increase of entropy organized in the electric field? This seems unlikely, as dQ/T has decreased over time. Does this process occur in nature, or does the second law forbid it from existence?

The only objection I can currently think of is to say that the outer sphere would not absorb electrons at a faster rate than the inner sphere. Naively, if the outer sphere needs a lot of energy to remove an electron, it seems like it would be willing to accept electrons. Perhaps no charge would be built up at all, as eventually the emitted electrons would fall back to the inner sphere, due to the electric field created.


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