Bistability and Fluctuations for an Incandescent Light Bulb.

We develop a simple kinetic model to explain the hysteresis that occurs when an incandescent light bulb is controlled by a rheostat in the external circuit. The model is based on changes in the temperature of the filament that are associated with internal energy changes due to radiation and Joule heating. The radiative processes are idealized as occuring via photons lost and gained by a black body while the dynamics of the electric current are treated via the Langevin equation. Quantum corrections to the elementary process description of black body radiation are derived. Like the ballast resistor, the model exhibits hysteresis due to a region of bistability of the temperature as a function of the resistance in the rheostat, the criterion for stability being that the temperature of the filament decrease with increasing resistance in the rheostat. Explicitly including variations in the current, we show that temperature and current fluctuations are correlated and that they diverge as the thresholds for stability are approached. It may be possible to study these divergences experimentally.
 

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