Cooling-times of tungsten filament lamps

During steady-state operation, hot-coiled filaments in incandescent lamps provide luminous flux for illumination, but when switched off, the temperature, as well as the light output drops quite fast. The cooling-time of a lamp is the time required for the hot filament to cool down to ten per cent light output after the circuit is opened. In this paper, the exercise of estimating luminous flux and cooling-times for typical 10, 100, 500 and 1000 W lamps has been undertaken for the first time for the benefit of students. This problem involves three disciplines: electricity, optics and heat. Information drawn from field of Electrical studies allows us to understand the power that quickly heats the filament, followed by that from optics that helps us in determining the light output, while heat studies are responsible for understanding the cooling of the hot filament. This last is largely explained through the Stefan-Boltzmann law. In this paper, we show that the supposition of linear configurations for the filaments neither matches luminous flux nor the cooling-times. Both fall short. H.S. Leff’s suggestion of introducing a shadow factor that reduces the exposed surface area, as it so happens in the coiled filaments, successfully explains the measured observations