Estimation of the filament temperature of an incandescent lamp from an energy balance in steady-state conditions

The detailed balances of the different energy contributions in a commercial electric light bulb are presented. Previous studies on the physics of electric bulbs have been accomplished under some simplifying hypotheses. The present study tries to establish a rigorous balance of the supplied and dissipated powers in the lamp, to quantify the different contributions to this energy balance. The energy balances have been carried out for the filament and the bulb. In steady state, the supplied energy to the light bulb is entirely dissipated by conduction, convection and thermal radiation. In such conditions, the filament acquires a constant temperature depending on the supplied power. In this paper, the temperature of both the filament and the bulb were estimated from the solution of the energy balance equations in the system. We have analyzed a vacuum lamp, in which the convection is only external, and a gas-filled lamp, in which the convection is both external and internal. In addition, the relevance of the thermal conduction versus the radiation has been evaluated. This thorough study aims to be a great contribution to the analysis of heat transfer processes so important nowadays due to the recent concern about scarcity energy and environmental questions.