The thermodynamics of a radiating and evaporating tungsten filament having a hot-spot defect are examined theoretically. Assuming quasi-steady-states for the main and the hot-spot segments, the time profiles of their temperatures and radii are derived in closed form. Explicit relations among the fractional mass loss, failure time and defect size ratio are obtained and compared against approximate expressions used by Gluck and King7 and by Elenbaas.14 Numerical results computed for vacuum lamps support our theory.
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