The distribution of temperature along a thin rod electrically heated in vacuo. VI. End-losses

Abstract

On the basis of the known distribution of temperature along a filament electrically heated in vacuo, the distributions of some of the other physical characteristics that are known functions of the temperature were investigated in part IV. By means of the expression thus obtained for the distribution of any given characteristic, the over-all performance of the filament for this particular purpose can be obtained by integration, and can be expressed in terms of a certain equivalent length of an ideal filament in which the loss by conduction at the ends is completely eliminated. The difference between the actual and the equivalent lengths, which is generally referred to as the correction for the end-losses, is calculated in the present part for some typical physical properties that are of practical interest. Among them are (1) properties like the heat capacity, the heat generated, and the total output of radiation, which are proportional to known powers of the temperature T; (2) properties like brightness and the rate of evaporation, which are proportional to known powers of exp (1/T); (3) properties like thermionic emission, which are proportional to known powers of T and of exp (1/T). The corrections for the end-losses thus calculated for a long filament of tungsten for the different properties are found to agree closely with those computed graphically by Worthing from the observed distributions of these properties along the filament. It is further shown that the correction for a filament of medium length, such as is used in high-frequency power-tubes, is practically the same as for a similar long filament heated by the same current.