A theory of the filament temperature distribution of the tungsten vacuum-lamp, with special reference to optical pyrometry

Abstract

The paper gives a general theory designed mainly for application to the two types of vacuum lamps commonly used in optical pyrometry: namely, the heavy-current strip lamps which serve as standards for calibration and the fine filament lamps embodied in the pyrometers themselves. Simplifying assumptions are made regarding the properties of tungsten, namely, that resistivity and emissivity both vary directly as the absolute temperature, while thermal conductivity remains constant. These allow a complete solution of the main differential equation governing temperature distribution. A comparison of results obtained in this way with a few computations, specially undertaken without resort to the resistivity and emissivity assumptions, shows that the simplifications suffice for all practical purposes. Further, the general agreement between the calculated and observed characteristics of lamps suggests that no great error results from the assumption of constant thermal conductivity. However, other simplifications are also briefly considered. The problems treated on the basis indicated are as follows: the distribution of temperature along a filament of known dimensions, carrying a constant current and with its ends at a constant temperature; the voltage on, and resistance of, such a filament; the temperature coefficients of calibration, i.e. the change in maximum temperature with change in surrounding temperature with the filament run at constant amps, volts or ohms, as the case may be; the modifications of the above mentioned characteristics due to appreciable gradients in the leads, and the asymmetry of distribution induced by the Peltier and Thomson effects. These subjects are treated generally for short filaments and also for the simpler case of infinitely long filaments to which, in fact, many lamps tend to conform. In addition to these matters, which are all concerned with the steady state of temperature distribution, the approach to that state is considered under conditions giving an estimate of the maximum speed of response attainable in practice. Numerical examples of the formulae developed are given for typical lamps and some of these are compared with other calculations and with observations. For pyrometer lamps a table is given showing how their main characteristics can be estimated, with fair accuracy, merely from a knowledge of the filament dimensions, or, in the case of existing lamps, by means of a simple test. Suggestions are also made for possible modifications in the design of standard strip lamps.