THE LONDON EDINBURGH. AND DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [SEVENTH SERIES.] NOVEMBER 1928. XCIV. The Escape of Heat from a Harmonically Oscillating Hot Wire. By R. S. MAXWELL, M.A., B.Sc. THE 1. INTRODUCTION. HE problem of the escape of heat by free convection from a thin cylindrical wire at rest has been studied by Langmuir † and others, while King has carried out an exhaustive research, both theoretically and experimentally, on the case when the stationary wire is cooled by a stream of air passing it with a certain velocity, i. e. cooling by forced convection. When the wire is not at rest the problem is considerably more complicated, and up to the present no complete mathematical analysis has been brought forward. A considerable amount of experimental work has, however, been done on the subject by Tucker and Paris § in connexion with their Hot-Wire Microphone. They measured the escape of heat from the electrically-heated wire when subjected to an alternating air-current. The converse effect, that of a hot wire oscillating in still air, has been dealt with by Richards . In both cases the wire is cooled, * Communicated by Prof. A. W. Porter, F.R.S. + Langmuir, Phys. Rev. xxxiv. pp. 401-422 (1912). King, Phil. Trans. Roy. Soc. A, ccxiv. pp. 373-430 (1914). Tucker & Paris, Phil. Trans. Roy. Soc. A, ccxxi. pp. 389-430 (1921). || Richards, Phil. Mag. xlv. pp. 926-934 (1923). Phil. Mag. S. 7. Vol. 6. No. 39. Nov. 1928. 3 Q and consequently its resistance alters. It is shown that the change can be divided into two categories : (a) A lowering of the resistance of the whole wire. This is known as the steady drop. (b) A periodic change of resistance. The object of the present work is to investigate these two resistance changes under varying conditions, and also to bring forward, at any rate approximately, a mathematical theory which will explain the observed effects. 2. EXPERIMENTAL WORK. (a) Steady Drop. (1) Description of Apparatus. The experiments were made with the very fine platinum wire-diameter 0.0006 cm.—in the grid of a Tucker hot-wire microphone. This grid was mounted on one prong of an electrically-maintained tuning-fork, and a compensating weight was mounted on the other prong, so that the fork would vibrate evenly. The tuning-fork and grid were completely enclosed in a large wooden box, so that all extraneous draughts were excluded. The The grid (W) was arranged in one arm of a Wheatstone's network, so that its resistance could be measured, and a milliammeter (A) was also included in the circuit. electrical connexions are shown in fig. 1. The method of taking observations was as follows. A rheostat (Rh) in the battery circuit was adjusted until the heating current through the grid had reached some definite value-say 30 milliamperes-when the fork was at rest, and the resistance of the grid was then measured. A long straight wire (ST) which had previously been calibrated, with an adjustable contact to the galvanometer, was used to obtain an accurate point of balance. When the fork was set in vibration, the resistance of the grid decreased as it became cooled, and the new resistance was measured by balancing the network again. In order to prevent much alteration of the grid heating current, the total resistance R1+ R2 in the two resistance boxes was kept constant throughout a given series of readings. The resistance of the grid was measured for various values of the amplitude of the fork, keeping the heating current constant. Nine such series of readings were taken for different values of the heating current: the resulting curves are shown in fig. 2. The amplitudes were measured by means of a microscope with an eyepiece scale which was calibrated against a linear steel scale. (2) Numerical Calculations. (a) Temperature.-Within the accuracy covered by these experiments, there is a linear relationship connecting the resistance of the grid when at rest with the excess temperature of the hot wire of the grid over that of the surrounding atmosphere. If R, resistance of grid at atmospheric temperature and R resistance of grid at a temperature excess of 0. above that of the atmosphere, then where a is the temperature coefficient of resistance of the wire of the grid. Table I. shows the resistance of the grid when at rest for different heating currents. On extrapolating the resulting graph, it is found that the resistance of the grid at atmospheric temperature, i. e when no current is flowing in the wire, is 120 ohms. The last column in the table gives the excess temperature (1), calculated with the aid of equation (1) and assuming a=0.00367 for platinum. |