Heat Generation by Electric Sparks and Rate of Heat Loss to the Spark Electrodes

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Abstract
In a capacitance spark the gas between the electrodes is heated almost instantaneously; subsequently, the spark‐generated heat flows from the gas to the material of the electrodes. In the present experiments sparks of 0.1 to 2 millijoules were passed between Pt electrodes in a bulb containing helium or argon or xenon, and either the pressure change, Δp, at constant volume v or the volume change, Δv, at constant pressure p was recorded, the former by means of a sensitive diaphragm and the latter by the movement of a droplet in a capillary tube attached to the bulb. The spark‐generated heat H residing in the gas at any instant was computed from the equations H=1.5vΔp and H=2.5pΔv, which apply to constant volume and pressure, respectively, and are derived from the gas law and the energy equation, using the heat capacity of monoatomic gases. From the values of H and the discharge energy corresponding to the measured capacitance and breakdown voltage, the percentage of spark‐generated heat residing in the gas was obtained. Immediately after discharge the percentage was found to exceed 95. The rate at which the percentage decreases with time was found to be independent of total energy and vessel diameter above a critical value of the latter. It was found to become smaller with decreasing heat conductivity of the gas, decreasing diameter of the spherical electrodes, and increasing gap length, as expected on the basis of heat loss from the gas to the electrodes. With electrode diameters of 1 mm, the heat loss after about 30 milliseconds ranged from a few percent for xenon and 10 mm gap length to 75 percent for helium and 1 mm gap length. An increase of the electrode diameter to 3 and 4.6 mm caused a substantial increase of the rate of heat loss; for example, for xenon and 10 mm gap length the heat loss after about 30 milliseconds was 28 percent and 35 percent, respectively. It was found that for constant electrode diameter the data for the several gases and gap lengths could be combined in a plot of percentage heat loss against a dimensionless parameter, θ, representing the product of thermal diffusivity and time elapsed since discharge, divided by the square of the gap length. By means of the latter parameter, one may estimate an upper bound of the heat loss during the formation of a combustion wave from a spark in an explosive gas, i.e., during the process of spark ignition, on the basis that the combustion wave is formed in a time interval smaller than the time required for the wave to travel a distance equal to its width. It is found that the loss of spark energy during the ignition process is always rather small.

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