HEAT DISSIPATION AT ELECTRODES OF SHORT ELECTRIC ARC 941 



"outer conduction."^ For Tq = 300°K and the emissivity € = 0.05 at 

 room temperature,® the second term of this expression reduced to ergs per 

 closure has the values listed as "radiation correction" on line 5 of Table I; 

 these corrections are negligible. 



The convection loss from a horizontal cylinder of diameter D has been 

 givenio ^s 0.27^(Ar)^/VD'^^ in B.T.U. per hour with AT in °F, D in feet and 

 A in square feet. For our system of units this becomes 4180^(Ar)^'V^^''* 

 ergs/sec. To make the differential equation for heat flow linear this can be 

 written approximately ^\mA{^TQ/2y'^^T/D^l\ and the heat put into the 

 end of the wire per second taking account of convection loss would then be 

 given by equation (1) with H = AlSOi^To/lDY'*. The second term of this 

 expression reduced to ergs per closure has the values listed as "convection 

 correction" on line 6 of the table. 



That the heat lost from the arc itself is quite negligible is clear from 

 estimates of the duration of the arc and of its superficial area. The arc 

 time is iriLCy^ which has the values 0.07 and 1.0 X lO"® sec respectively 

 for the inactive and for the active surfaces. The average area of the arc 

 which is effective in radiating is probably a great deal less than the area 

 of the pit formed on one of the electrodes Tr(P/4:. In some experiments it 

 was found^^ that d^ = 3.8 X 10"" cmVerg. If this estimate of pit diameter 

 is right for the present tests, and we take the arc temperature to be the 

 boiling point of platinum^^ 4803°C and the duration of the arc 1 X 10"* 

 sec, the radiation loss comes out to be 0.01 erg. This is a gross upper limit. 



Reduction or the Data 



Not all of the energy in the charged condenser is dissipated in an arc on 

 closure. During the arc some energy is dissipated by current flowing through 

 circuit resistance, including spreading resistance in the electrodes at the site 

 of the arc, and after the arc is over aU of the remaining energy is so dissi- 

 pated. We need to sort out the amounts of energy which are spent in these 

 different ways in order to make a careful analysis of the data represented 

 by the numbers on lines 7 and 8 of Table I. 



The total energy is eo = CVl/2 where C = lO-^/and Vo = 40 volts in all 

 of the experiments of this paper (eo = 80 ergs). The energy dissipated in an 

 arc is Ca = C(Vq — Vi)v, where Vi = —S volts is the potential across the 



8 H. S. Carslaw and J. C. Jaeger, "Conduction of Heat on Solids," Oxford, 1948, equa- 

 tion (6), p 119. 



^ This low value seems to be well established. See the paper by A. G. Worthing in a 

 book "Temperature," Reinhold Pub. Co., 1941, Fig. 7 on p. 1175. 



1° W. H. McAdams, "Heat Transmission," McGraw-Hill, 1942, equations (13a) and 

 (19), pp. 240-241. 



" L. H. Germer and F. E. Haworth, //. App. Phys. 20, 1085 (1949), Fig. 5 on page 1088. 



^ Reference 2, Table H on page 914. 



