118 PHENOMENA, ATOMS, AND MOLECULES 



temperatures is 5.6 watts per cm. Substituting this in equation (8) to- 

 gether with Wd = 1500 / watts, we obtain 5 = 267 cm. 



From equation (14) we see that a/r must then be 1.027. In otlier words 

 if the heat is to be carried by ordmary conduction the temperature would 

 have to drop from 2000 deg. to looo deg. within a region in which the 

 radius increases by less than 3 per cent. For the heat to travel any reason- 

 able distance from the arc by ordinary conduction would require a tempera- 

 ture drop of the order of 50,000 deg. 



Heat Carried by Convection 



To form a conception of the heat that can be carried from bodies at 

 very high temperatures by convection currents in a gas, let us consider a 

 stream of gas of cross-section A moving through a heated region having a 

 temperature To. Let Ti be the temperature of the gas before entering the 

 hot region and v be the velocity of the gas while in the hot region. The 

 number of gram-molecules of gas passing the hot region per second is then 

 Avp/(RT2) where p is the pressure in bars and R is the gas constant 

 (83.7 X 10^ ergs per deg.). If C is the specific heat of the gas per gram- 

 molecule expressed in joules per deg. (for hydrogen up to 2000 deg. C 

 may be taken to be 7.5 X 4-2 = 31.6) we thus find that the rate at which 

 the heat is carried from the hot region (in watts) is 



lV = AvpC(T2-T^)/(RT2) (15) 



To maintain the convection current through the hot region requires the 

 action of a force equal to the product of the velocity v by the mass of gas 

 which moves per second through the hot region. We thus find that the 

 pressure difference A p needed to maintain the movement of the gas is 



^p = Mpv''/{RTo) (16) 



where M is the molecular weight of the gas (2 for hydrogen). 



The available pressure difference in the gas near a heated body may be 

 looked upon as due to the difference in pressure between two columns of 

 gas of height h and of temperatures T2 and Ti, respectively. Thus we find 

 that 



where g is the acceleration of gravity (980 cm. per sec.^). From equations 

 (16) and (17) we find that the velocity of the gas in the heated region is 

 given by 



v^ = hg{T2-T^)/T^ (18) 



This must be looked upon as an upper limit to the velocity of convec- 

 tion currents in any gas, for the effect of viscosity, which we have neg- 



