FLAMES OF ATOMIC HYDROGEN 115 



This is expressed in small calories per gram-molecule oi nyolrogen (2.016 

 grams). The heat of reaction at constant volume Q is 



Q = 97,000 + 1.5 T - 0.00045 T^ {?) 



HEAT CONDUCTIVITY OF HYDROGEN 



The dissociation of the hydrogen greatly increases the heat conductivity. 

 First, let us consider the laws governing the rate of loss of heat through 

 hydrogen which is not dissociated appreciably. 



It has been shown ^ in this case that the loss of heat by conduction and 

 convection from a body of temperature 7*2 in a gas at temperature Ti is 



Wc = S{^2-^i) (8) 



where Wc is expressed for example in watts ; 5" is the shape factor which 

 is independent of the temperature but depends on the size and shape of the 

 body and on the effective thickness of the film of gas which surrounds it. 

 The quantities <^i and (^2 are expressed as an integral of the heat conduc- 

 tivity k over a temperature range from o to T\, or T2, thus 



<t> 



= CkdT (9) 



•^0 



For high temperatures {T2) with hydrogen, ^2 is approximately 1.06 X 

 io~^ To^'- and <^i at Tx = 300 is 0.3 watts per cm. 



The effect of the dissociation of the hydrogen is to increase the heat 

 carried from the body by an amount IV d given by 



Wn-SDQtC (10) 



where 6" is the shape factor, D the diffusion coefficient of hydrogen atoms 

 through molecular hydrogen, Qi the heat evolved (expressed in watt sec- 

 onds) when I gram of hydrogen atoms combine to form molecules, and c 

 is the concentration (grams per cu. cm.) of the atomic hydrogen at the 

 temperature T2. 



It was found that 



Z) = 0.00214 T2^^2 (^jj-) 



From equation (7) we see that at temperatures of 2000 deg. or 3000 deg. 

 Qi is about 49,000 calories or 205,000 watt-seconds. The value of c, accord- 

 ing to equation (4) and the ordinary gas laws, is 



0.0244 Px .. 



c= —^ — 7-7— (12) 



To l-\-x 



