Hate of Explosion in Gases. 99 



and the velocity of sound 



./ijg7 p "." 



.*. the velocity or sound + velocity of the gas 

 _ /2RA C/+C„ 2 



"V ,, ■g*(c p +v v ) 



The velocity of explosion 



v 



2R/i (,(V+0.) ! 

 0/(0, + 0.) 



The latter is evidently greater than the former. Therefore 

 the layer of uniform gas behind the wave will gradually 

 become greater as the explosion proceeds. 



Calculation of the Rates of Explosion. 



In attempting to calculate the rates of explosion from the 

 formula there is some doubt as to what value should be adopted 

 for the specific heat at constant volume. This constant, has 

 only been directly found at comparatively low temperatures. 

 MM. Berthelot, Le Chatelier, and Mallard have made attempts 

 to find the specific heats of the elementary gases and of carbon 

 monoxide at high temperatures by measuring the pressure of 

 explosion. Berthelot arrives at the conclusion that the specific 

 heat at constant volume increases with the temperature, and at 

 4400° C. attains the value 9*6. M. Berthelot's experiments 

 do not, however, agree with those of MM. Le Chatelier and 

 Mallard, and two series of experiments conducted by the latter 

 experimenters do not agree with one another. The specific 

 heat at constant volume may, however, be calculated from 

 the. velocity of explosion with the aid of the proposed formula. 

 A few explosions have therefore been selected and the specific 

 heats and temperatures calculated from them ; specific heats 

 at intermediate temperatures being found by interpolation. It 

 was immediately perceived that the specific heats of O a , H 2 , 

 N 2 , and CO might for all practical purposes be taken as 

 identical at all temperatures. 



A few words are necessary regarding explosions in which 

 water is formed. If the specific heat of steam is taken as 

 f x specific heat of the diatomic gases, the found rates of ex- 

 plosion fall below the calculated rates when the dilution with 

 inert gas is great, and vice versa when the dilution is small. 

 It is possible to account for this by two theories. The first 

 theory is that at high temperatures the water is dissociated, 

 whereas at low temperatures the combination of hydrogen and 

 oxygen is complete. The second theory is that the specific heat 



H 2 



