﻿Ignition of Gases by Sudden Compression. 97 



means of equation (10). For this purpose we have to estimate 

 to what extent the reaction occurs during the slow period of 

 combustion before the explosion occurs, and the pressure- 

 time curve becomes almost perpendicular to the time axis 

 (see fig. 7). Taking the experiments on heptane as an 

 example, we find (Table III.) that the biggest delay observed 

 was about 0'6 second ; that the ignition temperature under 

 these conditions is 250°C. = 553 absolute, and that the differ- 

 ence of temperature between the gas and the walls was about 

 210° C. The observed cooling factor was 0*51. Since the 

 specific heat of the mixture experimented with is approxi- 

 mately = 0*2, the rate of reaction at the ignition temperature 

 must correspond to a heat evolution of 



0'51 X 0"2 x 240 = 24 calories per gram per second. 



The total heat of combustion of 1 gram of the mixture 

 (containing about 75 per cent, of the theoretical amount of 

 heptane for complete combustion) is about 510 calories, so 

 that it is evident that during the period when the temperature 

 is only rising slowly, which is always less than half a second, 

 the amount of reaction and therefore the changes in con- 

 centration must be small. Once the temperature begins to 

 rise quickly, it is evident that the disappearance of oxygen 

 can have only a secondary effect on the rate of the reaction 

 compared with that of the rise of temperature until the com- 

 bustion is nearly complete, so that the error involved in the 

 calculation from equation (10) of the total time of combus- 

 tion, by ignoring the effect of changing concentration, must 

 be small. In view of the unavoidable experimental errors in 

 carrying out experiments of this kind and of our still in- 

 complete knowledge of the mechanism of combustion, we do 

 not, in fact, think that any attempt to take fully into account 

 such secondary effects is justified at present. 



VII. We therefore arrive at the conclusion that the time 

 for complete combustion of an explosive mixture of gases 

 when suddenly compressed to a temperature above its ignition 

 temperature is closely given by the integration of equation 

 (10), and is therefore 



t = — fh- - I at-^ d 



-(?} ' ' (11) 



1 p 00 1 



J-o /Jm ( > 



where T is the lowest ignition temperature under the con- 

 dition of the experiment, and T is the initial compression 

 temperature. 



Phil. May. Ser. 6. Vol. 44. No. 259. July 1922. H 



