290 Mr Lees, Note on constant volume explosion experiments 



the integral being taken over tlie shaded areas previously referred 

 to. It IS useful to note that the integral in (15) for each piece of 

 the shaded area is exactly twice the first moment* of the area of 

 the piece about AB. The expression (15) thus becomes in our case 

 numerically equal to ^ 



J. f(500)2 X 2,N , (300)2 X bN] 



^ The mean^ volumetric heat per gramme-molecule for air, from 

 C. to 1600° C, is probably about 5-55 gramme-calories.' Thus 

 for air at 1600° C, the internal energy reckoned from 0° C. is about 

 8880iV. The increase in value of the volumetric heat with tempera- 

 ture does not appear to follow exactly the linear law, but in the 

 neighbourhood of 1600° C. we may take the increase as being 

 roughly 0-5 gramme-calories per 1000° C. Thus from expression (6) 

 we see that B can be taken as 1 x lO-^. Thus expression (16) be- 

 comes 25iV, which expressed in terms of 8880iV is 0-283 % . With 

 the assumed conditions, this is the amount by which the observed 

 internal energy at 1600° C. should be diminished to give the 

 corrected value corresponding to uniform temperature throughout 

 It IS conceivable that the true shape of the temperature dis- 

 tribution curve may be something like the dotted curve DFCGE 

 of fig. 2, m which case the correction would be materially increased 

 It is also possible that the temperature differences in the gas may 

 dimmish during the early stages of cooling at a much slower rate 

 than the mean temperature. On the whole, however, it would seem 

 probable that the correction ought not to exceed 1 % of the value 

 of the internal energy, and might very well be much less. 



§7. Conclusion. An efEort has been made to investigate the 

 effect of temperature variations in an explosion vessel, on the 

 values of the total internal energy measured. Instead of approach- 

 ing the problem from the point of view indicated in the B.A. Report t 

 by modifying the temperature for a given internal energy determina- 

 tion, the author has modified the internal energy for a given mean 

 temperature, and has given reasons which seem to indicate that 

 7 «nnTn ^^ii'?'' '' probably not more than 1 % at a temperature of 

 ibOO U Ihis order of correction is within the limits of probable 

 error of experiments at the present time J. 



* For r-dN = 2 f| . dS, where dS = tdN. 



t Loc. cit. J See Pye, loc. cit. 



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