288 Mr Lees, Note on constant volume explosion experiments 



so that NT^ = SiViTi = SiVi(T„, + t^) = NT„, + llN^t^, from (3), 



i.e. SiVi^i = (11) 



We then have 

 1:N,T,^ = UN, (r,„ + t,r = TJllN, + 2T^l.N,t, + l:N,t,^ (12) 



so that from (11) 



SiViTj^ = NT J + SiV^i^i^ (13) 



Hence expression (8) is greater than expression (9) by the essentially 



positive quantity 



i^SiVj^i^ (U) 



To get the true value of the internal energy corresponding to 

 uniform temperature T^, we must therefore diminish the actually 



Fig. 1. 



i 



measured value (8) by expression (14). This means that the ex- 

 plosion experiments will give higher values, in general, for the 

 internal energy, than constant pressure experiments, ideal accuracj^t 

 in other respects being postulated for the determinations. l| 



§ 6. There remains the problem of estimating the order of this 

 difference of internal energy values, i.e. the order of magnitude o| 

 expression (14), 



The problem of temperature distribution at any instant inside 

 an explosion vessel requires the determination of the number dl 

 of gramme-molecules of mixture* whose temperature lies betM^eei 

 T and T + dT. If this be known, the temperature distribution cai 

 be represented by a graph like fig. 1. The graph is such that the 

 abscissa of any point on the curve DCE represents the total number 

 of gramme-molecules whose absolute temperature is not greater 



* To emphasise the simple algebraic character of the argument, the calculi 

 notation has been avoided in §§ 3 to 5. 



