Mr Lees, Note on constant volume explosion experiments 287 



In most experiments of this kind, the pressure jp is used as a means 

 of measuring the mean temperature T^ . For a chemically homo- 

 geneous mixture, this mean temperature will obviously be defined as 



HN^ N ' ^ ' 



where N is the total number of gramme-molecules in the vessel. 

 Hence from equations (2) 



pV = RNT,,, (4) 



which since F, R, N are constants, indicates how ]) may be used to 

 measure T^^^. 



§ 4. The total internal energy E oi a, gramme-molecule of the 

 gaseous mixture at a uniform temperature T (absolute), assuming 

 ' linear increase of volumetric heat with temperature, is given by 



E = AJ + \BT\ 



where Aq and B are constants. If as usual we measure E from a 

 standard temperature Tq, the internal energy E must be written 



E = A,{T~ To) + p (T^ - To^) = C + AJ + \BT\ ...(5) 



where C - - (^o^o + i^^o')- 



On dividing this value of E by (T — Tq) we get the mean 

 specific heat (at constant volume) per gramme-molecule, i.e. the 

 mean volumetric heat, between T and Tq , in the form 



A, + ^B{T + T,) = A + \BT, (6) 



where A = A^+ \BT^. 



The true volumetric heat at temperature T is given by dEjdT 

 and is therefore equal to 



A^ + BT (7) 



§5. Reckoned from T^, the internal energy of the mixture 

 defined in § 3 will be 

 C2i\^i + A,Y.N^T^ + ^B1:N,T^^ = CN + A,NT„, + \B1:N^T^\ 



(8) 



In explosion experiments, this is usually assumed to be equal to 

 the internal energy of the whole mass taken at the mean tempera- 

 \ ture T^ , i.e. is assumed to be equal to 



CN + A,NT„, + ^BNTJ (9) 



The first two terms of expression (8) are the same as the first two 

 terms of expression (9). We have, therefore, to compare IIN^T^^ 

 ( with NT J, To do this, put 



T, = T,n + h, T, = T,, + t,, T, ^T,,, + t„ etc. ...m 



19—2 



