286 Mr Lees, Note on constant volume explosion experiments || 



It may be stated at the outset that the corrections on this 

 account to be applied to the values of total energy obtained from 

 constant volume experiments appear to be of very small amounts, 

 and to be well within the limits of experimental error. In spite of 

 this, the method of computation given below may be of interest to 

 workers on this subject. 



§ 2. In discussing the state of affairs after a constant volume 

 explosion, some simplifying assumptions will be made. The con- 

 stituent gases of the exploded mixture are each assumed to follow 

 the ideal gas law pV = RT (1) 



where p is pressure, F is volume, T is absolute temperature, an(^j 

 R is the same constant for a gramme-molecule of each of the! 

 constituent gases. It is further assumed that these constituent 

 gases are intimately mixed, so that there is no variation in the 

 chemical composition of the gas mixture at different points of the 

 interior of the vessel. Finally it is assumed that the volumetric 

 heat of each constituent follows a linear law of increase with 

 temperature. Thus a given mixture will also follow a linear law of 

 increase of volumetric heat. 



§ 3. The calculations involved are made more simple if a mass 

 M of a constituent gas be replaced by iV -= M/m, where m. is its 

 molecular weight. The mass M is thus replaced by its equivalent 

 in gramme-molecules. In the case of any portion of a chemically 

 homogeneous gas mixture, the weights of the constituent gases 

 may be replaced by the number of gramme-molecules in each case, 

 and we may speak of the number of gramme-molecules of the 

 mixture without any difficulty. 



To take into account the variation of temperature at any 

 instant of the mixture at different parts of the interior of the 

 explosion vessel, we may divide up the contents of the vessel as 

 follows : 



iVj gramme-molecules of mixture at absolute temperature T^ , 

 N T^ 



■'■' 2 " " " " " 2' 



■'■'3 55 55 55 J5 55 "^ 3 » 



etc. etc. 

 If N be the total number of gramme-molecules of the mixture in 

 a vessel of volume V, the partial volumes V^, V^, etc. of the 

 constituents are given by 



pV^^RN.T,, pV, = RN,T^, pV, = RN,T^, etc., 

 where p is the uniform pressure in the vessel. Thus 



pV = p{V^+V^+Vs+ etc.) = R (iVjTi + N^T^ + N^T^ + etc.) 



=^R^iN,T,) (2) 



i\ 



