30 Kinetic Theory of Dissociation in Gases. 



The previous calculation, with /* = 0*886, gave the value 



V^= ^ a 2 = 0*66450 a 2 . 

 4 



This calculation can also be extended to the case Nj = 0, 

 and I have worked it out for that case. We may conclude 

 that if fjb represents the ratio of the energy of the molecules 

 formed to the atomic energy, the value of /jl always lies be- 

 tween § and | ; and the final ratio of the two energies, which 

 remains stationary, lies between jjl and 1. 



§ 6. The problem dealt with above appears to me to be of 

 great interest in the theory of dissociation. If the mean 

 values of the kinetic energies of a molecule and an atom are 

 different, and do not even stand in a constant ratio to each 

 other, it is difficult to decide which mean value should be 

 taken as a measure of the temperature. As previously in the 

 case of imperfect gases *, so also here it is seen that in the 

 kinetic theory of heat we are far from possessing a general 

 definition of temperature ; the usual one is applicable only to 

 perfect gases. 



§ 7. Now since the hypothesis (a) appears to be at variance 

 with experiment in actual dissociation phenomena (dissocia- 

 tion of iodine vapour, nitrous acid, &c), and would only be 

 applicable to phenomena of decomposition, which are due to 

 secondary causes (e. g. the dissociation of hydriodic acid), it 

 would be necessary to suppose that iodine atoms, N0 2 groups, 

 &c, only combine into molecules during collision. Since all 

 gases may probably dissociate under suitable circumstances, 

 this assumption would have to be extended universally to all 

 gaseous molecules. We should then have to make, for gases 

 like oxygen, hydrogen, &c, the further supposition that 0/T 

 is very large and nearly constant, or else free atoms would 

 occur in impossible numbers in these gases. According to 

 experiments hitherto made on atomic weights and densities of 

 gases, it must be assumed that in these cases 6 is far greater 

 than 500 T. 



* L. Natanson, Wied. Ann. xxxiii. p. 693 (1888). I have formerly 

 tried to prove that the energy of the "free" molecules should be taken as 

 a measure of the temperature. In a paper which I know only by an ab- 

 stract (Proc. R. S. E. xvi. p. 69, 1889), Tait arrives at the same conclusion 

 by quite another line of argument. 



