CHAPTEE X. 



THEORY OF A NON-CONSERVATIVE GAS (CONTINUED). 



CALORIMETRY. 



251. WE have seen that the hypothesis upon which we have been 

 working leads to a possible explanation of the difficulties connected with 

 the dissipation of energy. This hypothesis therefore puts us in a position 

 to continue the investigation into the behaviour of a gas, at the point at 

 which we had to abandon it before (Chapter VII.). We shall accordingly 

 attempt to investigate the calorimetry of a gas with, the help of this 

 hypothesis. Naturally the results obtained will give us further evidence 

 as to the tenability or the reverse of the hypothesis in question. 



Calculation of subsidiary temperatures. 



252. We have found that so long as a gas is at a temperature 

 comparable with the temperatures we find on this planet, or which we can 

 reproduce in the laboratory, the transfer of energy from the principal 

 degrees of freedom to the vibratory degrees of freedom is extremely slow. 

 If, then, TI, T 2 ... are the subsidiary temperatures corresponding to these 

 vibrations, we shall have an equation for the change in TJ of the form 



(500), 



where ^ is the rate of increase of T! caused by collisions. 



The number of collisions of any specified kind which occur per unit of 

 time is proportional to the square of the molecular density of the gas, so 

 that the consequent increase in r x is proportional simply to the density. 

 For the rest, since the subsidiary temperatures are small compared with the 

 principal temperature, the value of 6 l may be supposed to depend solely 

 on this principal temperature. We may therefore take l to be of the form 



(501). 



