274 SCIENCE PROGRESS. 



of the whole of the molecules, and let /3ST be the energy 

 that is taken up in vibrations of the atoms relatively to the 

 centre of mass of the molecule, and the other forms in- 

 cluded in C, D and E. It is not assumed here that /3 is 

 constant. It is probably not constant in the case of some 

 gases, but at any one temperature and pressure the heat 

 that goes to increase the intramolecular energy will bear 

 some definite proportion to that which increases the trans- 

 lational energy. 



We have then Q,St = ST + j3ST. 



Now if we consider what becomes of the heat that is 

 given to the gas at constant pressure, we get — 



C,S/ = ST + /3ST +ph> 

 where §v is the small amount the gas expands to prevent 

 the pressure rising with the rise of temperature, and hence 

 phj is the work done. We are supposing here that the gas 

 is perfect, and are neglecting the gain of potential energy 

 due to separation of the molecules. It would be quite easy 

 to take account of it, but it increases the complexity of the 

 equations, and only enters as a correction in the final result. 



If we assume that the pressure of the gas is due to the 

 impacts of small elastic molecules, we know that for unit 



2 2 • 



mass pv = - T, so that with/ constant p$v- = - ST. Putting 



in this value and dividing the second equation by the first 



C, 2 



we get -^ = y = i + 



0, ' 3 0+/:*) 



Hence if we know the ratio of the two specific heats of 



a gas we can calculate the relative rates of increase of the 

 translational and the internal energy of the molecule. /3 is 

 sometimes incorrectly described as being the proportion of 

 the energy that is internal. This is not justifiable. All 

 that /3 tells us is what proportion of a given increment 

 of energy becomes internal, so that, when we find that /3 is 

 zero for mercury vapour, we must not conclude that the 

 molecule has no energy of rotation for instance, but only 

 that under the circumstances under which y was deter- 

 mined the rotation did not change appreciably as the 

 temperature changed. 



