266-270] Ratio of Specific Heats 223 



Monatomic Gases. 



268. There are four gases in the table, namely mercury, krypton, helium 

 and argon, for which we may take n-\-3 = 3, corresponding to the value 7 = If. 

 For these gases, then, we have w = 0; and since n is the number of degrees 

 of freedom, other than those of translation for which the energy is governed 

 by the principal temperature, the result that n = must be interpreted to 

 mean that the whole energy of the molecules of these gases is translational. 

 This can only occur if the molecules of the gas are very approximately 

 spherical in shape, and spherically symmetrical as regards internal structure. 

 For if this were not so, an appreciable fraction of the translational energy 

 of a molecule would be transformed into rotational energy at each collision. 

 Now if on the one hand we" assume the dissipation of rotational energy to be 

 slight, this would be inconsistent with the value ry=l|; while if, on the 

 other hand, we do not assume the dissipation of rotational energy to be slight, 

 it would be inconsistent with the observed slowness of loss of energy by the 

 gas as a whole. We conclude then that the molecules of these substances 

 are spherical. It follows that the molecules of the gases in question cannot 

 be composed of two or more atoms, and we therefore conclude that the 

 substances are monatomic. This is the view generally accepted by chemists. 

 It rests primarily, at any rate in the case of krypton, helium and argon, 

 upon the observed value of 7, but it accords well with the known 

 chemical inertness of the substances. The Kinetic Theory, then, suggests 

 the additional information that the atoms of these elements are spherical 

 as regards both shape and internal structure. 



269. After n + 3 = 3, the next possible value for n + 3 allowed by theory is 

 n + 3 = 4, corresponding to the value 7 = 1. In the table there is no gas for 

 which n+3 = 4, and there is no gas known for which 7 = l, even approximately. 

 This, however, upon closer examination is seen to be additional confirmation 

 of the truth of the theory. As a matter of geometry, a body, if not spherical, 

 can either have one axis of symmetry, in which case its surface is a figure of 

 revolution, or none at all. In the former case the energy of one of the 

 three momentoids of rotation may be small; in the latter case none of these 

 three energies can be small. It is impossible for the energy of two of the 

 three momentoids of rotation to be small, while the third is not small. 

 Thus a molecule for which n= 1 is impossible, and therefore the value 7= 1 

 is shewn by the Kinetic Theory to be an impossible one for any element. 



Diatomic Gases. 



270. After n + 3 = 3, then, the next possible value is n + 3 = 5, giving 

 7 = If, and corresponding to a molecule possessing symmetry about an axis, 

 as regards both shape and structure. From the table it appears that n + 3 



