214 Theory of a Non-Conservative Gas [CH. x 



reabsorption of vibratory energy shall be perfect. Even if the first con- 

 dition is satisfied, while only a definite fraction K of the radiated energy is 

 reabsorbed, it will be seen that the equations of 252 are still true, except 

 that e must be replaced by e(l ). 



The Total Energy of a Molecule. 



258. In the expression for the energy of a molecule of the gas, there 

 will be momentoids other than those corresponding to the small vibrations 

 we have been considering. The most obvious instance is that of the energy 

 of rotation, which will be responsible for three momentoids. 



If we consider the simplest case of molecules represented by perfectly 

 symmetrical, smooth and elastic spheres, it is clear that these three 

 momentoids do not enter at all into the dynamics of the gas. A collision 

 cannot alter the rotation of the molecules, and the whole behaviour of the 

 gas is exactly the same as if these rotations were of zero amount throughout, 

 i.e., the same as if the three corresponding momentoids were ignored 

 altogether. In nature, it is possible that we have to deal with very approxi- 

 mately spherical molecules, but we may be sure that the perfect conditions 

 postulated for the ideal elastic spheres will not occur. If the molecules are 

 approximately spherical, it is clear that only very small rotations will be 

 set up by collisions. If, then, we suppose that rotations are accompanied by 

 dissipation of energy, the momentoids which represent the energy of rotation 

 may be supposed governed by a subsidiary temperature. 



If the molecule is of a shape far removed from spherical symmetry, it is 

 clear that the transfer of energy from translational to rotational energy at a 

 collision will be comparable with the whole energy of the molecule. In this 

 case the rotation will be governed by the principal temperature, if the 

 radiation from the rotation is nil or is very small. If this radiation is not 

 very small, the dissipation of energy from the gas will go on with great 

 rapidity, a condition which need not be discussed since it obviously does not 

 occur in nature. 



The potential energy of the molecule must also be taken into account. 

 The small vibrations will result in changes of potential energy, but these 

 may be represented by terms of the second degree in the coordinates, and 

 may therefore be regarded as momentoids. The potential energy of any 

 small vibration, averaged over a sufficient time, is equal to the kinetic 

 energy averaged over the same time, so that the potential energy of these 

 vibrations will be governed by subsidiary temperatures, these being the same 

 in every case as for the kinetic energy. 



We therefore suppose the total energy of the molecule to consist of 



(i) the energy of translation, proportional to the principal temperature ; 



