THE RATIO OF THE SPECIFIC HEATS OF GASES. 273 



amounts of energy of translation, but the mean value taken 

 over a large number of molecules is what is usually taken 

 to represent the temperature of the gas, so that to say that 

 the temperature of the gas rises is equivalent to saying that 

 the kinetic energy of translation of its molecules increases. 



The energy in class B is small compared with that in 

 A, but is generally quite appreciable. The most usual 

 conception of a gas is that of a large number of molecules 

 attracting each other with forces that fall off very rapidly 

 as the distance between the molecules increases, so that 

 any one molecule is moving freely in an approximately 

 straight line during the greater part of the time. It is 

 necessary to assume some slight attractions between the 

 molecules, even when they are not very close together, to 

 account for the divergence from Boyle's law, hence on 

 expansion work will be done against these forces, and 

 potential energy will be gained. The amount of this 

 energy is, however, easily calculated, if we know the 

 characteristic equation of the gas, and so it gives us no 

 theoretical difficulty. 



The remaining three classes constituting the internal 

 energy of the molecule are the real difficulty. D will be dis- 

 cussed later, and is perhaps so small as to be negligible, 

 or at least constant in amount during changes of temperature. 

 Classes C and E are completely outside any dynamical 

 theory of matter at present. We cannot* calculate their 

 amount theoretically until our knowledge of the dynamics 

 of a molecule is very greatly extended, but fortunately we 

 have the means of proceeding in the reverse direction. We 

 can find what proportion of the total energy given to the 

 gas takes the form of C, D and E together, if we know the 

 ratio of the specific heats. The formula by which this is 

 effected is well known to physicists, but it will be well to 

 give the proof in order to show more clearly what it is we 

 really learn from it. 



Let C v be the specific heat of the gas at constant 

 volume, then the heat required to raise the temperature of 

 one gramme of the gas by a small amount & is C v £/. Let 

 ST be the increase in the kinetic energy of translation 



