for Equal Volumes under Constant Pressure. 207 



and therefore 



»=g(y'-7) and yZ^ = | (1) 



Consequently the heat of molecular motion is to the heat of ex- 

 pansion in the constant ratio of 3 to 2. If the heat of expansion 

 increases, in consequence of the gas being subject to greater 

 pressure, the heat of molecular motion must increase also in the 

 same ratio, — a result which also follows from the consideration 

 that the number of molecules whose motion has to be augmented 

 likewise increases, for equal volumes, proportionally to the 

 pressure. 



If the heat of molecular motion and the heat of expansion be 

 deducted from the specific heat under constant pressure, the 

 remainder constitutes the heat of atomic motion, 



«=y-t(y-7)-(Y'-7)=y-3(y-7). - - w 



The simplest case that is theoretically conceivable is that the 

 heat of atomic motion should be proportional to the number of 

 atoms constituting a molecule — that consequently, if n be the 

 number of atoms contained in a molecule, and a the quantity of 

 heat required to increase the motion of one atom, we should have 



ct = na. 



Keeping in mind equation (1), the theoretical specific heat of 

 gases can now be calculated, after determining the value of «, 

 by the following equations : — 

 For constant volume, 



<y=.na + m = na-\- | (7' — 7) (3) 



For constant pressure, 



y' = na-\-m-\-ry'— <y—na+ % (7' — 7). . (4) 



If a gas departs notably from the laws of Mariotte and Gay- 

 Lussac, the actual specific heat will be greater than the theore- 

 tical, since in such gases the existence of molecular attractions is 

 indicated (for instance, by their greater compressibility), the 

 gradual overcoming of which as the temperature rises will require 

 an expenditure of heat. Hence, if the heat of atomic motion is 

 deduced for such a gas, by subtracting the heat of expansion 

 and of molecular motion from the specific heat as found by ex- 

 experiment, the value so obtained still includes the heat expended 

 in operations which do not occur in the case of perfect gases. In 

 order, therefore, not to find too great a value for the heat of mo- 



