56 MOLECULAE AND ATOMIC ENEEGY 127 



56. Approximate Calculation of the Atomic Energy 

 in Polyatomic Molecules 



A further series of approximately correct values of these 

 ratios can be obtained by a theoretical method which has 

 been used by Sadi C a r n o t * to calculate the values of the 

 specific heat at constant volume from the observed values of 

 the specific heat at constant pressure. 



To explain this method we introduce the values of the 

 specific heats F, 7, which are referred to unit volume, instead 

 of C, c, which refer to unit mass ; these are given by 



r = cp, 7 = cp, 



where p is the density of the gas referred to that of water as 

 unity. Then for the ratio of the kinetic energy of the mole- 

 cules to their whole energy we have the formula 



E_ = 3 F-7 



H 2 ~7~ 



This new form of the formula possesses an advantage 

 when we take account of a law discovered by Car not, which 

 can be directly deduced from the formula 



developed in 53. If we write it in the form 



it contains only two constants, the mechanical equivalent J 

 and the difference F 7 ; of these only the latter can depend 

 on the nature of the gas used in the experiment. But con- 

 sidering two different gases under equal pressures and at the 

 same temperature, we see that the difference F 7 of the 

 two specific heats referred to unit volume has the same value 

 for all gases. 



It follows for our purpose, from this law, that the value 

 of the ratio of K to H in different gases is inversely propor- 

 tional to the specific heat 7 of unit volume of the gas at 



1 Reflexions sur la Puissance Motrice du Feu, Paris 1824. Reprinted in 

 Ann. Sci. de VEcole Norm. Super. [2] i. 1872, p. 393. Translated into English 

 by Professor Thurston, London 1890. 



