406 MATHEMATICAL APPENDICES 25* 



Two different gases are at the same temperature when the mean 

 energy of the motion of the centroids of the molecules is the same in 

 both gases. 



If two gases are at the same pressure and temperature, equal 

 volumes of both gases contain equal numbers of molecules. 



The internal motion of the molecules 



not conform to such simple laws. Since the value of the potential 

 energy, which is spent in the form of chemical affinity when 

 atoms are combined to form molecules, is of different magnitude 

 in different compounds, the value of the energy (5 of the atomic 

 motions inside a molecule is by no means the same for all mole- 

 cules, but each kind of molecules has a different mean value of 

 t his species of energy. 



The sums total, therefore, of the energy in two gases at the 



same pressure and temperature are by no means equal, but only, 



as stated above, the amounts of the energy of motion of the 



centroids of the molecules. The correctness of this conclusion is 



/confirmed by experiment, which shows that gases do not in 



)/ general satisfy the law of Dulong and Petit, and that they 



therefore possess unequal atomic heats. 



