116 MOLECULAR MOTION AND ITS ENERGY 52 



m the contrary, in the GASEOUS state the kinetic energy of 

 each MOLECULE increases by the same amount. 



The analogy of the two laws, which, by the bye, can 

 claim only an approximate and limited validity, does not, 

 however, entitle us to consider them identical, and to take 

 as the specific heat the magnitude 



obtained above as constant for gases. In the next para- 

 graph we shall examine its meaning more closely. 



53. Ratio of the Molecular to the Total Energy 



From the calculation of the mean speed of the molecules 

 in absolute measure the value of the kinetic energy of mole- 

 cular motion present in the gas is at once known. On the. 

 other hand, the value of the total energy present in the gas 

 can be calculated from its heat-capacity and temperature, 

 since it is equivalent to the heat contained in it. The 

 question arises, whether the two values calculated by these 

 different methods are in harmony with each other, and the 

 /resolution of such a doubt rests on the following considera- 

 tions, which are borrowed from Clausius. 



We ought not to expect the two values to be quite 

 identical, so that the calculated kinetic energy should be the 

 exact equivalent of the heat-energy ; for the molecules, on 

 their side, consist of atoms that are separately movable. 

 The kinetic energy of those motions which the whole com- 

 plex of atoms in a molecule together execute need therefore 

 not be the whole energy contained in the gas, but there 

 may, in addition to the forward motion of the molecules as 

 they course to and fro, be other internal motions of the 

 single atoms. The whole energy, calculated from the con- 

 tained heat, may very well then be greater than the energy 

 of molecular motion. 



We find the total heat-energy contained in a gas by 

 assuming that it has been brought into its present condition 

 by being warmed at constant volume from the absolute zero 

 to the temperature 0. If the volume filled by the gas is 



