LEWIS. — FREE ENP^RGY AND EQUILIBRTUM. 25 



vapors in which -j is negligible compared with the atmospheric pres- 

 sure. 



The molecular specific heats at constant pressure of ether in the liquid 

 and gaseous states are 40.48 and 31.67 respectively. At 30 degrees, the 



coefficient of thermal expansion for the liquid is .000163; v = .10o4 



a 

 litres; a, calculated by means of equation (33), in such units that — ^ is 



in atmospheres, is equal to 10.84. From these data — [ -TTp] — .1590 



in litre-atmospheres, or 3.843 in gram-calories. Subtracting the latter 

 value from 40.48, we obtain 36.64 as the molecular specific heat at con- 

 stant volume of liquid ether. From the value 31.67, subtracting the 

 value of i?, 1.98, we obtain 29.69 as the molecular specific heat at con- 

 stant volume of ether vapor. The difference between these values is far 

 greater than could be explained by experimental errors. 



It is interesting to see whether an explanation of such variations in 

 specific heat at constant volume can be found from the kinetic point of 

 view. We must believe that the energy imparted to a substance for an 

 increase in the progressive motion of its molecules corresponding to a 

 definite rise in temperature must be independent of the conditions of the 

 substance. If, however, the heat energy of a body is due not only to 

 the progressive motion of its molecules, but also to some additional mo- 

 tion such as the vibration or rotation of molecules, then the energy given 

 to the body in raising its temperature would be in part used in increas- 

 ing the progressive motion and in part in increasing the secondary mo- 

 tions of vibration, rotation, etc. The quantity of energy required for the 

 latter would not necessarily be independent of the volume of the body, 

 but might depend upon the proximity or rate of collision of the molecules. 

 If, however, a body were composed of molecules incapable of any except 

 progressive motion, we should predict absolute constancy in the specific 

 heat at constant volume. Mercury vapor is believed to be such a body, 

 and if liquid mercury, as seems probable, also is composed of monatomic 

 molecules, the value of c^. in the two states should be identical. Unfor- 

 tunately the specific heat of mercury vapor is unknown, and we cannot 

 test the correctness of this supposition directly. But if it be true, equa- 

 tion (36) should give a correct result for the heat of vaporization of 

 mercury. A calculation similar to those whose results appear on page 

 23 gives, for T= 623, v^ = .01566, b^ = .01419, v., := 58.7, L = 13,070. 

 The value experimentally observed by Person (1846) was 12,400.* 



* Comptes Eendus, XXIII. 162 et seq. 



