LEWIS. — THERMAL PRESSURE. 165 



found that, if the two spaces were connected by a semipermeable mem- 

 brane, the partial pressure of the hydrogen was less in the space contain- 

 ing nitrogen. This could be easily explained by assuming a repulsion 

 between a molecule of hydrogen aud one of nitrogen, and this explana- 

 tion is asain in full accord with the observation of Joule and Thomson 

 that hydrogen mixed with nitrogen greatly decreased the cooling effect 

 of the latter when expanding through a porous plug. These bits of 

 evidence, accumulated, point decidedly to the truth of equation (16). 



It was stated above that in general a is a function of the temperature; 

 for if either in equation (16) or in the equation of van der Waals the 

 term representing intermolecular attraction should be independent of the 

 temperature, it would follow immediately from thermodynamics that 

 the specific heat at constant volume of a liquid or a vapor should be 

 independent of its volume, and also that a liquid and its vapor should 

 have the same specific heat at constant volume.* All our evidence, both 

 experimental f and theoretical,! is opposed to this conclusion. There is 

 little doubt that the specific heat at constant volume, even in gases, 

 changes in all cases, and sometimes considerably, with an isothermal 

 change in volume ; and it may be noted that while the equation of van 

 der Waals is incompatible with any deviation in the specific heat at con- 

 stant volume, such a deviation is a direct consequence of our present 

 theory. For, since the specific heat depends upon the energy required 

 to raise a substance from one temperature to another, and since that 

 energy, according to any kinetic theory, is partly consumed in increasing 

 the kinetic energy of the molecules, the specific heat must depend in 

 part upon the kinetic energy of the molecules at the two temperatures. 

 According to the accepted kinetic theory the energy of progression of 

 the molecules must be the same at any one temperature under all condi- 

 tions. The energy required to increase the progressive energy of the 

 molecules from one temperature to another would depend, therefore, on 

 the two temperatures, and would be independent of all other circum- 

 stances. On the other hand, according to the views expressed on pa^e 

 154, the kinetic energy of the molecules may vary at any temperature 

 according to the other conditions of a substance. Let us consider a gas 

 in which there is no attractive or repulsive force between the molecules. 

 According to the theory hitherto accepted, if the volume occupied by the 



* Cf. Nernst, Theor. Chem., p. 234 (1898). 



t Joly, Phil. Trans. Roy. Soc, 182 A, 73 ; Proc. Roy. Soc, XLVII. 218 ; LV. 390. 

 t Lewis, These Proceedings, XXXV. 1 (1899) ; Zeit. Pins. Chem., XXXII. 364 

 (1900). 



