24 Mr. J. Kara on van der Waals* Equation and 



In the above equation 



Po.V 



273 ' 

 whereas it will be remembered 



P =*N.m.c 2 ; 



N being the number of molecules per unit of volume, 

 m the mass of a molecule, c the velocity of mean square. 

 The molecules themselves are considered to be mathematical 

 points, and b (the volume of N molecules) here consequently 

 is zero. 



In realitv b has a positive and definite value and increases 



V 



the number of impacts, or the pressure, at the rate^= — -. , as 



was shown by van der Waals. ~~ 



An actual gas consequently exercises the same pressure P a 



at a greater volume ; i. e. the same volume V contains less 



molecules, say only N l5 having a volume /5, smaller than b. 

 Per unit of volume we thus get a decrease of impacts, 



caused by the decrease of the number of molecules at the 



Ni . y 



rate ^ , and an increase of impacts at the rate ^ — 9-= , caused 



by the influence of /3, and the effect of the former is com- 

 pensated by the latter. 



It is evident that the greater the compression, the smaller 

 the number of molecules per unit of volume of an actual gas 

 as compared with a perfect gas of the same pressure and 

 temperature. 



We may call ^ the specific density of a gas ; its value is 



greatest when the density is smallest, but always smaller 

 than 1 ; it decreases in value as the compression proceeds. 



This circumstance not being fully considered by van der 

 Waals' equation, causes large deviations. 



II. 



If at the volume Y and temperature T, N molecu]es of a 

 " perfect " gas exert a pressure 



y » 



then N molecules of an actual gas would exert this pressure 

 at a volume <j) = (Y + b) and the same temperature, b being 

 the volume of these N molecules. 



