20 PROCEEDINGS OF Till: AMERICAN ACADEMY. 



the molecules, we cannot say a priori how it will change with the dis- 

 tance between the molecules. In fad it i- not accessary to suppose that 



dWi 

 a or must always bave a positive value. Joule and Thomson 



I r 



found in the case of hydrogen a rise of temperature instead of the usual 

 cooling effect en free expansion. This would indicate a Bmall negative 

 value of ''. corresponding to a preponderance «>t' repulsive Force between 

 the molecules. The unreliability of the experimental data, however, 

 pr< clu lea certainty <>u this point. 

 Jn place of the equation 



RT dm RT a 



P ~v -/('•) " dv' P == v - b ~ ' 



the equation of van der Waals, can be applied to liquids with the under- 

 standing that a and b are not constants hut volume functions to be deter- 

 mined. In all liquids p is small compared with tlie other two terms. 

 "When p = 0, if we represent the volume by r 0) 



R T a 



A= : (82) 



but since the volume of liquids is only slightly changed by changing the 

 external pressure, r — b will not differ materially from V — b at 

 atmospheric pressure. We may write, then, as the equation for liquids at 

 atmospheric pressure, 



RT _ a 



v — b f- ' 



From this equation may be found the values of a and h when the vol- 

 ume of a liquid is known at two different temperatures. Prom the 

 values thus found it should he theoretically possible to calculate the com- 

 pressibility of the liquid at constant temperature. Thus by differentiating 

 the van der Waals equation we obtain the reciprocal of the COmpressi- 



biHty ' d P = RT o!L 



practically this method fails on account of the fact that the difference 

 between the last two terms is very small compared with their total val- 

 ues, and therefore any error in either of these terms is multiplied enor- 

 mously in the determination of . 



' dv 



The values of a and l> obtained from equation (33) will be of service 



