26 THE TEÜE VALUE OF a OF VAN DIB WAALS' 



Prom Albertoni ] ) : 



a = «5Jf 2 . 4 2/3 /3— jSJf 2 (17) 



If these three formulas were correct then the value of a 

 computed from them should of course be the same, lîut all three 

 are in part at least empirical. The formulas of Mills and Dieterici 

 give values for a which, ou the whole, are quite similar, altho 

 seldom identical, and 1 have used both of these equations for 

 computing a. Albertoni's equation gives always a value of a 

 which is 10 — 20 °/ too low and this amount lower than either of 

 the other equations. For example a for ether from Albertoni's 

 equation has the value 15.31 X " )1J ' n place of the value of about 

 18.87 from Dieterici and 19.3 1- from Mills. The other methods 

 of determining a show that the proper value for ether is about 

 19.12 X 10 12 - With benzene, Albertoni gives 1 8.1 2, whereas the 

 others give from 19.17 to 20.78. Albertoni's equation gives a very 

 accurate determination of L — E except close to the critical tempe- 

 rature. Close to the critical temperature it agrees remarkably well 

 with the value of // — E which lone calculates using the figures for 

 the vapor pressure, or / ; , calculated by Biot's formula. Now it is 

 known that Biot's formula does not give the proper value of P 

 close to the critical temperature. Consequently Albertoni's equation, 

 which accurately follows Biot's, breaks down close to the critical 

 point, just as Biot's does and cannot be used to calculate a at 

 the limit of the critical temperature for this reason. We get too 

 low a value for a if we use Albertoni's equation, just as we 



do if we compute a from ( ■ - J derived from Biot's formula. It 



will be recalled that V,.-\-a\V ( r is equal to {TdP/dT) c at the 

 critical temperature. If we determine dP\dT at T c by differentiation 

 of Biot's formula the value of dPjdT thus found is from 10 — 20 °/ 

 too low so that a is also this amount too low. Biot's and 

 Albertoni's equations, while permitting a very accurate calculation 

 of P, and so of X — J'J, at other temperatures, do not, then, give 

 reliable results close to the end of the curve and cannot be used 

 for that reason at the limit. As regards the other two equations 

 each is at least partially empirical and it is clear from the fact 

 that they do not give exactly the same results that one or both 

 are only more or less close approximations to the truth. The values 



l ) Albertoni: Jour, de China. Phys. , 13, 379 (1915). 



