196 HEAT. 



areas above and below, as bgh and Me in Fig. 110. This is expressed by 



V 3 



pdv 



where pv relate to the continuous curve, P is the vapour pressure, V l 

 and V 3 the liquid and vapour volumes. 



If we now substitute in terms of the critical values, putting p = ep ey 

 v = nv a P = E> C , Y x = Wjz; c , V 3 = n s v e , p c v c divides out and we have 



n l 



an expression which shows that the areas cut off by the E line on the en 

 diagram are equal above and below. Substituting from equation (1) put 

 in the form 



_ 8m _ 3 

 3n-l n* 



we see at once that we can integrate. Then using the equations which 

 state that E x , n v E 1? n z are on the curve, we get two more equations which 

 might enable us to find E, n^ and n 3 if this were needed. But it is enough 

 to note that for the same value of m, E, n^ and n s are the same for all 

 substances. In other words, at corresponding temperatures the saturated 

 vapour pressures are the same fraction of their critical pressures for all 

 substances, and the liquid volumes and the vapour volumes are the same 

 fractions of the critical volume for all substances. 



Corresponding Pressures and Corresponding Volumes. If 



we take corresponding temperatures for different substances, the vapour 

 pressures at those temperatures are corresponding pressures. The 

 liquid volumes just before evaporation begins and the vapour volumes 

 just when it is completed are termed corresponding liquid and corre- 

 sponding vapour volumes. 



This constancy of E, n^ and n 2 for given m gives us a result which 

 can be more easily compared with observation than the original equation 

 between p, v, and 6. Thus Van der Waals used it to calculate the 

 boiling point of carbon dioxide from its known constants and those of 

 ether. The critical pressure of carbon dioxide is 72 atmos. and its 



critical temperature is 303*9 absolute. For 1 atmosphere, then, e = 



72. 



Now the critical pressure of ether is 36 '9 atmos. and the critical tempera- 

 ture is 463. The corresponding pressure is 36 - 9 x 760 x e = 384 mm., 

 which is the vapour-pressure of ether as obtained by direct experiment 



9SQ-Q 



at 16-9 0. or 289'9 absolute. Then m=- -1=0-625, and the corre- 



463 



spending temperature for carbonic acid is 303'9 x 0'625 = 190 absolute, 

 which is very nearly in agreement with observation of the boiling-point. 

 Young (Phil. Mag., xxxiii., 1892, p. 153, and in later papers) has examined 

 the behaviour of a number of liquids and vapours with regard to their 

 corresponding quantities. He finds that Van der Waals' result is not 





