32 Mr. J. Kam on van der WaaW Equation and 



We here find the same values as found in (12) and (13) 



\ G=v2 ' a = yy^l) a - See equations A & B, pp. 25, 26.) 



Apart from being a point of the critical isothermal the 

 critical point thus appears to belong as well to two other 

 curves of the equations : 



2P e .V c =l (constant), 

 and 



P+ — =1 



The latter curve cuts a horizontal equal pressure-line 

 twice, denoting the two values of V satisfying the equation. 



At the vertex of the curve for which -J-~ =0 and the two 



av 



values of V become equal, we have the critical point. Thus 



we wouldffind for the critical point, -— - =0: 



* r ' dv 



2c J^ 



or 



-* 



(14) 



which value substituted in the original equation gives us 



p + JL_A 



or 



and 



P c =9y, 2 P C V C =1 (constant), 



» p. 



in accordance with (12) and (13). 



It will be seen that the curve satisfying equation (d) is 

 formed by the line drawn through the points where the 

 i^otherinals below the critical temperature change into and 

 from the horizontal straight line, and which is known as the 

 4 " border-curve. " As the temperature approaches the critical 

 temperature, the horizontal straight line gets shorter and 

 shorter and the two volumes converge more and more 

 towards the same value, L e. the critical volume, which is 

 reached at the vertex of the border line. 



