CHANGE OF STATE LIQUID VAPOUR. 



193 



We give below a few critical constants, but it must be remembered 

 that the results obtained by different observers are not coincident : 



Van der Waals' Equation The equation of Van der Waals' (p. 152) 



is of great interest in connection with the critical constants of pressure 

 volume and temperature, in that above a certain value of 6 it is repre- 

 sented by curves having the general form found by Andrews, while 

 below that value the curves are of the form suggested by J. Thomson, 

 and represented in Fig. 110. 



The equation may be arranged as a cubic in v, viz., 



p 



p 



and this has either one or three real roots for given values of p and 6. 



Taking a given isothermal, say the lower curve in Fig. 115, it will 

 be cut only once by an equal pressure line if the pressure is less than 

 that at B, and only once again if the pressure is greater than that at D. 

 Between these values it will be cut three times as in A, 0, E. 



In the first case the substance is a vapour; in the second, a liquid ; 

 while in the third case it may be either a liquid, at A, or a vapour at E. 

 The volume is only realisable experimentally if ACE represents the 

 vapour-pressure at the temperature chosen. It is then a definite mixture 

 of vapour and liquid. But the equation hardly means this. It rather 

 indicates that it is conceivable that the substance might be brought quite 

 continuously all in one state round the curve EDCBA. We shall suppose 

 that if ACE is at the height of the vapour-pressure then the areas 

 ABO, CDE are equal (p. 187). Now plotting all the isothermals: the 

 equation agrees with observation in showing that ABODE gets less and 

 less, and that ACE draw nearer and nearer together as the critical 

 temperature is reached. At that temperature they coincide. Hence, 

 if we insert in the equation the critical values p e and d e the equation has 

 three equal roots, each equal to v c , the critical volume. 



Comparing then 



a 

 V s 



/, R#A 9 , av a b A 

 - [b + c I v 2 + --- = 



\PcJ PC PC 



with 



V s - 



