158, 159] 



The Critical Point 



VALUES FOR |<r. 



141 



The Critical Point. 



159. Referring to figure 9 on p. 131, we see that at a temperature 

 below the critical temperature there are two points on every isothermal 

 (e.g., R, Q in the figure) at which dp/dv = 0. At the critical point P these 

 two points coincide. It therefore follows that at the critical point 



dp _ 

 dv 



0, 



Combining these equations with Van der Waals' equation, written in the 



form 



a_ = RNT 



v* v b ' 



we obtain, as the equations satisfied at the critical point, 



2a = RNT 

 v 3 (v b) 2 ' 

 Ga 2RNT 



from which we obtain 



(v - 6) 3 



276 



.(328), 

 (329), 



P = 



276 2 



giving the critical volume, temperature and pressure, 

 for the value of pv at the critical point 



(330), 



From these we find 



(331). 



It appears from this that at this point the deviation of pv from the 

 value given by Boyle's Law is represented by a factor f , and therefore that 

 this deviation cannot legitimately be treated as small. In spite of this, 

 equations (328) to (331) lead to values which are in surprisingly good agree- 

 ment with observation, when we consider the rough method by which the 

 equations are arrived at. 



7*C 11 - 



