232 THE REALITIES OF MODERN SCIENCE 



ture these two volumes are the same. For higher 

 temperatures the substance cannot exist as a liquid 

 and the isothermals are the hyperbolic curves of a gas.) 



As the temperature rises the three volumes which Van 

 der Waals's equation indicates (two of which exist only 

 on the hypothetical portion of the isothermal) approach 

 each other in value. For some particular values, say 

 P c and T c , they will be equal. This occurs when the 

 maximum volume of the liquid and the minimum 

 volume of the saturated vapor are equal. This is 

 the critical volume, and P c and T c are the critical pres- 

 sure and temperature. 



The equation of Van der Waals has value as indicat- 

 ing the general character of the relations between the 

 molecules of any substance and the fact that all sub- 

 stances behave essentially alike, but it gives only 

 approximate relations. It fails particularly to give 

 accurate values for the critical state. 



It has been found, however, that an extension of this 

 equation may be used to considerable advantage. 

 Instead of using P, V, and T to represent the actual 

 pressures, volumes, and temperatures, there are sub- 

 stituted the fractions which these are of the critical 

 values. For example, when two different substances 

 are under pressures which are the same fractions of 

 their respective critical pressures, they are said to be 

 in corresponding states of pressure. Similarly there 

 are corresponding temperatures and volumes. These 

 substitutions give rise to an equation which should be 

 applicable to all substances. All substances, since 

 they are composed of molecules, provided the mole- 

 cules do not change (chemically), should act in the 



