CHANGE OF STATE LIQUID VAPOUR. 195 



From this the critical pressure is 977,2 = ^1 atmospheres, 



while the critical temperature is = 32*5, 



27011 



which are values not very far distant from those found by Andrews. 



The values of a and b, however, are not determined very exactly, and 

 the best test of the equation is probably to be found in the comparison 

 with experiment of certain deductions from it which we shall now 

 discuss. 



Reduced Isothermals Corresponding Temperatures. If we 



express the pressure, volume, and temperature for a given condition of a 

 substance as fractions of the critical values, viz. : 



ea 



v = nv = Srib 



and substitute these values in Van der Waals' equation, it at once 

 reduces to 



from which a and b, which refer to a particular gas, have entirely dis- 

 appeared. 



If the same value of m is taken for different gases which have critical 

 points Q c , #', &c., the temperatures indicated by mO c , mO c ', &c,, are " cor- 

 responding temperatures." Thus the absolute critical temperatures for 



ether and water are 470 and 638 about. If we put m = -, then a temper- 

 ature of 235 absolute, or - 38 C. for ether corresponds to 319 absolute, 

 or + 46 0. for water. The above equation shows that if m is constant, 

 i.e. if different substances are taken at corresponding temperatures, then 

 the relation between e and n is definite, and the same for all substances. 

 We have in fact a cubic in n, a Van der Waals' equation, in which 



1 8 



a = 3, &= o>R = o> an( ^ giving to m a succession of values we obtain a 

 o o 



family of curves representing the relation between e and n, of the same 

 general form as the isothermal curves given by the original equation. 

 These general isothermals are called Reduced Isothermals. To apply 

 any reduced isothermal to a particular gas we must multiply the m for it 

 by B c to get the temperature, and must multiply the values of e and n at 

 any point by p e and v c respectively to get p and v. 



The line on a reduced isothermal corresponding to the horizontal 

 vapour-pressure line on a pv diagram is the same for all substances. We 

 may prove this as follows : The horizontal vapour-pressure line cuts the 

 continuous pv curve in three points, and, as we have seen, makes equal 



