and the Properties of Liquids. 573 



an equation that is sometimes useful. Since the heat of 

 evaporation is zero at the critical point we must have 



l + * + /3 + 7-f- ... =0. 



An interesting case is obtained when </> 2 is put equal to 

 7 / n 1 

 —, f-<l>x( rfr ) in the general equation for the heat of evaporation, 



/ T\ . T 



where <j>A ^ J is a function of T - g The equation then becomes 



where c^ is a numerical constant. Substituting this value of 

 L in Clapeyron's equation 



HH)( T S-> 



where p denotes the pressure of the saturated vapour, we 

 obtain 



MV^g)' /3 .*<|)=Tg-p. ... (2) 



Dividing by T 2 and integrating we obtain 



^=c+ fl (v^) 2 g;)' 3 JV(tJ-?' 



where C is an arbitrary constant whose value can be 

 obtained in terms of the critical quantities by applying the 

 equation to the critical point. By choosing the form of 



<£*(rjr) so that the above integral can be evaluated we 



can pass at once from a formula for the internal heat of 

 evaporation to one connecting p and T, and in which all the 

 constants are determined. 



If we are given an empirical relation connecting p and T 

 we can determine the nature of the constants it contains by 

 means of equation (2). This is best illustrated by an 

 example. Let us take the equation 



log p =A-y- Clog T, 



which perhaps better than any other agrees with the facts *. 

 * "Winkeknann's Handbuch der Pkysik, YVarme, sec. editiori, p. 957. 



