143-146] 



Isothermals 



127 



Isothermals of an ideal gas. 



145. When p b is put equal to p, and the cohesion factor e~^ IRT ignored, 

 equation (303) becomes identical with the original equation (268) 



R T RT 



p pi = 

 - 1 m mv 



.(305), 



and the isothermals are the family of curves 



pv = constant (306). 



Plotted out with p, v as rectangular coordinates, these curves are a 

 family of similarly situated rectangular hyperbolas, having the axes for 

 asymptotes. These, then, are the isothermals of an ideal gas. 



P 



FIG. 6. 



Isothermals of a real gas. 



146. For extremely small values of p it will still be legitimate to replace 

 equation (303) by (305), so that the isothermals represented by equation 

 (303) will be similar to those of fig. 6, at the extreme right-hand of the 

 figure, but will require correction as we approach the region in which v is 

 small. 



The nature of one correction is at once obvious. The molecules being of 

 finite size cannot be compressed into a volume less than a certain minimum 

 volume v . When v is only just greater than v 0> the average free path of the 



