174 PHENOMENA, ATOMS, AND MOLECULES 



proximately proportional to \/K. At high temperatures, however, the two 

 terms in the denominator must tend to become equal, so that Wi> would 

 approach a limiting value. From Equation 31 we can readily derive simple 

 equations for these limiting cases. 



At low temperatures the second term of the denominator is negligible, 

 so that 



K= VT2/T,W„2(BP + E)VP. (35) 



At low pressures this gives: 



At high pressures (here T„ = T2). 



w.> = Vk7p/b. (37) 



At intermediate pressures W/> increases to a maximum. Differentiating 

 (35) with respect to P and placing (IJVo/(fP = O leads to following maxi- 

 mum value of Wz) (here To = T2) : 



W„.ax. = VK/4BE. (38) 



The pressure at which this maximum occurs is 



P' = E/B. (39) 



At high temperatures Wd increases so that ultimately Wi)(BP-hC) 

 becomes nearly equal to P. Beyond this value it cannot go. Therefore, 

 at high temperatures W^* must graduall}' approach a limiting value. This 

 limit is 



at low pressures 



W^ = P/C (40) 



at high pressures 



Wz,= i/B. (41) 



The higher the pressure the higher is the temperature at which Wd ap- 

 proaches its limiting value. 



We shall see that the case where C = E is of special importance. If we 

 make this substitution in (31) and place 



F = BP-fE (42) 



we obtain the very simple equation 



K = VVT. p2^^. (43) 



At higher pressures T^ becomes practically equal to T2, so the equation 

 is still further simplified. 



K = F2WV(P - FW^). (43«) 



