396 Dr. R. D. Kleeman on Fundamental 



Conditions to be satisfied at the Absolute Zero by the 



Equation of State. 



One of these conditions is p = 0, .... (15) 



when v = v x and v = v 2 = oo . 



Two more conditions are obtained on applying equations 

 (2) and (6) to the substance. The equations can then be 

 simplified. Since p = () and v 1 is finite, pv 1 = 0. The satu- 

 rated vapour then behaves as a perfect gas, and consequently 



RT 

 pv 2 = =0. It follows therefore that p(v 2 — v)=0. In 



m . dp 



a subsequent paper it will be shown that -^,=0. The 



equations then become 



U 1+Ui -u a =-~-^, .... (16) 



j; 



p.dv=0 (17) 



nJV x 



We must also have / dp\ , 



{^K =0 > (18) 



when u = -y 2 = oo . This follows at once from a consideration 

 of the isothermals of the substance. If the volume of the 

 substance keeping its temperature at the absolute zero is 

 gradually increased the pressure will decrease, since the 

 substance increasingly behaves as a perfect gas. The p axis 

 is therefore asymptotic to the isothermal for T = 0, and hence 

 when ii = oo the above equation must hold. 



It should be pointed out that the foregoing conditions are 

 not included in the conditions applying to the critical point. 

 Thus suppose that the constants in the equation of state are 

 determined by means of all these conditions. Let us assume, 

 for example, that the equation of state contains expressions 

 of the form (A+TB). In the first of equations (7) this 

 expression becomes (A + T C B), and in equation (15) it becomes 

 A. Thus the equations obtained would not be the same. 



The Laiv of Corresponding States. 



This law has been deduced by van der Waals from his 

 equation of state. It does not seem to be generally recog- 

 nized, however, that the deduction rests on very weighty 

 tacit assumptions. It is necessary therefore to investigate 

 it a little more closely. 



The constants in the equation of state will obviously 

 depend on the units of pressure, volume, and temperature 



