Criterion for determining the Critical Point of a Gas. 41 

 ET 



V 



-2/3 + a=3<£, 



^-2/3^-2«/3 + / S 2 =3^ 



giving, for 0, the cubic 



whose roots are 3a + 2/3, — /3, — j3. Of these, the first alone 

 is admissible, from which 



5?=8(« + 0), and^ = 27( a + /S) 2 , 



whence the temperature and pressure of the critical point are 

 given by 



T 2_ _8_ 

 27 



and the volume at the 



c 2 _ 1 Re *) 



R(a + /3)> ^ - 216 (a + £T V (4) 

 ? critical point is <£>, i. e. 3a + 2#. J 



The substitution of Clausius's numbers (2) in equations (4) 

 give, 



T-274 = 30° 



15 — -1- ) 



V ~ 223' J 



(5) 



From Andrews's table for carbonic acid at 31°*1 (the near- 

 est recorded to the critical temperature), the following table 



indicates the values of . * between successive values of pi — 

 Av r 



Table.— Temp. 31°*1. 



P 



v 



— Ap-r-Av 



77-64 



75-40 



73-83 



73-26 



71-25 



1 



51*3 



60-9 



108-7 



112-2 



128-2 



18950 



•233 -033 -163 -126 





where the last column is calculated from the same table. At 

 this temperature the least change of pressure for a finite change 

 of volume takes place between the pressures 73*83 and 7 5 '40 — 

 that is (say), at the pressure 74J ; and between these pressures 



