290 
temperatures (higher than the critical transition temperature 7;,=47;, 
in Hg). The same thing is also the case with great values of », 
for then @/,2 has only slight influence by the side of p. 
As regards the values of v near b, here too “*/g, will always be 
positive, because v cannot become smaller than 6, and « not smaller 
than 0. In consequence of the increase of a the volume will 
indeed become somewhat smaller; but this decrease can only be 
exceedingly small, as v is already almost = 6. 
Remark. In the equation (c) the constant C will contain the 
term (1/, (é3)>—(@))): RY = —Q,: RT (on account of (*/, C,—C,): RY), 
in which Q, represents the — always positive — heat of dissocia- 
tion (see § 9), while @ contains the term (1/2 — 1) log (v — 6) (for 
v—b=(v—b,) Xx B%/y,); hence #:W1-—a? will have the form 
Wa.AVa\ 
k wb)" De { ar anes ): pa in which & will contain ex- 
ponentially eae rb nor 7. If, therefore, the term with AVa 
is smaller than Q,, then 2 will shae O exponentially at 7=0 
vb. (If the term with Ap/a should be larger than Q,, ee 
approaches 0 exponentially). Hence according to (1) the differential 
quotient 42/7, will approach exponentially to O at any rate at 7==0, 
y=, as it contains the factor «(1—w«) : (v—b). If, however, 7 is 
> 0, everything depends at v—6 on the exponent of v—b, which 
will evidently be '/.;—1. In ‘ideal’ substances, where 8 = 1, this 
exponent is negative, hence 4/7, approaches to oo. But for “ordinary” 
substances, in which !/g, ranges between a little more than 2 and 
a little more than 4 (according as, in view of the factor 1: a oc- 
curring in 8, the temperature is higher or lower), the exponent in 
question will be positive, and @*/g, will thus approach 0. 
L 
§ 11. The Differential Quotient (5) and the Value of RT. 
t 
de) RT 
Al : 5 a |. 
From the equation of state p= ae follows : 
‘r) WRT (de) 1), +a) RT (, (00 DD (de 
& 1 v—b & (vb) ( a Gr Ge). 5; 
06 
Putting again (5 = Ab=0, just as before Ab, and writing 
G/]y 
