a 



V' 



( -i45 ) 



(v—b) = RT. 



1 f dv\ 

 The value tor — I 77 J wliich we may calculate from this equa- 

 tion a[>|)lies only to the pressure y> = 0, and is therefore not the 

 same as would he found for another constant pressure; neither 

 is it that Avhich corres[)Onds to the points of the border curve. 

 For very low temperatures the difference will probably be small. 

 For higher temperatures the diifereuces might l)e consideraijle; and 

 for the temperature which is so high that the isothermal in its lowest 



1 fdv 



])oint touches the r-axis, in which case — I —=, 



1 ('dv\ 

 •ase — \ -^\ = X , it would even 

 V \dTJj, 



be absurd to suppose the two values to be mutually equal. 



1 f dv\ 

 An accurate calculation ot the value of — — ;;, yields accor^ 



ding to the relations chosen above: 



We will put /i = i and the following approximated relation 

 T Ulv \ 2z 



v\dTJ^,^o l—2z 



1 

 With z =:= ■ — (sec p. 140) this yields 0,4 for the value of ^«c or 



0,4 

 c(v = — - (tor ether) = 0,001 4(5. Our assumptions therefore appear to 



lead to a value for the coefficient of dilatation which does not deviate 

 much from the experimental value. 



If we had taken the form (f c k for a^ (hen the corresponding 



value of J woidd have l)een —— and we should have had: 



13,5 



'v \d^r)~ V^+ 7V 7 l"^2T' 



which is only about ', , of the true value. From this we conclude 

 that the assumption that oui- rclalions are satisfied and that at the 



1-jC 

 same time a has the form ac ^^- leads to inaccurate results. 



10* 



