( 130 ) 



staiit. Wliat modification niiist the equation of state be subjected to 



in order to account for this twice greater value? Clausius answered 



this question bj^ supposing a to be a function of the temperature 



273 

 e. g. by substituting a —;z^ for it 



When we consider the question superficially, the difficulty seems 

 to be solved. But it is only seemingly so. At T= Tk this modifica- 

 tion really causes ƒ to assume the value 7 — but this supposition 

 has consequences which for lower temperatures are contrary to the 

 experiment. If we calculate the value of 



dp f,-f, 



dl i\ — Vj 



a 273 



as on page 4 and if we take into account that s = — 2 — - we 



V I 



find 



a 273 



Tdp V J T 



^ ~ ~ RT 



For lower temperatures we will put t\ = h and we deduce 



approximately : 



Tdp _ a 273 



pdT b RT' 



or^) 



p dT -^ syr 



For — = — we find then for a value which is not twice 



Ti: 2 p dl 



as great as that which follows from a constant value of a, but a 



value which is four times as great. 



The equation : 



pv — \pdv -= pv = ipdv 

 yields for this value of a : 



-'<.=«¥©-"("?^)+'' 



In order to agree with ƒ f-^'— 1 j the positixe term of the right- 



27 Tt 

 hand member of this equation should have the form ^ X -^ y ; ^^nd 



the negative term should not be % 2 X 27, but lo(j 27'. 

 1) Gontinuitat, p. 171. 



