MECHANICAL EQUIVALENT OF PRESSURE MARGULES 505 



a' the relative change of density in k and k r ; we now have 



jadk + j o'dk' = 

 and for the limiting case 



jo' 2 dk' = 



which latter equation and similar ones for the higher powers of 

 a' hold good for an infinite volume k' of gas. 



Therefore the expressions (la*) and (16*) remain unchanged if the 

 integrals are extended only over the disturbed portion. 



In order to formulate expressions for the work, or potential energy 

 of a closed system, we note that the share contributed by the 

 volume k' to the potential energy is given for isothermal condi- 

 tions by 



A' = Lim RT jdk' ft' log(-) =RT } t Q jo' 

 = - RTJ(fi -fi )dk 



or for adiabatic conditions by 



i'-==iJV-A)«»-~£?i.r 



-— JCf-A)"- -f^j^dk 



If again A indicates the potential energy of the whole mass of 

 gas, then we have: 

 for isothermal conditions: 



A=RTJdk^t\og ! " + (i - ft)=fdk[p \og-£ +p -p)...(Ia') 



N Po 



or for adiabatic conditions: 



a= *° 



Po r 

 ~ r -i J 



Po \f*o 



dk . . . (16') 



The integrals are to be extended over the disturbed portion, or 

 indeed over the whole volume, since the terms that are added to 

 the previous expressions (la) or (16) contribute nothing more to 

 the result that pertains to the volume k + k' . 



