In Equation (13), we have an infinite integral by the means of Gillespie (the lower integration boundary is 0), but which has a finite value and, therefore, is harmless and solvable if we have an EOS. Equation (13) provides the definition of the fugacity coefficient for a pure fluid:
(14)
Equation (14) defines the fugacity coefficient at any pressure dependent only on the upper integration boundary, either P or Pr in Equation (13). It is important to note that for the derivation of Equation (14), no assumptions were necessary and no general limits have to be considered but the ideal gas law per se.
As in Equation (13) we can also write
(15)
which leads with Equation (14) to:
(16)
