Virial expansion and condensation with a new generating function

•A new generating function for canonical partition function is presented.•It directly depends on irreducible cluster integral, unlike Mayer’s work.•With this generating function, we revisit Mayer’s theory of virial expansion.•Mayer’s convergence method with this new generating function.•It sheds light on to the problem of virial expansion and condensation.

Mayer’s convergence method for virial expansion and condensation is studied using a new generating function for canonical partition function, which directly depends on irreducible cluster integral, βkβk, unlike Mayer’s work where it depends on reducible cluster integral, blbl. The virial expansion, criteria for its validity and criteria for condensation, etc. are derived from our generating function. All earlier Mayer’s results are obtained from this new generating function.