Remarks on the Theory of Fusion and Condensation

We have re-examined the relation between the thermodynamic functions and the energy level density $\rho$ of a substance consisting of $N$ interacting particles for a class of hypothetical but (in the case $1\ll N\ll {10}^{23}$) not unreasonable functions $\rho$ defined by certain regularity conditions. We have shown that the specific features of $\rho$ which lead to condensation—in the sense of a discontinuous change of the most probable volume—under a volume independent force per unit area can yield partition functions which, in the condensation region, are smooth and of a shape similar to the van der Waals function. This is not a contradiction since for a substance under a volume independent force, the results of the conventional ad hoc re-interpretation of the van der Waals curve can be proved directly from the canonical ensemble, without the ad hoc assumptions.