A Simple Theory of Condensation

TL;DR

This paper presents a simple theoretical model explaining gas condensation as a phase separation caused by atomic cluster formation, predicting a critical temperature and anomalous heat capacity behavior.

Contribution

It introduces a straightforward assumption linking atomic clusters to phase transition, providing analytical predictions for critical temperature and heat capacity exponents.

Findings

Identification of a forbidden density range indicating phase separation.

Prediction of a specific heat capacity divergence near the critical temperature.

Estimation of the heat capacity exponent as approximately 0.077 for c=13.

Abstract

A simple assumption of an emergence in gas of small atomic clusters consisting of $c$ particles each, leads to a phase separation (first order transition). It reveals itself by an emergence of ``forbidden'' density range starting at a certain temperature. Defining this latter value as the critical temperature predicts existence of an interval with anomalous heat capacity behaviour $c_p\propto\Delta T^{-1/c}$. The value $c=13$ suggested in literature yields the heat capacity exponent $\alpha=0.077$.