Representation of the Thermodynamic Properties of Helium through a Temperature-Dependent Effective Potential

Abstract

This work presents a theoretical study of the thermodynamic properties of pure helium  within the framework of statistical mechanics, based on an extended lattice gas model. In this approach, particles are represented on a regular lattice with single-site occupancy and short-range pairwise interactions, providing a simplified description of weakly interacting systems.

The conventional lattice gas model is extended by introducing a temperature-dependent effective potential, which is extracted directly from high-precision experimental data of the second virial coefficient B(T) of helium. This procedure allows the effective incorporation of quantum correction effects into a classical statistical framework without altering the fundamental mathematical structure of the model.

The theoretical results are compared with reference data reported in the NIST database, and good agreement is obtained over a wide temperature range, particularly the intermediate and low-temperature regimes. In addition, the behavior of pressure, internal energy, isothermal compressibility, and correlation length is analyzed. The results reveal the emergence of quasi-critical behavior in the attractive interaction regime and the formation of a periodic lattice ordering in the repulsive regime at low temperatures.

These findings demonstrate that the extended lattice gas model, when experimentally calibrated through the second virial coefficient, constitutes an effective tool for interpreting the macroscopic thermodynamic properties of helium from a well-defined microscopic perspective.