Approaching the Thermodynamic Limit of an Ideal Gas

For a gas confined in a container, particle-wall interactions produce modifications to the partition function involving the average surface density of gas particles. While such correlations have a vanishing effect in the thermodynamic limit, examining them is beneficial for a sharper understanding of how the limit is attained. We contrast a classical and a quantum model of particle-wall correlations within the canonical ensemble.

💡 Research Summary

The paper investigates how particle‑wall interactions modify the canonical partition function of an ideal gas and how these modifications vanish in the thermodynamic limit. Two complementary models are examined: a classical description with a finite‑height step potential and a quantum mechanical description using Dirichlet boundary conditions. In the classical case the single‑particle partition function separates into a momentum factor and a coordinate factor. The coordinate factor involves an “excluded length” ℓ(β)=a