Thermal properties of diffusing species into some host metals

Abstract

The study rigorously explored the thermodynamic properties of diffusing species by solving the spherical coordinate equation using the Frobenius method. This mathematical approach enabled the derivation of the partition function and energy equation, which were crucial in determining key thermal properties, including Helmholtz free energy, entropy, internal energy, and heat capacity. It was observed that internal energy and entropy exhibited a strong dependence on temperature, reflecting the dynamic nature of diffusing species in varying thermal environments. The findings provide valuable insights into the behavior of entropy within the classical domain, with both analytical expressions and graphical representations used to illustrate these thermal properties comprehensively. The graphical analysis highlighted the temperature-dependent trends and the critical points where classical and quantum mechanical effects influence the thermodynamic behavior of the system, offering a deeper understanding of the underlying physics.