This study explores the virial equation of state as a model for approximating thermodynamic data for methane. We review the historical development of thermodynamic geometry, highlighting foundational contributions by Lychagin, who applied geometric methods to derive physical insights into energy con-servation, thermodynamic stability, and phase transitions. Using data from the National Institute of Standards and Technology (NIST) and prior studies, we modeled the second and third virial coefficients with polynomial expressions to achieve a high degree of accuracy in describing the thermodynamic behavior of methane across a range of temperatures and pressures.
