On heat capacity of liquid mercury under pressure

This study investigates the heat capacity of liquid mercury under pressure using experimental data, a linear isothermal regularity equation of state, and a power law equation of state. A key finding is the identification of a new linear isothermal regularity. The derived density, isobaric thermal expansion coefficient, and isothermal bulk modulus from the linear isothermal regularity equation of state show excellent agreement with experimental data. Analytical expressions for isobaric ($C_{pm}$) and isochoric ($C_{vm}$) molar heat capacities reveal extreme values specifically, $C_{vm}$ shows a maximum at higher temperatures, while $C_{pm}$ exhibits both a minimum and a maximum within a narrow temperature range. These results highlight the complex thermodynamic behavior of liquid mercury and provide insights into heat capacity anomalies in liquid metals, emphasizing the need for further research into microscopic origins under high-pressure conditions.