Thermodynamic properties of liquid bismuth under pressure: New regularities and an equation of state

A new regularity for internal pressure has been introduced based on the suggested potential energy function in liquid bismuth. Both the experimental data and the calculated quantities from the power law equation of state have been used to show the validity of the regularity. The quantity X3Z−1 is a linear function of ln(X) with crossing points for all isotherms at high temperature, where X=VVm0, V, Vm0, and Z are molar volume, the molar volume at melting point and zero pressure, and compressibility factor. For the reduced isothermal bulk modulus B*=BTVRT and the quantity Zint=PintVRT, where BT, R, T and Pint are isothermal bulk modulus, the gas constant, temperature and internal pressure, the new regularities have been introduced that both calculated X3B*−1 and X3Zint from the equation of state of a power law form versus ln(X) are nearly linear along each isotherm. However, those derived values from experiments become nonlinear functions of ln(X) at large pressure for all isotherms. Based on the new equation of state, analytical expression of thermodynamic properties of liquid bismuth can be obtained. The different extreme values exist along the isotherms for the calculated internal energy, isobaric heat capacity, and isochoric heat capacity for the new equation of state and the power law form equation of state.