Thermodynamic validation of the form of unified equation of state for liquid and gas

Proceeding from strict thermodynamic equations, a preferable structure of the unified equation of state (EOS) for liquid, gas, and fluid is determined. It is shown that the equation for the compressibility factor must contain the function of only one variable as one of the terms, namely, the function of volume (density). The physical meaning of this function as the compressibility factor is revealed with the temperature asymptotically tending toward infinity. It is shown that, in a wide range of parameters of state for fluids, the proposed three-parameter equation of state adequately describes the experimental data on the thermal properties of a number of monatomic $(\mathrm{Ne}$, $\mathrm{Ar}$, $\mathrm{Kr}$, $\mathrm{Xe})$, diatomic $(\mathrm{N}_2$, $\mathrm{O}_2$), and polyatomic $(\mathrm{CO}_2$, $\mathrm{NH}_3$, $\mathrm{CF}_4$, $\mathrm{CH}_4$, $\mathrm{C}_2\mathrm{H}_4$, $\mathrm{C}_2\mathrm{H}_6$, $\mathrm{C}_3\mathrm{H}_8)$ substances. The proposed equation of state is compared to a number of other known three-parameter equations of state, and it is shown that the proposed equation described the thermal properties several times more accurately than the known equations.