Description of heat capacity $C_v$ of simple liquids using a thermal equation of state, including regular and scaling parts

The $p,\rho,T$-data for $\mathrm{CO}_2$ are approximated in the ranges of $0 < \rho/\rho_c < 2$, $217 < T < 430$ K, and $0 < p \le 25$ MPa and for $\mathrm{SF}_6$ in the ranges of $0 < \rho/\rho_c < 2.5$, $225 < T < 340$ K, and $0 < p \le 10$ MPa using a new unified equation of state. In this equation, pressure p is an explicit function of $\rho$ and $T$. It includes a new regular part to approximate $p,\rho,T$-data in the liquid and gaseous regions of state outside the critical region, a singular part that is a scaling equation of state for the critical region, and a crossover function for combining these equations. The regular part consists of the sum of eight terms with eight constants, three of which are determined by the conditions at the critical point. The total number of system-dependent constants is fourteen, including the critical values of $p$, $\rho$, and $T$. In the scaling part of the equation of state, the critical exponents of the three-dimensional Ising model are used. The mean-square error of the description by pressure of the $p,\rho,T$-data for $\mathrm{CO}_2$ is $\pm0.63\%$, and for the $p,\rho,T$-data obtained for $\mathrm{SF}_6$, it is $\pm0.70\%$ over the entire range of gas and liquid states. Using the constants of the combined equation, heat capacity $C_v$ is calculated at isochores, isotherms, and a binodal, including those in the critical region. The calculation results describes the known experimental data of $C_v$ with an error of $\pm8\%$.