Nonparametric scaling equation of state for description of critical behavior of liquid

A new nonparametric scaling equation of state is suggested for the description of equilibrium thermodynamic properties of liquids in the vicinity of the critical point. The equation contains three system-dependent fitting constants. This equation is used to perform approximation of experimental $P$–$\rho$–$T$ data for $\text{He}^4$ in the range of reduced densities of $-0.45 < (\rho - \rho_c)\rho_c < 0.37$ with mean-square error with respect to pressure of $18\%$ for the values of critical exponents adopted for the three-dimensional Ising model. The behavior of isochoric heat capacity of $\text{He}_4$ in the critical region is calculated using the fitting constants obtained as a result of approximation of $P$–$\rho$–$T$ data. The error of calculation by the new equation of the experimental data with respect to $C_V$ for $\text{He}^4$ in the ranges of reduced temperatures $(T - T_c)/T_c$ from $-0.3$ to $-0.001$ and from $0.001$ to $0.2$ does not exceed $4\%$.