Equation for the coexistence curve of alkanes near critical temperature,based on the van der Waals Model

According to the fluctuation theory of phase transitions, a real liquid near the critical point is an ideal gas of the fluctuations of the order parameter, the size of which is determined by the correlation length of the system. We deduce the extended equation of state of liquids near the critical temperature by including the properties of the real van der Waals gas in this model, i.e., taking into account the own volume of the fluctuations of the order parameter and the interaction forces between them. We use this equation to analyze the temperature dependence of the density of a series of alkanes (C _n H_{2n + 2}, n = 1 − 12) along the line of the liquid-gas equilibrium near their critical temperatures. We show that the parameters of this extended equation of the state of substance are linear functions of the compressibility factor of alkanes.