Further Results on a Generalized van der Waals Model

Abstract

AbstractA generalized van der waals model is considered to study the thermodynamic properties of pure fluids. Analytical solution of the equivalent cubic equation of state is presented and the critical properties in the general form are derived. The fluctuations of number of particles are calculated in the grand canonical ensemble by using three quantities (scaled variance $$\omega (N)$$ ω ( N ) , skewness $$S\sigma, $$ S σ , and kurtosis $$k\sigma ^2$$ k σ 2 ). The critical behavior of these quantities is investigated in terms of the dimensionless particle number density and temperature for different models. It is found that the fluctuations have a singular behavior close to the critical point.