New method to calculate the virial coefficients at critical point

Many empirical and semiempirical relations have been used to describe the pressure -volume-temperature relationships of gases and liquids. Among those most frequently used are the equations of Van der Waals, Fowler-Guggenheim, Dietrici, Berthelot, Clausius, Beattix and Bridgeman and the most important equation of Virial (for one mole): PV/RT=Σ2pi=0[(-1)iCi2p/(i+1)(VC/V)i where P,V and T are respectively the pressure, volume and temperature of gas, and R the gas constant. The virial coefficients B1(T), B2(T), ..., Bn(T), ... are functions of temperature. The forms of these functions depend on the types of intermolecular forces in the gas. B1(T) is called the second virial coefficient, B2(T) the third virial coefficient, etc... The aim of this paper is to propose a new method to calculate the Virial coefficients at critical point. If we truncate the Virial series until the order (2p) and if we suppose that at critical point C all derivatives of P versus V at critical temperature Tc are until the order (2p), then, we obtain a linear system whose solution gives the various expressions of the Virial coefficients. The bidimentional critical isotherm of Virial was given. Our model was then tested experimentally and compared with the classical models of Van der Waals, Fowler and Guggenheim. Our results concur the best of experiments and allow us to explain the transitions of bidimentional phases. (author). 18 Refs. 2 Figs