Calculation of the Phase Diagrams (T – X and T – P) and the Thermodynamic Quantities for the Solid – Liquid Equilibria in n-tridecane

Abstract

The solid – liquid equilibria in n-tridecane is investigated by calculating phase diagrams and the thermodynamic quantities using the Landau phenomenological model. By expanding the free energy in terms of the order parameter of the solid phase, the phase line equations are fitted to the experimental data for the T – X and T – P phase diagrams from the literature. The temperature dependences of the thermodynamic quantities (order parameter ψ, susceptibility χ_ψ, free energy F, the heat capacity C, entropy S and the enthalpy H) are predicted for the n-tridecane from this model. Our results give that the slope dT⁄dP≅2 "K/MPa" for n-C13 to n-C17. ψ varies with T as ψ~(T-T_m )^(1⁄2) above T_m. It is linear for the 〖χ_ψ〗^(-1), S(T) and C(T), and quadratic for the F(T) and H(T) in n-tridecane. This indicates that the Landau model, describes the observed behaviour of the phase diagrams satisfactorily for the solid – liquid equilibria in n-tridecane. Predictions of the thermodynamic quantities can also be compared with the measurements and predictions of some other theoretical models. The pressure effect, in particular, on the solid – liquid equilibria in n-tridecane can also be investigated under the model studied here.