A theoretical model of gas-liquid phase transition near the critical point

Abstract

In this study, the internal pressure strength term in the Van der Waals multiphase interface equation has been adjusted to better fit the interface region. By applying the principle of normal isopressure, we can ascertain the thickness of the gas-liquid interface and the material's density distribution along the normal direction. At the gas-liquid interface, molecules experience both an attractive force pulling them into the liquid and a repulsive force from collisions with the gas. By considering the combined effect of these two forces, we can derive an expression for the latent heat of evaporation that includes the molecular volume parameter b, using the normal path integral. This expression is capable of predicting the latent heat of evaporation for substances like water, ranging from the boiling point to the critical point. The maximum deviation for conventional substances is under 30 %, while the prediction error using the Boltzmann distribution ranges from 40 % to 60 %. After introducing the dimensionless parameter τ_c, the maximum prediction deviation for H₂O drops to below 8 %, significantly enhancing the prediction accuracy for other substances as well. For subcritical temperatures (T_c-3 K < T< T_c), the new expression successfully predicts the latent heat of evaporation for over 30 substances, with an error margin of no >1 %. Additionally, it predicts the critical volume of a substance with a deviation of no >2.4 %. Thus, the latent heat of evaporation expression that incorporates molecular volume parameters demonstrates excellent predictive capability in the gas-liquid phase transition process near critical temperatures, providing a foundation for advancing the average field theory of gas-liquid phase transitions for various substances at near-critical temperatures.