A New Regularity for Internal Pressure of Dense Fluids

Abstract

In this paper, we derive a new regularity for dense fluids, both compressed liquids and dense supercritical fluids based on the Lennard-Jones (12-6) potential function and using speed of sound results. By considering the internal pressure by modeling the average configurational potential energy, and then taking its derivative with respect to volume, we predict that isotherm [(partial differential E/partial differential V)(T)/rhoRT]V(2) is a linear function of rho(2), where E is the internal energy, (partial differential E/partial differential V)(T)) is the internal pressure, and rho = 1/V is the molar density. The regularity is tested with experimental data for ten fluids including Ar, N(2), CO, CO(2), CH(4,) C(2)H(6), C(3)H(8), C(4)H(10), C(6)H(6), and C(6)H(5)CH(3). These problems have led us to try to establish a function for the accurate calculation of the internal pressure based on speed of sound theory for different fluids. The results of the fitting show limited success of the pure substances. The linear relationship appears to hold from the lower density limit at the Boyle density and from the triple temperature up to about double the Boyle temperature. The upper density limit appears to be reached at 1.4 times the Boyle density. The results are likely to be useful, although they are limited.

Calculation of Thermal Pressure Coefficient of Lithium Fluid by pVT Data

“…A relationship that has recently been derived for dense fluids is the internal pressure regularity, which ((∂E/∂V ) T /ρRT)V 2 is linear with respect to ρ 2 for each isotherm, where ρ = 1/V is the molar density, E is the internal energy, and V is the molar volume [7]. The internal pressure regularity, which was originally devised for normal dense fluids, is based on the cell theory and considers only nearest adjacent interaction.…”

“…LennardJones potential function suitably describes the interactions 2 ISRN Physical Chemistry between the molecules of a fluid under the condition that it behaves as a normal fluid. The internal pressure regularity was attempted to calculate the internal pressure by modeling the average configurationally potential energy and then taking its derivative with respect to volume [7,8].…”

Determination of Molecular Diameter by PVT

“…Combining the foregoing results, it finds the internal pressure for dense fluids based on Lennard-Jones (12-6) potential function. It shows that the isotherm ((∂E/∂V ) T /ρRT)V 2 is linear function of ρ 2 and so predicted the temperature dependence of its parameters [8]. The final result is therefore of the form:…”

“…In the case of an ideal gas, the internal pressure is zero because intermolecular forces are absent. In the case of imperfect gas, the internal pressure becomes appreciable, and in the case of a liquid, it may become much greater than the external pressure [8].…”

“…This equation of state works very well for all types of dense fluids, for densities greater than the Boyle density. The regularity was originally suggested on the basis of a simple lattice-type model applied to a Lennard-Jones (12-6) fluid [7,8].…”