A rotational equation of state for normal paraffins

Abstract

The hard convex body and hard sphere equations of state are used to derive a partition function that considers the effect of density on ratational motion in addition to translation. The inclusion of the rotational contribution in the perturbation theory gives rise to a more general principle of corresponding states for thermodynamic properties of polyatomic fluids. The argon equation of state developed by Twu—Lee—Starling is used to calculate the properties of a reference system in the perturbation expansion. In addition to adding the rotational pressure to the argon equation of state, the size of the reference system is also scaled up to that of real systems of interest to describe the properties of systems with either small or large molecules. The equation of state contains a structure parameter which acts as a third parameter in addition to molecular size and energy parameters. The size parameter can be calculated from the critical volume, the energy parameter from the critical temperature, and the structure parameter from the normal boiling-point temperature. Furthermore, the generalized equation of state for normal alkanes can be reduced to a function only of normal boiling-point temperature. The rotational equation of state represents accurately the vapor pressures, densities and enthalpy departures of the vapor, liquid and fluid states over the entire range of practical interest for the normal paraffins. For normal-paraffins, methane through n-eicosane, the average absolute deviation percent for all properties is less than 1% for 1541 points.