# Single Property Equations (Binary)

Single properties are represented either Directly (e.g., heat capacity, viscosity, etc.) or as Excess properties (e.g., excess volume, excess enthalpy, etc.). In TDE one equation formulation is used for each type of data representation.

## General Property Ψ Representation

Ψ = x1×Ψ1 + x2×Ψ2 + Σai×x1×x2×(x1 - x2)i, where xj and Ψj are the mole fraction and property value for component j, and the summation is from i = 0 to nTerms.

### Special Case 1: Viscosity

ln(h/ho) = x1×ln{h(1)/ho } + x2×ln{h(2)/ho} + Σ ai×x1×x2×(x1 - x2)i, where ho = 1 Pa×s and the summation is from i = 0 to nTerms.

### Special Case 2: Density

r = (x1×M1 + x2×M2)/Vm, where

Vm = x1×M1/r1 + x2×M2/r2 + Σ ai×x1×x2×(x1 - x2)i, where the summation is from i = 0 to nTerms.

r is density (kg×m-3), Vm is molar volume (mol×m-3), and M is the molar mass (kg×mol-1).

## General Excess Property ΨEX Representation

ΨEX = Σ ai×x1×x2×(x1 - x2)i, where xj is the mole fraction of component j, and the summation is from i = 0 to nTerms.

The Vector ai is temperature dependent with 1 to 5 terms.