# Entropy

Ideal entropy is determined from

where for the vapor phase,

For the heat capacity Cp, the Temperature Correlation is used.

For the liquid phase,

For compound for which T > TC, the heat of vaporization is taken to be zero, and Psat,i is taken to be equal to P, so that SLi,ideal reduces to SVi,ideal.

## EOS

When using an equation of state, departure entropy can be determined from fugacity coefficient and its temperature derivative:

For both vapor and liquid, the vapor ideal entropy is used in the above, since the saturated vapor pressure and heat of vaporization are accounted for in the fugacity terms.

## From activity coefficient

If an activity model is used for the liquid phase, excess entropy can be determined from the activity coefficient and its temperature derivative:

The ideal entropy for the liquid phase is used in the above.

## From fugacity coefficient

When not using an equation of state, the equation for determining entropy from fugacity (as used for equations of state) still holds:

Again, for both vapor and liquid, the vapor ideal entropy is used in the above, since the saturated vapor pressure and heat of vaporization are accounted for in the fugacity terms. Any fugacity calculation method can be used with this routine.

Temperature and pressure derivatives for the above entropy calculations are determined by perturbation.

## Solids

For solid compounds, only ideal entropy is currently available. By default, the assumption is that the solids do not mix within the phase (representing multiple separate solid phases within an overall solid phase):

Alternatively you can select ideal mixing for the solid phase:

Here, Θi represents the (ideal) volume fraction of compound i (evaluated from mole fractions and pure compound solid densities).

The reference state entropy for solid-only compounds is zero for the solid state at reference pressure and temperature, and the solid compound heat capacity is configured per compound. Other solids are currently not supported.

The solid compound entropy is mixed ideally:

For these compounds, the absolute entropy needs to be in the solid phase for the calculation of EntropyF (see below).

# EntropyF

EntropyF, as opposed to entropy, includes the absolute entropy:

For EntropyF, the same models are available as for Entropy.

The absolute entropy Si,abs for each compound is tabulated in TEA's PCD data files.

# EntropyNF

EntropyNF is defined as entropy that is sure not to include entropy of formation. In TEA, this property is available and synonymous to Entropy.