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**Residual Property Calculation from EOS**

From Virial EOS:

Using 5.35 and 2.12 one obtains:

...(5.39)

Next, on substituting eqns. 2.13 – 2.15 in 5.37 the following relations result:

...(5.40)

Similarly using 5.36 and 2.12 we get:

...(5.40)

Finally employing eqns. 2.13 – 2.15 in 5.38:

...(5.41)

**From Cubic EOS:**

One may use the following form of the cubic EOS :

...(2.21)**Or equivalently: ** .....(2.23)

While the eqns. 5.35 and 5.36 are useful for volume explicit EOS, they are unsuitable for cubic EOS which are pressure explicit. For the latter type of EOS one may show that the appropriate equations for residual enthalpy and entropy are

...(5.42)

...(5.43)

The above relations may be applied to the various cubic EOSs to obtain the necessary residual property relations. The final results are shown below

From RK-EOS:

...(5.44)

...(5.47)

**where, **

**For SRK-EOS: **

...(5.48)

...(5.49)

...(5.51)

**For PR-EOS:**

...(5.52)

...(5.53)

...(5.54)

As part of computing the residual enthalpy or entropy (and internal energy) at any set of temperature and pressure, the molar volume or correspondingly Z^{vap} needs to be first computed employing the usual algorithm for solving cubic EOS described in section 2.3.3.

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