## Solution Library

# Determine Numeric Solutions To Cubic Equations Of State

**Question**

Develop a numeric solution to the following cubic equations of state (EoS).

- Ideal EoS
- van der Waals EoS
- Redlich-Kwong EoS
- Soave-Redlich-Kwong
- Peng-Robinson EoS

between 1 bar and the chosen substance's critical pressure, P . Choose three substances of c varying polarity (i.e. nonpolar, moderately polar and highly polar) to show the differences between the above equations of state. Comment on the strengths and weaknesses of each EoS considered. Show the PV relationship across a suitable range of isotherms that lie between 1 bar and the substance's P c (i.e. Tn up to Tc). Your PV diagram should be represented on a semilog plot (i.e. P vs log(V)).

In order to determine the range of temperatures involved (i.e. Tn up to Tc), you will need to use an Antoine equation (3-parameter version or modified, 2-parameter version). Comment on the difference between the two versions of the Antoine equation. On the same plot, show the "envelope" of saturated liquid and vapour volumes (V and *V*) at the isotherms chosen above. Use two methods to solve for these volumes: an iterative approach, ideally using the DUPLICATE directive in EES; using the cubic equation solver that can be incorporated into the EES external library. Comment on the accuracy of these predictions against published values. Predict the latent heat of vaporization, Ã¢Ë†â€ H, for your chosen substances, comparing the *vap. *Clapeyron with its simplified version, the Clausius-Clapeyron. Comment on the differences observed. Comment on the accuracy of these predictions against the tabulated values.

**Summary**

The question belongs to Electrical Engineering and it discusses about numeric solutions to cubic equations of state for Ideal EOS, van der Waal EOS, Redlich-Kwong EOS, etc.

**Total Word Count 1607**

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