Proving the Equality of Gibbs Energies for Vapor-Liquid Equilibrium Use the information in the steam tables of Appendix A.III to show that Eq. 7.1-9c is satisfied at 100°C and 0.101 35 MPa.

Question

Proving the Equality of Gibbs Energies for Vapor-Liquid Equilibrium
Use the information in the steam tables of Appendix A.III to show that Eq. 7.1-9c is satisfied at 100°C and 0.101 35 MPa.

[latex]\left(\frac{\partial S}{\partial N^{\mathrm{I}}} ight)_{U^\mathrm{I}, V^{\mathrm{I}}}=0 \quad ext { so that } \quad \frac{\underline{G}^{\mathrm{I}}}{T^{\mathrm{I}}}=\frac{\underline{G}^{\mathrm{II}}}{T^{\mathrm{II}}} \quad ext { or } \quad \underline{G}^{\mathrm{I}}=\underline{G}^{\mathrm{II}}[/latex] (7.1.9c)

Accepted Answer

From the saturated steam temperature table, we have at 100°C and 0.10135 MPa

[latex]\begin{aligned}\hat{H}^{\mathrm{L}} &=419.04 \mathrm{~kJ} / \mathrm{kg} & \hat{H}^{\mathrm{V}} &=2676.1 \mathrm{~kJ} / \mathrm{kg} \\\hat{S}^{\mathrm{L}} &=1.3069 \mathrm{~kJ} /(\mathrm{kg} \mathrm{K}) & \hat{S}^{\mathrm{V}} &=7.3549 \mathrm{~kJ} /(\mathrm{kg} \mathrm{K})\end{aligned}[/latex]

Since [latex]\hat{G}=\hat{H}-T \hat{S}[/latex], we have further that

[latex]\hat{G}^{\mathrm{L}}=419.04-373.15 imes 1.3069=-68.6 \mathrm{~kJ} / \mathrm{kg}[/latex]

and

[latex]\hat{G}^{\mathrm{V}}=2676.1-373.15 imes 7.3549=-68.4 \mathrm{~kJ} / \mathrm{kg}[/latex]

which, to the accuracy of the calculations here, confirms that [latex]\hat{G}^{\mathrm{L}}=\hat{G}^{\mathrm{V}}[/latex] (or, equivalently, that [latex]\underline{G}^{\mathrm{L}}=\underline{G}^{\mathrm{V}}[/latex] ) at this vapor-liquid phase equilibrium state.

Question 7.1.2: Proving the Equality of Gibbs Energies for Vapor-Liquid Equi...

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