Alternative Fugacity Calculation Use other data in the superheated vapor steam tables to calculate the fugacity of steam at 300°C and 8 MPa, and check the answer obtained in the previous illustration.

Question

Alternative Fugacity Calculation
Use other data in the superheated vapor steam tables to calculate the fugacity of steam at 300°C and 8 MPa, and check the answer obtained in the previous illustration.

Accepted Answer

At 300°C and 0.01 MPa we have from the steam tables [latex]\hat{H}[/latex] = 3076.5 kJ/kg and [latex]\hat{S}[/latex] = 9.2813 kJ/(kg K).

Therefore,

[latex]\begin{aligned}\hat{G}\left(300^{\circ} \mathrm{C}, 0.01 \mathrm{MPa} ight) &=\hat{H}-T \hat{S} \\&=3076.5-573.15 imes 9.2813=-2243.1 \mathrm{~kJ} / \mathrm{kg}\end{aligned}[/latex]

and G(300°C, 0.01 MPa) = -2243.1 J/g × 18.015 g/mol = -40409 J/mol. Since the pressure is so low (0.01 MPa ) and well away from the saturation pressure of steam at 300°C (which is 8.581 MPa ), we assume steam is an ideal gas at these conditions. Then using Eq. 7.4-3 for an ideal gas, we have

[latex]\underline{G}\left(T_{1}, P_{2} ight)-\underline{G}\left(T_{1}, P_{1} ight)=\int_{P_{1}}^{P_{2}} \underline{V} d P[/latex] (7.4.3)

[latex]\begin{aligned}\underline{G}^{\mathrm{IG}}\left(300^{\circ} \mathrm{C}, 8 \mathrm{MPa} ight) &=\underline{G}^{\mathrm{IG}}\left(300^{\circ} \mathrm{C}, 0.01 \mathrm{MPa} ight)+\int_{0.01 \mathrm{MPa}}^{8 \mathrm{MPa}} \underline{V}^{\mathrm{IG}} d P \\&=-40409+\int_{0.01 \mathrm{MPa}}^{8 \mathrm{MPa}} \frac{R T}{P} d P \\&=-40409+R T \ln \frac{8}{0.01} \\&=-40409+8.134 imes 573.15 \ln 800 \\&=-8555.7 \frac{\mathrm{J}}{\mathrm{mol}}\end{aligned}[/latex]

For real steam at 300°C and 8 MPa, we have, from the steam tables, [latex]\hat{H}[/latex] = 2785.0 kJ/kg and [latex]\hat{S}[/latex] = 5.7906 kJ/(kg K), so that

[latex]\hat{G}\left(300^{\circ} \mathrm{C}, 8 \mathrm{MPa} ight)=2785.0-573.15 imes 5.7906=-533.88 \frac{\mathrm{kJ}}{\mathrm{kg}}[/latex]

and

[latex]\underline{G}\left(300^{\circ} \mathrm{C}, 8 \mathrm{MPa} ight)=-9617.9 \frac{\mathrm{J}}{\mathrm{mol}}[/latex]

Now using Eq. 7.4-6a in the form

[latex]f(T, P)=P \exp \left[\frac{\underline{G}(T, P)-\underline{G}^{\mathrm{IG}}(T, P)}{R T} ight][/latex]

results in

[latex]\begin{aligned}f\left(300^{\circ} \mathrm{C}, 8 \mathrm{MPa} ight) &=8 \mathrm{MPa} \exp \left[\frac{-9617.9-(-8555.7)}{8.314 imes 573.15} ight] \\&=8 \mathrm{MPa} \exp [-0.2229] \\&=6.402 \mathrm{MPa}\end{aligned}[/latex]

which is in excellent agreement with the results obtained in the previous illustration.

Question 7.4.2: Alternative Fugacity Calculation Use other data in the super...

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