Computing Fugacity from Volumetric Data Use the volumetric information in the steam tables of Appendix A.III to compute the fugacity of superheated steam at 300°C and 8 MPa.

Question

Computing Fugacity from Volumetric Data
Use the volumetric information in the steam tables of Appendix A.III to compute the fugacity of superheated steam at 300°C and 8 MPa.

Accepted Answer

With tabulated volumetric data, as in the steam tables, it is most convenient to use Eq. 7.4-6a:

[latex]f=P \exp \left[\frac{1}{R T} \int_{0}^{P}\left(\underline{V}-\frac{R T}{P} ight) d P ight][/latex]

From the superheated vapor steam tables at 300°C, we have

P (MPa)	[latex]\hat{V}\left(\mathrm{~m}^{3} / \mathrm{kg} ight)[/latex]	[latex]\underline{V}\left(\mathrm{~m}^{3} / \mathrm{mol} ight)[/latex]	[latex][\underline{V}-R T / P]\left(\mathrm{m}^{3} / \mathrm{mol} ight) imes 10^{4}[/latex]
0.01	26.445	0.47641	−1.02
0.05	5.284	0.095191	−1.121
0.10	2.639	0.047542	−1.101
0.20	1.3162	0.023711	−1.145
0.30	0.8753	0.015769	−1.154
0.40	0.6548	0.011796	−1.167
0.50	0.5226	0.0094146	−1.157
0.60	0.4334	0.0078077	−1.342
0.80	0.3241	0.0058387	−1.178
1.0	0.2579	0.0046461	−1.191
1.2	0.2138	0.0038516	−1.194
1.4	0.18228	0.0032838	−1.199
1.6	0.15862	0.0028575	−1.207
1.8	0.14021	0.0025259	−1.214
2.0	0.12547	0.0022603	−1.222
2.5	0.0989	0.0017817	−1.244
3.0	0.08114	0.0014617	−1.267
3.5	0.06842	0.0012326	−1.289
4.0	0.05884	0.00106	−1.313
4.5	0.05135	0.00092507	−1.339
5.0	0.04532	0.00081644	−1.366
6.0	0.03616	0.00065142	−1.428
7.0	0.02947	0.0005309	−1.498
8.0	0.02426	0.00043704	−1.586

Numerically evaluating the integral using the data above, we find

[latex]\int_{0}^{8 \mathrm{MPa}}\left(\underline{V}-\frac{R T}{P} ight) d P \approx-1.093 imes 10^{-3} \frac{\mathrm{m}^{3} \mathrm{MPa}}{\mathrm{mol}}[/latex]

and

[latex]\begin{aligned}f &=8 \mathrm{MPa} e x p\left[\frac{-1.093 imes 10^{-3} \frac{\mathrm{m}^{3} \mathrm{MPa}}{\mathrm{mol}}}{573.15 \mathrm{~K} imes 8.314 imes 10^{-6} \frac{\mathrm{MPa} \mathrm{m}^{3}}{\mathrm{~mol} \mathrm{~K}}} ight]=8 \exp (-0.2367) \mathrm{MPa} \\&=8 imes 0.7996 \mathrm{MPa}=6.397 \mathrm{MPa}\end{aligned}[/latex]

Also, the fugacity coefficient, [latex]\phi[/latex], in this case is

[latex]\phi=\frac{f}{P}=0.7996[/latex]

COMMENT

Had the same calculation been done at a much higher temperature, the steam would be closer to an ideal vapor, and the fugacity coefficient would be closer to unity in value. For example, the result of a similar calculation at 1000°C and 10 MPa yields f = 9.926 MPa and [latex]\phi[/latex] = f /P = 0.9926.

Question 7.4.1: Computing Fugacity from Volumetric Data Use the volumetric i...

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