Question 6.5: Supercritical CO2 can be used as an environmentally friendly...
Supercritical CO_2 can be used as an environmentally friendly solvent for cleaning applications, ranging from dry cleaning clothing to degreasing machine parts to photoresist stripping. A key advantage of CO_2 is the ease with which it is separated from “dirt” and detergents. When its temperature and pressure are reduced below the critical temperature and vapor pressure respectively, it vaporizes, leaving dissolved substances behind. For a change in state of CO_2 from 70°C and 150 bar to 20°C and 15 bar, estimate the changes in its molar enthalpy and entropy.
We follow the three-step computational path of Fig. 6.3. Step 1 transforms the real fluid at 70°C and 150 bar into its ideal-gas state at the same conditions. Step 2 changes conditions in the ideal-gas state from the initial to the final conditions of T and P. Step 3 transforms the fluid from its ideal-gas state to the real-gas final state at 20°C and 15 bar.
The residual-property values required for calculating the changes of steps 1 and 3 depend on the reduced conditions of the initial and final states. With critical properties from Table B.1 of App. B:
T_{r_1}=1.128 \quad P_{r_1}=2.032 \quad T_{r_2}=0.964 \quad P_{r_2}=0.203
A check of Fig. 3.10 indicates that the Lee/Kesler tables are required for the initial state, whereas the second-virial coefficient correlation should be adequate for the final state.
Thus, for step 1, interpolation in Lee/Kesler tables D.7, D.8, D.11, and D.12 provides the values:
\frac{\left(H^R\right)^0}{R T_c}=-2.709, \quad \frac{\left(H^R\right)^1}{R T_c}=-0.921, \quad \frac{\left(S^R\right)^0}{R}=-1.846, \quad \frac{\left(S^R\right)^1}{R}=-0.938
Then:
\Delta H_1=-H^R(343.15 K , 150 bar )
Delta S_1=-S^R(343.15 K , 150 bar )
\Delta S_1=-S^R(343.15 K , 150 bar )
\Delta H_2=8.314 \times ICPH \left(343.15,293.15 ; 5.547,1.045 \times 10^{-3}, 0.0,-1.157 \times 10^5\right)
For step 2, the enthalpy and entropy changes are calculated by the usual heatcapacity integrals, with polynomial coefficients from Table C.1. The ideal-gas-state entropy change caused by the pressure change must also be included.
\Delta H_2=8.314 \times ICPH \left(343.15,293.15 ; 5.547,1.045 \times 10^{-3}, 0.0,-1.157 \times 10^5\right)=-1978 J \cdot mol ^{-1}
\Delta S_2=8.314 \times \operatorname{ICPS}\left(343.15,293.15 ; 5.547,1.045 \times 10^{-3}, 0.0,-1.157 \times 10^5\right)− ( 8.314 ) ln ( 15 / 150 )
=-6.067+19.144=13.08 \mathrm{~J} \cdot \mathrm{mol}^{-1} \cdot \mathrm{K}^{-1}
Finally, for step 3,
\Delta H_3=H^R(293.15 K , 15 bar )=8.314 \times 304.2 \times HRB (0.964,0.203,0.224)=-660 J \cdot mol ^{-1}
\Delta S_3=S^R(293.15 K , 15 bar )=8.314 \times \mathrm{SRB}(0.964,0.203,0.224)=-1.59 \mathrm{~J} \cdot \mathrm{mol}^{-1} \cdot \mathrm{K}^{-1}
Sums over the three steps yield overall changes, \Delta H=4734 J \cdot mol ^{-1} and \Delta S=28.6 J \cdot mol ^{-1} \cdot K ^{-1} \text {. } . The largest contribution here comes from the residual properties of the initial state, because the reduced pressure is high, and the supercritical fluid is far from its ideal-gas state. Despite the substantial reduction in temperature, the enthalpy actually increases in the overall process.
For comparison, the properties given in the NIST fluid properties database, accessed through the NIST Chemistry WebBook, are:
H_1=16,776 J \cdot mol ^{-1} \quad S_1=67.66 J \cdot mol ^{-1} \cdot K ^{-1}
H_2=21,437 J \cdot mol ^{-1} \quad S_1=95.86 J \cdot mol ^{-1} \cdot K ^{-1}
From these values, considered accurate, overall changes are ΔH = 4661 J⋅mol^−1 and ΔS = 28.2 J⋅mol^−1⋅K^−1. Even though the changes in residual properties make up a substantial part of the total, the prediction from generalized correlations agrees with the NIST data to within 2 percent.
