A New Thermodynamic Model to Approximate Properties of Subcritical Liquids
Abstract
:1. Introduction
2. Materials and Methods
2.1. Development of the Model
2.1.1. Caloric Equations
2.1.2. Constant Pressure Specific Thermal Capacity
2.1.3. Entropy Equations
2.2. Calculation of Properties According to the Model
2.2.1. Specific Enthalpy
2.2.2. Specific Internal Energy
2.2.3. Specific Entropy
2.3. Applications of the Model
- For the approximation of compressed liquid property values when saturation values are known.
- For the calculation of the specific internal energy , specific enthalpy and specific entropy of any incompressible system with data of specific volume and specific thermal capacity at a reference pressure as a function of temperature.
2.3.1. Approximation of Compressed Liquid Properties from Saturation
2.3.2. Calculation of of an Incompressible System
3. Results and Discussion
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Conflicts of Interest
Appendix A
(%) | (%) | (%) | (%) | (%) | (%) | |
---|---|---|---|---|---|---|
0.3 | 1.94 × 10−13 | 1.25 × 10−12 | 3.48 × 10−13 | 1.14 × 10−2 | 1.90 × 10−3 | 9.48 × 10−3 |
0.5 | 8.82 × 10−10 | 5.63 × 10−12 | 6.96 × 10−12 | 7.72 × 10−2 | 2.87 × 10−2 | 3.67 × 10−2 |
0.6 | 5.68 × 10−8 | 6.56 × 10−10 | 6.91 × 10−10 | 6.06 × 10−2 | 3.09 × 10−2 | 3.42 × 10−2 |
0.75 | 5.84 × 10−6 | 1.47 × 10−7 | 1.25 × 10−7 | 1.04 × 10−1 | 6.98 × 10−2 | 6.12 × 10−2 |
0.9 | 3.60 × 10−4 | 3.00 × 10−5 | 2.19 × 10−5 | 3.13 × 10−1 | 2.51 × 10−1 | 1.85 × 10−1 |
0.99 | 9.14 × 10−2 | 5.83 × 10−2 | 4.02 × 10−2 | 1.55 × 100 | 1.38 × 100 | 9.48 × 10−1 |
(%) | (%) | (%) | (%) | (%) | (%) | |
---|---|---|---|---|---|---|
0.5 | 3.10 × 10−11 | 6.33 × 10−14 | 1.94 × 10−13 | 1.82 × 10−2 | 7.56 × 10−3 | 1.21 × 10−2 |
0.6 | 7.61 × 10−9 | 9.06 × 10−11 | 1.04 × 10−10 | 2.55 × 10−2 | 1.36 × 10−2 | 1.61 × 10−2 |
0.75 | 1.98 × 10−6 | 5.04 × 10−8 | 4.33 × 10−8 | 6.13 × 10−2 | 4.22 × 10−2 | 3.70 × 10−2 |
0.9 | 1.99 × 10−4 | 1.62 × 10−5 | 1.14 × 10−5 | 2.28 × 10−1 | 1.85 × 10−1 | 1.32 × 10−1 |
0.99 | 5.89 × 10−2 | 3.70 × 10−2 | 2.43 × 10−2 | 1.25 × 100 | 1.12 × 100 | 7.35 × 10−1 |
(%) | (%) | (%) | (%) | (%) | (%) | |
---|---|---|---|---|---|---|
0.75 | 1.41 × 10−5 | 3.48 × 10−7 | 3.04 × 10−7 | 2.97 × 10−1 | 1.92 × 10−1 | 1.75 × 10−1 |
0.8 | 5.07 × 10−5 | 1.70 × 10−6 | 1.42 × 10−6 | 3.62 × 10−1 | 2.52 × 10−1 | 2.19 × 10−1 |
0.85 | 1.86 × 10−4 | 9.23 × 10−6 | 7.40 × 10−6 | 4.89 × 10−1 | 3.63 × 10−1 | 3.00 × 10−1 |
0.9 | 7.83 × 10−4 | 6.50 × 10−5 | 5.01 × 10−5 | 7.35 × 10−1 | 5.77 × 10−1 | 4.53 × 10−1 |
0.95 | 5.11 × 10−3 | 9.14 × 10−4 | 6.85 × 10−4 | 1.29 × 100 | 1.07 × 100 | 8.06 × 10−1 |
0.99 | 1.88 × 10−1 | 1.19 × 10−1 | 8.86 × 10−2 | 3.31 × 100 | 2.91 × 100 | 2.15 × 100 |
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… | … | … |
(%) | (%) | (%) | (%) | (%) | (%) | |
---|---|---|---|---|---|---|
0.45 | 9.98 × 10−11 | 2.11 × 10−13 | 6.32 × 10−11 | 2.42 × 10−3 | 2.24 × 10−1 | 1.38 × 10−1 |
0.5 | 3.46 × 10−10 | 6.90 × 10−14 | 7.02 × 10−12 | 6.26 × 10−2 | 3.50 × 10−2 | 1.15 × 10−2 |
0.6 | 3.33 × 10−8 | 1.63 × 10−10 | 2.72 × 10−10 | 7.79 × 10−2 | 2.34 × 10−2 | 4.33 × 10−2 |
0.75 | 5.23 × 10−6 | 1.09 × 10−7 | 1.03 × 10−7 | 1.52 × 10−1 | 9.65 × 10−2 | 9.42 × 10−2 |
0.9 | 4.26 × 10−4 | 3.41 × 10−5 | 2.59 × 10−5 | 5.05 × 10−1 | 4.05 × 10−1 | 3.12 × 10−1 |
0.99 | 1.31 × 10−1 | 8.45 × 10−2 | 6.04 × 10−2 | 2.76 × 100 | 2.48 × 100 | 1.77 × 100 |
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Sánchez-Orgaz, S.; Varela, F.; Rodríguez, J.; González, C. A New Thermodynamic Model to Approximate Properties of Subcritical Liquids. Entropy 2023, 25, 1002. https://doi.org/10.3390/e25071002
Sánchez-Orgaz S, Varela F, Rodríguez J, González C. A New Thermodynamic Model to Approximate Properties of Subcritical Liquids. Entropy. 2023; 25(7):1002. https://doi.org/10.3390/e25071002
Chicago/Turabian StyleSánchez-Orgaz, Susana, Fernando Varela, Javier Rodríguez, and Celina González. 2023. "A New Thermodynamic Model to Approximate Properties of Subcritical Liquids" Entropy 25, no. 7: 1002. https://doi.org/10.3390/e25071002