On Determination of Azeotrope Coordinates from <i>g<sup>E</sup></i> for Binary Isothermal and Isobaric Systems
Bibliographic record
Abstract
Abstract A relatively simple procedure is described to calculate the coordinates, temperature ( T az ), pressure ( P az ), and composition ( x 1 az ), of an azeotrope (for either an isothermal or isobaric binary system at low pressure and with a single or double homogeneous azeotrope) from an expression for the liquid‐phase excess molar Gibbs function ( g E ). General results are based on (∂ g E /∂ x 1 ) az = RT az ln[ p 2 *( T az )/ p 1 *( T az )], and P az = (γ 1 p 1 *) az = (γ 2 p 2 *) az , where R is the gas constant, p* is saturation vapour pressure, and γ is liquid‐phase activity coefficient. Specific results are given for the Redlich‐Kister, van Laar, Wilson, and NRTL equations. Numerical examples are provided for both an isothermal and an isobaric system. The procedure provides a means to obtain azeotrope coordinates that are consistent with a g E expression obtained either from experimental data or from a model. It is applicable to polyazeotropy, whereas the criteria given previously are generally not applicable to polyazeotropy.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".