A Flexible Mixing Rule Satisfying the Ideal-Solution Limit for Equations of State
Bibliographic record
Abstract
While the ideal solution is an important reference for the thermodynamic modeling of mixtures, the one-fluid approach for equations of state (EOSs) fails to meet this limit. In this work we present additional evidence supporting this fact. A conceptually new treatment previously proposed for EOSs that meets the ideal solution limit at zero values for the interaction parameters is further developed here. A flexible composition dependence is proposed to cover the entire spectrum from symmetrical to highly asymmetrical, highly nonideal, mixtures. The new composition dependence gives the ideal solution limit, and it accounts for the effect of density on the excess properties of nonideal mixtures. The model treats vapor and liquid phases using a single formalism. For vapor−liquid equilibrium calculations, the new mixing rule can be considered as a hybrid between the well-known φ−φ and γ−φ approaches.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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".