Explicit Frost‐Kalkwarf type equations for calculation of vapour pressure of liquids from triple to critical point by the Adomian decomposition method
Bibliographic record
Abstract
Abstract The general form of explicit, analytical solution of the Frost‐Kalkwarf equation was developed for the first time by means of the Adomian decomposition method as a reliable mathematical tool. The accuracy of the obtained formulas was further improved by applying the diagonal Padé approximants. We have demonstrated that our developed formulas are at least 30 times faster than the original Frost‐Kalkwarf equation in computation of vapour pressures and are highly accurate with an overall absolute relative deviation of 2.25 % for 88 different substances over 26 400 experimental data points from triple to critical point temperatures. As another unique advantage, our formulas avoid any divergent behaviour in using iterative methods unlike the implicit Frost‐Kalkwarf equation. Based on the conducted statistical analyses, our formulas have excellent predictability of vapour pressure values with a probability of 90.33 % for absolute relative errors of less than 5 %.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".