Bibliographic record
Abstract
The inviscid hydrodynamics of inert compressible media governed by the Euler equations of motion only require knowledge of a caloric equation of state e(p, v) for the material relating the internal energy e to the fluid pressure p and specific volume v (or density). For departures from the ideal gas behavior, simple equations of state such as the stiffened gas, Noble-Abel, or a hybrid recently generalized by Le Métayer and Saurel [“The Noble-Abel stiffened-gas equation of state,” Phys. Fluids 28, 046102 (2016)] can correctly model compressible flows in gases, liquids, and solids. However, reactive and multicomponent descriptions require a formal definition of temperature. In the present note, we formulate a general thermodynamically based method to determine the thermal equation of state T(p, v) compatible with a generic e(p, v) relation. We apply our method to the Noble-Abel Stiffened Gas equation of state and recover the closed form solution of Le Métayer and Saurel. We also show that variations of the model taking its exponent different from the ratio of specific heats do not permit to define a thermodynamic temperature.
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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".