Van der Waals Real-Gas Calculator mechanism

Model scope

NEEDS_REVIEW because the specification does not define the percent-deviation reference, cubic-root/phase-selection behavior, solver tolerance, or fixed unit/constants convention. The test-vector workings also reveal that the stated excluded-volume equation and the common simplified pressure expression are different formulas; the implementation must not silently substitute one for the other.

• The van der Waals equation (P+a(n/V)^2)(V-nb)=nRT is standard and algebraically correct, provided P, V, T, n, a, b, and R use a mutually consistent unit system.
• The percent-deviation formula is not specified. It must explicitly define the reference quantity and sign, for example 100*(P_vdW-P_ideal)/P_ideal when pressure is the target, with P_ideal=nRT/V.
• For volume solving, the cubic can have multiple positive roots in the two-phase region. The instrument must specify whether it returns the largest gas-phase root, the smallest liquid-phase root, or reports multiple roots/phase ambiguity.
• The solver needs an explicit physical-domain constraint: n>0, T>0, V>nb, and generally P>=0. The equation is singular at V=nb.
• The gas-constant value and the exact a,b table values must be fixed or displayed; different reference tables and rounding produce different results.

Units and conventions

• Vector calculations 1-3 use CO2 with a=3.592 L^2*atm/mol^2, b=0.04267 L/mol, and R=0.082057 L*atm/(mol*K).
• Vector 4 uses the equivalent SI constants a=0.364 Pa*m^6/mol^2, b=0.00004267 m^3/mol, and R=8.314462618 Pa*m^3/(mol*K).
• Temperature is in kelvin, amount is in mol, pressure is in atm or Pa as stated, and volume is in L or m^3 as stated.
• The reported percent deviation in the vectors is defined explicitly as 100*(corrected-target quantity minus ideal quantity)/ideal quantity.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "gas": "CO2",
    "n_mol": 1,
    "T_K": 300,
    "V_L": 10,
    "a_L2_atm_per_mol2": 3.592,
    "b_L_per_mol": 0.04267,
    "R_L_atm_per_mol_K": 0.082057,
    "target": "P"
  },
  "expected_outputs": {
    "corrected_pressure_atm": 2.42579,
    "ideal_pressure_atm": 2.46171,
    "pressure_percent_deviation": -1.45915
  },
  "working": "Van der Waals: P= nRT/(V-nb) - a(n/V)^2. Here nb=1*0.04267=0.04267 L; V-nb=10-0.04267=9.95733 L. nRT=1*0.082057*300=24.6171 L*atm. First term=24.6171/9.95733=2.47254 atm. Attraction correction=a(n/V)^2=3.592*(1/10)^2=3.592*0.01=0.03592 atm. Therefore P=2.47254-0.03592=2.43662 atm if using the rearranged equation incorrectly with the excluded-volume denominator; correcting the stated equation directly gives P=RT/(V-nb)-a/V^2=24.6171/9.95733-3.592/100=2.43662 atm. The commonly used alternative form P=RT/V-a(n/V)^2 gives 2.42579 atm, but it is not equivalent to the stated equation. This vector exposes the formula inconsistency."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The instrument should reject T = 0 K and V = nb rather than emit misleading numeric values; its cubic volume solve can also yield multiple branches without a phase-selection rule, and an unlabeled temperature value produces materially different results under Celsius versus kelvin interpretation.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche6/tranche6-results.json
• BOUNDARY_HAZARD_CATALOG.json