Isothermal / Adiabatic / Polytropic Process Calculator mechanism

Model scope

The listed relations are conditionally standard, but the specification is not complete enough to verify the claimed outputs for all process types. The empty honest_label is a concern: the instrument should explicitly label its results as reversible ideal-gas calculations, identify the heat/work sign convention, distinguish amount of substance from the polytropic exponent, and state that polytropic heat requires additional gas-property inputs.

• The isothermal work formula W=nRT·ln(V2/V1) is correct only for a reversible or quasi-static ideal-gas process; this constraint is not stated.
• The adiabatic relation PV^γ=constant and work formula W=(P1V1−P2V2)/(γ−1) are correct for a reversible adiabatic ideal-gas process with γ≠1. The specification does not state reversibility, ideal-gas behavior, or Q=0.
• The polytropic formula PV^n=constant gives a state relation but does not provide the required work formula. For n≠1, the standard reversible-path work is W=(P2V2−P1V1)/(1−n); for n=1, the logarithmic isothermal formula is required.
• Heat transfer is not computable from the listed formulas alone. It requires the sign convention, internal-energy model, gas amount, and Cv or equivalent property data. For a reversible adiabatic ideal-gas process, Q=0.
• The input label n is ambiguous because n commonly denotes amount of substance in the isothermal formula and the polytropic exponent in PV^n=constant.
• The final state is underdetermined unless the initial state includes sufficient independent variables, the ideal-gas equation is assumed, and the process type plus final V or P is constrained consistently.

Units and conventions

• Ideal gas is assumed.
• Use SI units: pressure in Pa, volume in m³, temperature in K, amount in mol, and R=8.314 J/(mol·K).
• Work is positive when done by the gas; heat is positive when transferred into the gas.
• Isothermal and polytropic work calculations assume a reversible or quasi-static path.
• Adiabatic means Q=0; the adiabatic examples assume air with γ=1.4.
• For the polytropic heat example, air is assumed with Cv=20.785 J/(mol·K), and the amount of gas is computed from PV=nRT.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "process_type": "isothermal",
    "n_moles": 1,
    "T1_K": 300,
    "V1_m3": 0.01,
    "V2_m3": 0.02,
    "R_J_per_molK": 8.314
  },
  "expected_outputs": {
    "P1_Pa": 249420,
    "P2_Pa": 124710,
    "T2_K": 300,
    "work_by_gas_J": 1728.85,
    "heat_into_gas_J": 1728.85,
    "delta_U_J": 0
  },
  "working": "P1=nRT/V1=(1×8.314×300)/0.01=249420 Pa. P2=nRT/V2=(1×8.314×300)/0.02=124710 Pa. T2=T1=300 K. W=nRT ln(V2/V1)=(1×8.314×300)ln(0.02/0.01)=2494.2×ln(2)=2494.2×0.69314718=1728.85 J. For an ideal-gas isothermal process, ΔU=0, so Q=W=1728.85 J."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The adiabatic formula is undefined at gamma = 1 because its denominator gamma - 1 vanishes. If the calculator accepts gamma = 1 instead of rejecting it, it may emit NaN, Infinity, or an inconsistent result.

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-tranche2/tranche2-results.json
• BOUNDARY_HAZARD_CATALOG.json