Source: https://guthlabs.ai/docs/instruments/isothermal-adiabatic-polytropic-process-calculator/mechanism/

instrument mechanism / verified-clean

# Isothermal / Adiabatic / Polytropic Process Calculator mechanism

The inspectable method record for Isothermal / Adiabatic / Polytropic Process Calculator, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## 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

[01**Overview**](<https://guthlabs.ai/docs/instruments/isothermal-adiabatic-polytropic-process-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/isothermal-adiabatic-polytropic-process-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/isothermal-adiabatic-polytropic-process-calculator/qualification/>)

## 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`