Thermal Expansion Calculator mechanism

Model scope

The linear-length calculation is standard when its assumptions are made explicit, but the specification is not honest as written because it advertises area expansion without an area input or formula. Either relabel the instrument as a linear thermal-expansion calculator or add a documented isotropic area-expansion mode, including whether the displayed result is the small-strain approximation or the exact constant-α geometric result.

• ΔL=αL0ΔT is the standard linear-expansion formula only for isotropic material, constant α over the temperature interval, and sufficiently small strain; these assumptions are not stated.
• The instrument claims area expansion but provides no area input or area formula. For isotropic material, the usual small-strain approximation is ΔA≈2αA0ΔT; the exact constant-α geometric result is A1=A0(1+αΔT)^2.
• The stated formula defines ΔL but not the advertised new length; the implementation must explicitly calculate L1=L0+ΔL.
• CTE is temperature-dependent for many materials, so a single tabulated α is only valid over a stated temperature range or as an engineering approximation.

Units and conventions

• α is supplied in 1/K or 1/°C; temperature differences in kelvins and degrees Celsius have equal numerical magnitude.
• L0 and new length use the same length unit; ΔL has that same unit.
• For area calculations, A0 and ΔA use the same squared-length unit.
• The tabulated CTE values below are representative room-temperature engineering values and are treated as constant over each stated interval.
• The area result labeled linearized uses ΔA=2αA0ΔT; the exact constant-α result uses A1=A0(1+αΔT)^2.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "material": "copper",
    "alpha_per_K": 0.0000165,
    "L0_m": 2,
    "T0_C": 20,
    "T1_C": 120,
    "delta_T_C": 100
  },
  "expected_outputs": {
    "delta_L_m": 0.0033,
    "new_length_m": 2.0033
  },
  "reference_data": {
    "material": "copper",
    "alpha_per_K": 0.0000165,
    "table_fragment": "Copper linear CTE near room temperature = 16.5 × 10^-6 K^-1",
    "source_convention": "widely tabulated standard value"
  },
  "working": "ΔT=T1−T0=120−20=100 °C. ΔL=αL0ΔT=(16.5×10^-6 K^-1)(2.0 m)(100 K)=0.0033 m. New length=L0+ΔL=2.0+0.0033=2.0033 m."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The calculator needs explicit range handling because an extreme but syntactically valid input overflows to infinity. It also has a unit-convention hazard when ΔT is supplied in °F while α is per °C.

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-tranche7/tranche7-results.json
• BOUNDARY_HAZARD_CATALOG.json