Apparent α against L²: the intercept is the intrinsic value

Each point is a full measurement of the same material at one suspended length. Distributed surface losses add an apparent-diffusivity term that grows with L², so longer samples read higher. The fit against L², extrapolated to zero (dashed), isolates the intrinsic value at the orange intercept — and under adequate vacuum with geometry and heat capacity known, the slope can be read as an effective emissivity. Raise the loss-strength slider and watch the slope steepen while the intercept holds; add noise to see why the length series must span a real range.

Preset:
measured pointsfitted lineextrapolated intercepttrue unperturbed value

Model: apparent diffusivity with a linearized distributed-loss term proportional to L², α(L²) = α₀(1+cL²), independent Gaussian noise per point, ordinary least squares extrapolated to L² = 0. Here c is a SYNTHETIC distributed-loss coefficient: it can be interpreted as emissivity only when residual-gas heat transfer is negligible and the geometry, temperature and volumetric heat capacity are independently supplied. Real campaigns verify per-point transient fits, sameness of material across the length series, and residual straightness. Axes normalized; schematic teaching tool, not an instrument.