One material, three numbers: the k = α·ρc_p triangle, live

Thermal conductivity k, thermal diffusivity α and volumetric heat capacity ρc_p are one relation wearing three hats: k = α × ρc_p. Measure any two and the third follows — which is why a diffusivity-first method plus a heat-capacity input yields conductivity, and why an error in either propagates straight into k. Slide the dials, or load a material preset, and watch the triangle close on the map.

Model: the exact identity k = αρc_p on a log-α map with constant-k contours; reference dots are textbook-order room-temperature values for orientation (illustrative, not certified data). Units: α in mm²/s times ρc_p in MJ m⁻³K⁻¹ gives k in W m⁻¹K⁻¹ directly. A working tool and a teaching aid in one.