Each cup's cooling constant is derived from real material properties instead of a picked-by-hand number. The wall conducts heat with resistance d/λ (thickness over conductivity) in series with convective resistance 1/h at the outer surface, giving an overall transfer coefficient U = 1/(d/λ + 1/h). That combines with the liquid's mass and specific heat into Newton's cooling constant:
U = 1 / (d/λ + 1/h) [W/m²K]
A = side area + 3·(open-surface area) [m²] (open surface weighted up — evaporation)
m = volume(L) × 1.0 kg/L
k = U·A / (m·c_p) [1/s], c_p = 4186 J/kg·K
T(t) = T_room + (T0 − T_room)·e^(−k·t)
Ceramic and steel share the same wall-conduction model but differ in λ and thickness (steel's thin, high-conductivity wall barely adds resistance, so it tracks the airflow-driven convective coefficient closely). The vacuum thermos is modelled differently on purpose: its evacuated double wall makes conduction and convection across the gap negligible, so heat loss is capped by a small, fixed radiative-limited U regardless of the airflow slider — which is why blowing a fan on it barely changes its curve, while it visibly speeds up the ceramic and steel cups.
- Volume slider — more liquid means more thermal mass (m) but also a taller cup with more side area (A); the two partially cancel, which is why k changes only modestly with volume.
- Airflow buttons — raise h from "still air" (8 W/m²K) to "fan" (50 W/m²K); ceramic and steel visibly cool faster, thermos barely responds.
- Half-life t½ = ln(2)/k — time for the temperature excess above room to halve; independent of the starting temperature.