Food

The time it takes to properly roast a whole turkey is proportional to its weight to the ⅔ power. My old mathematical modelling textbook specifically recommends 45 minutes per lb^2/3 when cooked at 350℉.

For a spherical turkey of uniform thermal conductivity $\alpha$ and density $\rho$, a precise formula has been derived:

$$t = \ln\left(\frac{2(T_h - T_0)}{T_h - T_f}\right) \frac{1}{\pi^2\alpha} \left(\frac{3}{4\pi\rho}\right)^{2/3} m^{2/3}$$

where the oven is set at $T_h$ and the center of the turkey needs to reach a temperature of $T_f$ from $T_0$.

The more general ⅔ power law does not depend on unrealistic assumptions about the turkey’s shape or thermodynamic properties; it can be derived from pure dimensional analysis and applied to turkey-shaped meat-based objects by fitting a curve to specific cook times used by chefs.