Physics and Christmas dinner!

Christmas is quickly arriving upon us. A classic problem that comes with it, is how long should I cook my turkey to get a tasty and moist roast on Christmas day.
A British doctor in physics and food lover: Peter Barham, has decided to apply Fick's law of diffusion to calculate the best timing for his traditional Christmas roast.
Fick's law says that the diffusion coefficient at different temperatures is often found to be well predicted by J= -D * D C/Dx.
Molecular scientists calculate the heat diffusion process in an animal supposing that the temperature is constant, that the bird is a cylinder and homogeneous, etc. and can achieve an accurate but complex results involving the radius of the animal, the thermal diffusion coefficient, the temperature in the turkey and the temperature in the oven.
Luckily P Braham found simplified way to apply the flick's law to cook his Christmas diner. The flick's law applied to the cooking of a turkey says that the heating time (t) required to reach a known temperature in the center of a turkey is proportional to the square root of the radius of the turkey. As the mass (M) of a sphere is proportional to cubic root of its radius we can find out how long it will take to cook our Christmas diner using this formula:
Now, not everybody has a PHD in physics so there are some of the results that were found:
  • At 180 degrees Celsius a turkey of 5kg requires 2h25 of cooking, a bird of 7kg, 3h00.
  • At 160 degrees Celsius a 5kg turkey will require 3h35 in the oven, a 7kg bird 4h30.