A Formula for Soft-Boiling Eggs
The Derivation
To obtain a simple formula the problem must be idealised somewhat, so the egg will be treated as a spherical homogeneous object of mass M and initial temperature Tegg. If the egg is placed straight into a pan of boiling water at Twater, it will be ready when the centre temperature of the yolk has risen to Tyolk. It turns out that Tyolk~45°;C is about right and the cooking time t can be deduced from the solution to the heat diffusion equation.
where the constant of proportionality a depends on the specific heat capacity and thermal conductivity of 'egg'. According to this formula, a medium egg (M~50 g) that takes four and a half minutes to cook when it has come from the fridge Tegg=4°C, would have taken a few seconds less than four minutes to cook if it had been stored at room temperature Tegg=21°C. If all the eggs are stored in the 'fridge, then a small (size 6, 47 g) egg, will require about 4 minute 15 seconds to cook, and a large egg (size 2, 67 g) will take almost five and a half minutes.
Grog lol!