What time does it take in minutes for a soft-boiled egg to become a hard-boiled one?

Note: A soft boiled egg is when only the egg white is solid, whereas a hard boiled egg is when both the egg white and yolk are solid.

Details and assumptions
The egg can be modeled as a sphere of radius 2 cm and density 1000 kg/m3.
Egg white solidifies at 50∘C while yolk solidifies at 65∘C
The heat capacity of an egg is c=4200Jkg⋅K
The power transferred from the heater to the egg is P=20 W

Question

What time does it take in minutes for a soft-boiled egg to become a hard-boiled one?

Note: A soft boiled egg is when only the egg white is solid, whereas a hard boiled egg is when both the egg white and yolk are solid.

Details and assumptions
The egg can be modeled as a sphere of radius 2 cm and density 1000 kg/m3.
Egg white solidifies at 50∘C while yolk solidifies at 65∘C
The heat capacity of an egg is c=4200Jkg⋅K
The power transferred from the heater to the egg is P=20 W

festinger · Answer

When the egg is soft boiled, the temperature is 50∘C

Recall that heat needed is
$$Q=mc\Delta T=\frac{1000kg}{m^{3}}*\frac{4}{3}*\pi (0.02m)^{3}*4200*(65-50)=2111J$$

This is performed in 2111/20=106seconds.