Physicist in the kitchen - run for your lives!

You prefer soft-boiled to hard-boiled eggs, but you hate waiting next to your eggs to check if they're cooked. Therefore, you want to determine how often do you need to check the eggs so that they're not overcooked.

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 \(2~\mbox{cm}\) and density \(1000~\mbox{kg/m}^3\).
• Egg white solidifies at \(50^\circ\mbox{C}\) while yolk solidifies at \(65^\circ\mbox{C}\)
• The heat capacity of an egg is \(c = 4200 \frac{\mbox{J}}{\mbox{kg}\cdot\mbox{K}}\)
• The power transferred from the heater to the egg is \(P = 20~\mbox{W}\)