While making the perfect soft-boiled egg is hard, making a good hard-boiled egg is equally hard. The problem lies at the interface between the yolk and egg. If you boil too long, the yolk turns green at the interface. If you boil too little, the yolk remains soft. Egg yolk proteins denature virtually instantaneously if the temperature climbs to \(\sim 340 \mathrm{~K}\). [7]

a. Repeat the calculation we did for the soft-boiled egg problem but calculate how long it will take to get the center of the egg up to \(340 \mathrm{~K}\). You can use the one-term approximation and data supplied in the example.

b. If you cook the egg for the time specified in part (a), to what temperature will you heat the yolk/white interface?