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 cm and density 1000 kg/m3.
Egg white solidifies at 50¡ãC while yolk solidifies at 65¡ãC
The heat capacity of an egg is c=4200Jkg⋅K
The power transferred from the heater to the egg is P=20 W
To determine how long it takes for a soft-boiled egg to become a hard-boiled one, we need to consider the cooking process and the time it takes for the center of the egg to reach the desired temperature.
Given the details and assumptions provided, we can calculate the time it takes for the egg to cook based on its specific heat capacity and the power transferred from the heater.
The heat transferred to the egg can be calculated using the formula: Q = Pt, where Q is the heat, P is the power, and t is the time.
To reach the desired temperature, both the egg white and yolk need to exceed their respective solidification temperatures. Let's assume the desired temperature is 65°C.
First, we need to calculate the heat required to raise the temperature of the egg from room temperature to the solidification temperature of the yolk (65°C).
The heat required to raise the temperature of the egg can be calculated using the formula: Q1 = mcΔT, where Q1 is the heat, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
Since the egg is modeled as a sphere of radius 2 cm, we can calculate its volume using the formula: V = (4/3)πr^3.
The mass of the egg can be calculated using the formula: m = ρV, where ρ is the density.
We then substitute the values into the heat equation and solve for Q1.
Once we have Q1, we can calculate the time required to reach the solidification temperature of the yolk using the formula: t1 = Q1 / P.
Next, we need to calculate the heat required to raise the temperature of the egg from the solidification temperature of the yolk (65°C) to the solidification temperature of the egg white (50°C).
Similarly, we calculate Q2 using the heat equation.
Finally, we calculate the total time required to cook the egg by summing t1 and t2.
So, to determine how often you need to check the eggs to avoid overcooking, calculate the time required to cook the eggs as explained above. Then, you can check the eggs at regular intervals within this cooking time to ensure they are not overcooked.