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 often you need to check the eggs, we first need to determine the time it takes for a soft-boiled egg to become a hard-boiled one.
We can approach this problem by considering the heat transfer between the egg and its surroundings. The power transferred from the heater to the egg is given as P=20W.
To calculate the time it takes for the egg to become hard-boiled, we can use the formula:
Q = mcΔT
where Q is the heat transferred, m is the mass of the egg, c is the specific heat capacity, and ΔT is the change in temperature.
First, we need to calculate the mass of the egg. The egg can be modeled as a sphere with a radius of 2 cm. The volume of a sphere is given by V = (4/3)πr^3, and the density can be used to calculate the mass:
V = (4/3)π(2cm)^3 = (4/3)π(8cm^3) = (32/3)π cm^3
Since the egg is spherical and uniform, we can assume the density is constant throughout. Therefore, the mass can be calculated by multiplying the volume by the density:
m = (32/3)π cm^3 * 1000 kg/m^3 = (32000/3)π g
Next, we need to determine the change in temperature ΔT. For a soft-boiled egg to become hard-boiled, the temperature needs to increase from the soft-boiled yolk temperature of 65°C to the hard-boiled yolk temperature of 100°C.
ΔT = 100°C - 65°C = 35°C
Now we can calculate the heat transferred Q using the formula:
Q = mcΔT = (32000/3)π g * 4200 J/kg∙K * 35°C
Finally, we can determine the time it takes for the egg to become hard-boiled using the formula:
Q = Pt
where P is the power transferred and t is the time.
t = Q / P = [(32000/3)π g * 4200 J/kg∙K * 35°C] / 20 W
Simplifying the equation, we divide the grams by 1000 to convert to kilograms and convert π from g to kg:
t = [(32/3) * π kg * 4200 J/kg∙K * 35°C] / 20 W
t = [(32/3) * 3.14 kg * 4200 J/kg∙K * 35°C] / 20 W
t = (32 * 3.14 * 4200 * 35 / 3) / 20 s
Calculating the result:
t ≈ 2996.4 s
Therefore, it takes approximately 2996.4 seconds or 49.9 minutes for a soft-boiled egg to become a hard-boiled one.
To avoid overcooking the eggs, you will need to check them periodically. Dividing the total time by the number of checks you want to make will give you the interval between each check.