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
i got 33.8 minutes im not sure what im doing wrong :/
I have the same answer with you, but its wrong, and it can't make sense too..cause 33 minutes is too long right ?
I doubt about the heat capacity, as long as i know, the tempereture is in celcius, if se use kelvin, the result will makes nonsense
i researched online and it says J/kgK is the same as J/kgC so im gunna try just using 15 as the temperature, tell me what u get?
There are lots of assumptions made in this question.
In reality, there is a temperature gradient between the outer part of the egg and the (yolk) in the middle, which means that the inner part of the egg is always cooler than the outer part.
This gradient diminishes with time, which makes it a time dependent problem, solvable using a differential equation.
However, (intended) simplifications make the problem solvable.
By considering
1. a constant input of heat to the egg, and
2. the egg temperature is uniform,
then we only have a single temperature to contend with, which varies linearly with time.
mass of egg:
m=ρ(4/3)πr³
=1 g/cm³ * (4/3)π(2³)
=32π/3 g
=32π/3000 kg
Heat capacity
C = m (kg) *4200 J-kg/°K (given)
=224π/5 J/°K
Power supplied, P = 20W
Temp difference, ΔT
= (65-50)=15 °K
Time required
=ΔT * C/P °K * J/°K * s/J
=15*(224π/5)/20 s
=105.6 s
about 1 minute 45 seconds.
okey then,,, same with Mr.Mathmate, over one minute too..and it make sense
heyy..steven..lets discuss about other complex question forth, its fun trading assumptions each other, right ?
To determine the time it takes for a soft-boiled egg to become hard-boiled, we need to consider the rate at which heat is transferred to the egg and the temperature at which the egg white and yolk solidify.
First, let's calculate the mass of the egg. Since the egg can be modeled as a sphere of radius 2 cm and density 1000 kg/m^3, we can use the formula for the volume of a sphere (V = 4/3 * π * r^3) to find the volume and then multiply it by the density to get the mass:
V = 4/3 * π * (0.02 m)^3
V ≈ 0.001008 m^3
Mass = density * volume
Mass ≈ 1000 kg/m^3 * 0.001008 m^3
Mass ≈ 1.008 kg
Now, let's calculate the energy required to raise the temperature of the egg from room temperature (assumed to be 25°C) to the temperature at which the egg white solidifies (50°C). We can use the formula for heat energy:
Q = mcΔT
where Q is the heat energy, m is the mass, c is the heat capacity, and ΔT is the change in temperature.
ΔT = 50°C - 25°C
ΔT = 25°C
Q = 1.008 kg * 4200 J/kg⋅K * 25°C
Q ≈ 105840 J
Now, let's calculate the time it takes to transfer this amount of energy to the egg. The power transferred from the heater to the egg is given as P = 20 W, so we can use the formula for power:
P = ΔQ/Δt
where P is the power, ΔQ is the change in heat energy, and Δt is the change in time.
ΔQ = 105840 J
P = 20 W
ΔQ = P * Δt
105840 J = 20 W * Δt
Δt ≈ 5292 s
Therefore, it takes approximately 5292 seconds (or 88.2 minutes) to transfer enough heat to the egg to reach the temperature at which the egg white solidifies.
To determine how often you need to check the eggs, you need to take into account the desired outcome - which is a soft-boiled egg.
Since the temperature at which the egg white solidifies is 50°C, you can start checking the eggs when the temperature reaches around 48-49°C. This will give you a small window of time to catch the eggs before they become overcooked.
To check the eggs, you can use a food thermometer or the water test method. For the water test method, you can place the eggs in a pot of boiling water and start timing once the water comes to a rolling boil. After about 5-6 minutes, remove one of the eggs and run it under cold water. Carefully crack it open and observe the consistency of the egg white. If it is still runny, you can continue checking the eggs every 30 seconds until you achieve the desired soft-boiled texture.
By checking the eggs around the estimated time it takes to transfer enough heat to the egg (88.2 minutes), you can ensure that they are not overcooked and achieve the desired soft-boiled consistency.