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
6 answers
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 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.
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 ?
0 answers