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An egg with a mean diameter of 4 cm and initially at 25°C is placed in a boiling water pan for 4 minutes and found to be boiled to the consumer’s taste. For how long (in seconds) should a similar egg for the same consumer be boiled when taken from a refrigerator at 5°C? Use lumped parameter theory and presume the following properties for egg
k = 12 W/m-°C
h = 125 W/m2-°C
c = 2kJ/kg-K
And ? = 1250 kg/m3
- a)271
- b)272
Correct answer is between '271,272'. Can you explain this answer?
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Verified Answer
An egg with a mean diameter of 4 cm and initially at 25°C is placed i...
Characteristic length l
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Biot number Bi
Since Biot number is less than 0.1, the solution can be worked out by applying lumped-parameter theory which states that
= 0.0075
Let Ta = temperature of boiling water in pan
= 100°C
Now, we have to find time for the temperature values
Ti = 5°C;Ta = 100°C and t = 87.6°C
Or 0.0075 t = loge7.66 = 2.036
= 271.47 s
Most Upvoted Answer
An egg with a mean diameter of 4 cm and initially at 25°C is placed i...
Given data:
Mean diameter of egg, D = 4 cm = 0.04 m
Initial temperature of egg, T1 = 25°C
Temperature of boiling water, T∞ = 100°C
Time taken to boil the egg, t = 4 minutes = 240 seconds
Properties of egg:
Thermal conductivity, k = 12 W/m-°C
Heat transfer coefficient, h = 125 W/m2-°C
Density, ρ = 1250 kg/m3
Specific heat, Cp = 2 kJ/kg-K
Assumptions:
1. The egg is assumed to be a sphere.
2. The properties of the egg are constant.
3. The heat transfer is one-dimensional and the temperature is uniform throughout the egg.
4. The egg is initially at uniform temperature.
Calculation:
1. Surface area of the egg, A = πD2
A = π(0.04)2
A = 0.0050 m2
2. Volume of the egg, V = (4/3)π(D/2)3
V = (4/3)π(0.02)3
V = 3.35 × 10-5 m3
3. Mass of the egg, m = ρV
m = 1250 × 3.35 × 10-5
m = 0.042 kg
4. Heat capacity of the egg, C = mCp
C = 0.042 × 2000
C = 84 J/°C
5. The rate of heat transfer to the egg can be calculated using Newton's law of cooling as follows:
q = hA(T∞ - T1)
q = 125 × 0.0050 × (100 - 25)
q = 468.75 W
6. The rate of heat transfer to the egg can also be calculated using Fourier's law of heat conduction as follows:
q = kA(dT/dx)
Since the egg is assumed to be a sphere, dT/dx = (T∞ - T1)/r, where r is the radius of the egg.
q = kA(T∞ - T1)/r
r = D/2 = 0.02 m
q = 12 × 0.0050 × (100 - 25)/0.02
q = 468.75 W
7. The time taken to raise the temperature of the egg from T1 to T2 can be calculated using the equation:
q = C(T2 - T1)/t
T2 = T1 + q(t/C)
T2 = 25 + 468.75(240)/(84)
T2 = 100°C
8. The time taken to raise the temperature of a similar egg from 5°C to 100°C can be calculated using the same equation as follows:
T1 = 5°C = 278 K
T2 = 100°C = 373 K
q = C(T2 - T1)/t
t = C(T2 - T1)/q
t = 84(373 - 278)/(468.75)
t = 271 seconds
Therefore, the correct answer is between 271 and 272 seconds.
Mean diameter of egg, D = 4 cm = 0.04 m
Initial temperature of egg, T1 = 25°C
Temperature of boiling water, T∞ = 100°C
Time taken to boil the egg, t = 4 minutes = 240 seconds
Properties of egg:
Thermal conductivity, k = 12 W/m-°C
Heat transfer coefficient, h = 125 W/m2-°C
Density, ρ = 1250 kg/m3
Specific heat, Cp = 2 kJ/kg-K
Assumptions:
1. The egg is assumed to be a sphere.
2. The properties of the egg are constant.
3. The heat transfer is one-dimensional and the temperature is uniform throughout the egg.
4. The egg is initially at uniform temperature.
Calculation:
1. Surface area of the egg, A = πD2
A = π(0.04)2
A = 0.0050 m2
2. Volume of the egg, V = (4/3)π(D/2)3
V = (4/3)π(0.02)3
V = 3.35 × 10-5 m3
3. Mass of the egg, m = ρV
m = 1250 × 3.35 × 10-5
m = 0.042 kg
4. Heat capacity of the egg, C = mCp
C = 0.042 × 2000
C = 84 J/°C
5. The rate of heat transfer to the egg can be calculated using Newton's law of cooling as follows:
q = hA(T∞ - T1)
q = 125 × 0.0050 × (100 - 25)
q = 468.75 W
6. The rate of heat transfer to the egg can also be calculated using Fourier's law of heat conduction as follows:
q = kA(dT/dx)
Since the egg is assumed to be a sphere, dT/dx = (T∞ - T1)/r, where r is the radius of the egg.
q = kA(T∞ - T1)/r
r = D/2 = 0.02 m
q = 12 × 0.0050 × (100 - 25)/0.02
q = 468.75 W
7. The time taken to raise the temperature of the egg from T1 to T2 can be calculated using the equation:
q = C(T2 - T1)/t
T2 = T1 + q(t/C)
T2 = 25 + 468.75(240)/(84)
T2 = 100°C
8. The time taken to raise the temperature of a similar egg from 5°C to 100°C can be calculated using the same equation as follows:
T1 = 5°C = 278 K
T2 = 100°C = 373 K
q = C(T2 - T1)/t
t = C(T2 - T1)/q
t = 84(373 - 278)/(468.75)
t = 271 seconds
Therefore, the correct answer is between 271 and 272 seconds.
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An egg with a mean diameter of 4 cm and initially at 25°C is placed in a boiling water pan for 4 minutes and found to be boiled to the consumer’s taste. For how long (in seconds) should a similar egg for the same consumer be boiled when taken from a refrigerator at 5°C? Use lumped parameter theory and presume the following properties for eggk = 12 W/m-°Ch = 125 W/m2-°Cc = 2kJ/kg-KAnd ? = 1250 kg/m3a)271b)272Correct answer is between '271,272'. Can you explain this answer?
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An egg with a mean diameter of 4 cm and initially at 25°C is placed in a boiling water pan for 4 minutes and found to be boiled to the consumer’s taste. For how long (in seconds) should a similar egg for the same consumer be boiled when taken from a refrigerator at 5°C? Use lumped parameter theory and presume the following properties for eggk = 12 W/m-°Ch = 125 W/m2-°Cc = 2kJ/kg-KAnd ? = 1250 kg/m3a)271b)272Correct answer is between '271,272'. Can you explain this answer? for Chemical Engineering 2024 is part of Chemical Engineering preparation. The Question and answers have been prepared according to the Chemical Engineering exam syllabus. Information about An egg with a mean diameter of 4 cm and initially at 25°C is placed in a boiling water pan for 4 minutes and found to be boiled to the consumer’s taste. For how long (in seconds) should a similar egg for the same consumer be boiled when taken from a refrigerator at 5°C? Use lumped parameter theory and presume the following properties for eggk = 12 W/m-°Ch = 125 W/m2-°Cc = 2kJ/kg-KAnd ? = 1250 kg/m3a)271b)272Correct answer is between '271,272'. Can you explain this answer? covers all topics & solutions for Chemical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An egg with a mean diameter of 4 cm and initially at 25°C is placed in a boiling water pan for 4 minutes and found to be boiled to the consumer’s taste. For how long (in seconds) should a similar egg for the same consumer be boiled when taken from a refrigerator at 5°C? Use lumped parameter theory and presume the following properties for eggk = 12 W/m-°Ch = 125 W/m2-°Cc = 2kJ/kg-KAnd ? = 1250 kg/m3a)271b)272Correct answer is between '271,272'. Can you explain this answer?.
An egg with a mean diameter of 4 cm and initially at 25°C is placed in a boiling water pan for 4 minutes and found to be boiled to the consumer’s taste. For how long (in seconds) should a similar egg for the same consumer be boiled when taken from a refrigerator at 5°C? Use lumped parameter theory and presume the following properties for eggk = 12 W/m-°Ch = 125 W/m2-°Cc = 2kJ/kg-KAnd ? = 1250 kg/m3a)271b)272Correct answer is between '271,272'. Can you explain this answer? for Chemical Engineering 2024 is part of Chemical Engineering preparation. The Question and answers have been prepared according to the Chemical Engineering exam syllabus. Information about An egg with a mean diameter of 4 cm and initially at 25°C is placed in a boiling water pan for 4 minutes and found to be boiled to the consumer’s taste. For how long (in seconds) should a similar egg for the same consumer be boiled when taken from a refrigerator at 5°C? Use lumped parameter theory and presume the following properties for eggk = 12 W/m-°Ch = 125 W/m2-°Cc = 2kJ/kg-KAnd ? = 1250 kg/m3a)271b)272Correct answer is between '271,272'. Can you explain this answer? covers all topics & solutions for Chemical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An egg with a mean diameter of 4 cm and initially at 25°C is placed in a boiling water pan for 4 minutes and found to be boiled to the consumer’s taste. For how long (in seconds) should a similar egg for the same consumer be boiled when taken from a refrigerator at 5°C? Use lumped parameter theory and presume the following properties for eggk = 12 W/m-°Ch = 125 W/m2-°Cc = 2kJ/kg-KAnd ? = 1250 kg/m3a)271b)272Correct answer is between '271,272'. Can you explain this answer?.
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