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A spherical aluminium shell of inside diameter 2 m is evacuated andused as a radiation test chamber. If the inner surface is coated with carbon black and maintained at 600 K, the irradiation on a small test surface placed inside the chamber is:
(Stefan-Boltzmann constant σ = 5.67 × 10-8 W/m2K4)
(Stefan-Boltzmann constant σ = 5.67 × 10-8 W/m2K4)
- a)1000 W/m2
- b)3400 W/m2
- c)5680 W/m2
- d)7348 W/m2
Correct answer is option 'D'. Can you explain this answer?
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A spherical aluminium shell of inside diameter 2 m is evacuated anduse...
Ans. (d) Irradiation on a small test surface placed inside a hollow black spherical chamber = σT4 = 5.67 × 10-8 × 6004 = 7348 W/m2
Most Upvoted Answer
A spherical aluminium shell of inside diameter 2 m is evacuated anduse...
Given:
- Inside diameter of the spherical aluminium shell = 2 m
- Inner surface of the shell is coated with carbon black
- Inner surface temperature of the shell = 600 K
- Stefan-Boltzmann constant (σ) = 5.67 x 10^-8 W/m^2K^4
To find:
The irradiation on a small test surface placed inside the chamber.
Solution:
The irradiation on the test surface can be calculated using the Stefan-Boltzmann law, which states that the power radiated by a black body is proportional to the fourth power of its absolute temperature.
The formula to calculate the irradiation is given by:
Irradiation = σ * (T^4 - T_s^4)
Where:
σ = Stefan-Boltzmann constant
T = Temperature of the test surface
T_s = Temperature of the inner surface of the shell
In this case, the temperature of the test surface is not given, but we can assume it to be the same as the inner surface temperature of the shell, which is 600 K.
Plugging in the values into the formula, we get:
Irradiation = 5.67 x 10^-8 * (600^4 - 600^4)
Simplifying the equation:
Irradiation = 5.67 x 10^-8 * (0)
As we can see, the term (T^4 - T_s^4) evaluates to zero, as the temperatures are the same. Therefore, the irradiation on the test surface will be zero.
However, the given options do not include zero as a possible answer. Therefore, there seems to be an error in the options provided.
Conclusion:
Based on the given information, the irradiation on the small test surface placed inside the chamber is zero.
- Inside diameter of the spherical aluminium shell = 2 m
- Inner surface of the shell is coated with carbon black
- Inner surface temperature of the shell = 600 K
- Stefan-Boltzmann constant (σ) = 5.67 x 10^-8 W/m^2K^4
To find:
The irradiation on a small test surface placed inside the chamber.
Solution:
The irradiation on the test surface can be calculated using the Stefan-Boltzmann law, which states that the power radiated by a black body is proportional to the fourth power of its absolute temperature.
The formula to calculate the irradiation is given by:
Irradiation = σ * (T^4 - T_s^4)
Where:
σ = Stefan-Boltzmann constant
T = Temperature of the test surface
T_s = Temperature of the inner surface of the shell
In this case, the temperature of the test surface is not given, but we can assume it to be the same as the inner surface temperature of the shell, which is 600 K.
Plugging in the values into the formula, we get:
Irradiation = 5.67 x 10^-8 * (600^4 - 600^4)
Simplifying the equation:
Irradiation = 5.67 x 10^-8 * (0)
As we can see, the term (T^4 - T_s^4) evaluates to zero, as the temperatures are the same. Therefore, the irradiation on the test surface will be zero.
However, the given options do not include zero as a possible answer. Therefore, there seems to be an error in the options provided.
Conclusion:
Based on the given information, the irradiation on the small test surface placed inside the chamber is zero.
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A spherical aluminium shell of inside diameter 2 m is evacuated andused as a radiation test chamber. If the inner surface is coated with carbon black and maintained at 600 K, the irradiation on a small test surface placed inside the chamber is:(Stefan-Boltzmann constant σ = 5.67 × 10-8 W/m2K4)a)1000 W/m2b)3400 W/m2c)5680 W/m2d)7348 W/m2Correct answer is option 'D'. Can you explain this answer?
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A spherical aluminium shell of inside diameter 2 m is evacuated andused as a radiation test chamber. If the inner surface is coated with carbon black and maintained at 600 K, the irradiation on a small test surface placed inside the chamber is:(Stefan-Boltzmann constant σ = 5.67 × 10-8 W/m2K4)a)1000 W/m2b)3400 W/m2c)5680 W/m2d)7348 W/m2Correct answer is option 'D'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A spherical aluminium shell of inside diameter 2 m is evacuated andused as a radiation test chamber. If the inner surface is coated with carbon black and maintained at 600 K, the irradiation on a small test surface placed inside the chamber is:(Stefan-Boltzmann constant σ = 5.67 × 10-8 W/m2K4)a)1000 W/m2b)3400 W/m2c)5680 W/m2d)7348 W/m2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A spherical aluminium shell of inside diameter 2 m is evacuated andused as a radiation test chamber. If the inner surface is coated with carbon black and maintained at 600 K, the irradiation on a small test surface placed inside the chamber is:(Stefan-Boltzmann constant σ = 5.67 × 10-8 W/m2K4)a)1000 W/m2b)3400 W/m2c)5680 W/m2d)7348 W/m2Correct answer is option 'D'. Can you explain this answer?.
A spherical aluminium shell of inside diameter 2 m is evacuated andused as a radiation test chamber. If the inner surface is coated with carbon black and maintained at 600 K, the irradiation on a small test surface placed inside the chamber is:(Stefan-Boltzmann constant σ = 5.67 × 10-8 W/m2K4)a)1000 W/m2b)3400 W/m2c)5680 W/m2d)7348 W/m2Correct answer is option 'D'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A spherical aluminium shell of inside diameter 2 m is evacuated andused as a radiation test chamber. If the inner surface is coated with carbon black and maintained at 600 K, the irradiation on a small test surface placed inside the chamber is:(Stefan-Boltzmann constant σ = 5.67 × 10-8 W/m2K4)a)1000 W/m2b)3400 W/m2c)5680 W/m2d)7348 W/m2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A spherical aluminium shell of inside diameter 2 m is evacuated andused as a radiation test chamber. If the inner surface is coated with carbon black and maintained at 600 K, the irradiation on a small test surface placed inside the chamber is:(Stefan-Boltzmann constant σ = 5.67 × 10-8 W/m2K4)a)1000 W/m2b)3400 W/m2c)5680 W/m2d)7348 W/m2Correct answer is option 'D'. Can you explain this answer?.
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