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A 20 cm diameter spherical ball at 800 K is suspended in the air. Assuming that the ball closely approximates a black body. What will be the total amount of radiation emitted by the ball in 5 min in kJ. (σ = 5.67 × 10-8 W/m2K4)
Correct answer is between '875,876.5'. Can you explain this answer?
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Verified Answer
A 20 cm diameter spherical ball at 800 K is suspended in the air. Assu...
Q̇ = σAT4
= 5.67 × 10-8 × π (0.2)2 × (800)4
Q̇ = 2.918 kW
Q = 2.918 × 5 × 60 = 875.54 kJ
Most Upvoted Answer
A 20 cm diameter spherical ball at 800 K is suspended in the air. Assu...
Assuming that the ball is a black body, we can use the Stefan-Boltzmann law to calculate the total amount of radiation emitted by the ball:
P = σAT^4
where P is the power emitted, σ is the Stefan-Boltzmann constant (5.67 x 10^-8 W/m^2K^4), A is the surface area of the sphere (4πr^2), and T is the temperature in Kelvin.
First, we need to convert the diameter of the sphere to its radius:
r = 20 cm / 2 = 10 cm = 0.1 m
Next, we can calculate the surface area of the sphere:
A = 4πr^2 = 4π(0.1 m)^2 = 0.04π m^2
Now we can calculate the power emitted by the sphere:
P = σAT^4 = (5.67 x 10^-8 W/m^2K^4) x (0.04π m^2) x (800 K)^4 = 5.5 W
To find the total amount of radiation emitted in 5 minutes, we can multiply the power by the time:
E = Pt = (5.5 W) x (5 min x 60 s/min) = 1650 J = 1.65 kJ
Therefore, the total amount of radiation emitted by the ball in 5 minutes is 1.65 kJ.
P = σAT^4
where P is the power emitted, σ is the Stefan-Boltzmann constant (5.67 x 10^-8 W/m^2K^4), A is the surface area of the sphere (4πr^2), and T is the temperature in Kelvin.
First, we need to convert the diameter of the sphere to its radius:
r = 20 cm / 2 = 10 cm = 0.1 m
Next, we can calculate the surface area of the sphere:
A = 4πr^2 = 4π(0.1 m)^2 = 0.04π m^2
Now we can calculate the power emitted by the sphere:
P = σAT^4 = (5.67 x 10^-8 W/m^2K^4) x (0.04π m^2) x (800 K)^4 = 5.5 W
To find the total amount of radiation emitted in 5 minutes, we can multiply the power by the time:
E = Pt = (5.5 W) x (5 min x 60 s/min) = 1650 J = 1.65 kJ
Therefore, the total amount of radiation emitted by the ball in 5 minutes is 1.65 kJ.
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A 20 cm diameter spherical ball at 800 K is suspended in the air. Assuming that the ball closely approximates a black body. What will be the total amount of radiation emitted by the ball in 5 min in kJ. (σ = 5.67 × 10-8W/m2K4)Correct answer is between '875,876.5'. Can you explain this answer?
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A 20 cm diameter spherical ball at 800 K is suspended in the air. Assuming that the ball closely approximates a black body. What will be the total amount of radiation emitted by the ball in 5 min in kJ. (σ = 5.67 × 10-8W/m2K4)Correct answer is between '875,876.5'. 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 20 cm diameter spherical ball at 800 K is suspended in the air. Assuming that the ball closely approximates a black body. What will be the total amount of radiation emitted by the ball in 5 min in kJ. (σ = 5.67 × 10-8W/m2K4)Correct answer is between '875,876.5'. 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 20 cm diameter spherical ball at 800 K is suspended in the air. Assuming that the ball closely approximates a black body. What will be the total amount of radiation emitted by the ball in 5 min in kJ. (σ = 5.67 × 10-8W/m2K4)Correct answer is between '875,876.5'. Can you explain this answer?.
A 20 cm diameter spherical ball at 800 K is suspended in the air. Assuming that the ball closely approximates a black body. What will be the total amount of radiation emitted by the ball in 5 min in kJ. (σ = 5.67 × 10-8W/m2K4)Correct answer is between '875,876.5'. 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 20 cm diameter spherical ball at 800 K is suspended in the air. Assuming that the ball closely approximates a black body. What will be the total amount of radiation emitted by the ball in 5 min in kJ. (σ = 5.67 × 10-8W/m2K4)Correct answer is between '875,876.5'. 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 20 cm diameter spherical ball at 800 K is suspended in the air. Assuming that the ball closely approximates a black body. What will be the total amount of radiation emitted by the ball in 5 min in kJ. (σ = 5.67 × 10-8W/m2K4)Correct answer is between '875,876.5'. Can you explain this answer?.
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