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A spherical black body with a radius of 12 cm radiates 450 W power at 500 K. if the radius were halved and the temperature doubled, the power radiated in watt would be
- a)255
- b)450
- c)900
- d)1800
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A spherical black body with a radius of 12 cm radiates 450 W power at ...
The energy radiated per second by a black body is given by Stefan's Law
Dividing (ii) and (i), we get
Most Upvoted Answer
A spherical black body with a radius of 12 cm radiates 450 W power at ...
Solution:
Given,
Radius of the black body, R1 = 12 cm
Power radiated, P1 = 450 W
Temperature, T1 = 500 K
New values,
Radius of the black body, R2 = R1/2 = 6 cm
Temperature, T2 = 2T1 = 1000 K
Let P2 be the power radiated by the black body for the new values.
We know that the power radiated by a black body is given by Stefan's law as,
P ∝ T^4 A
where P is power radiated, T is the temperature of the black body, and A is the surface area of the black body.
Now,
The surface area of the black body is given by,
A = 4πR^2
where R is the radius of the black body.
So,
P ∝ T^4 R^2
or,
P1/T1^4 R1^2 = P2/T2^4 R2^2
Substituting the given values,
450/500^4 × 12^2 = P2/1000^4 × 6^2
Simplifying,
P2 = 1800 W
Hence, the power radiated by the black body for the new values is 1800 W.
Therefore, the correct option is (D).
Given,
Radius of the black body, R1 = 12 cm
Power radiated, P1 = 450 W
Temperature, T1 = 500 K
New values,
Radius of the black body, R2 = R1/2 = 6 cm
Temperature, T2 = 2T1 = 1000 K
Let P2 be the power radiated by the black body for the new values.
We know that the power radiated by a black body is given by Stefan's law as,
P ∝ T^4 A
where P is power radiated, T is the temperature of the black body, and A is the surface area of the black body.
Now,
The surface area of the black body is given by,
A = 4πR^2
where R is the radius of the black body.
So,
P ∝ T^4 R^2
or,
P1/T1^4 R1^2 = P2/T2^4 R2^2
Substituting the given values,
450/500^4 × 12^2 = P2/1000^4 × 6^2
Simplifying,
P2 = 1800 W
Hence, the power radiated by the black body for the new values is 1800 W.
Therefore, the correct option is (D).
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A spherical black body with a radius of 12 cm radiates 450 W power at 500 K. if the radius were halved and the temperature doubled, the power radiated in watt would bea)255b)450c)900d)1800Correct answer is option 'D'. Can you explain this answer?
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