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Question

If the radius of a star R and it acts as a black body, what would be the temperature of the star, in which the rate of energy production is Q?
(σ for stefan's constant.)

A
(4πR2Qσ) 1/4
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B
(Q4πR2σ) 1/4
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C
Q4πR2σ
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D
(Q4πR2σ) 1/4
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Solution

The correct option is B (Q4πR2σ) 1/4
We know that

σAT4= rate at which black body absorbs energy

Q= rate of energy production (given)

at equilibrium
σAT4=Q

where A=4πr2

T=(Qσ4πr2)1/4

answer B

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