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Q.

If the radius of a star is R and it acts as a black body, what would be the temperature of the star, in whichthe rate of energy production is Q?

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a

Q/4πR2σ

b

Q/4πR2σ−1/2

c

4πR2Q/σ1/4

d

Q/4πR2σ1/4

answer is D.

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Detailed Solution

From Stefan' law,  E=σT4So, the rate of energy production, Q=E×A⇒Q=σT4×4πR2Temperature of star,   T=Q4πR2σ1/4
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If the radius of a star is R and it acts as a black body, what would be the temperature of the star, in whichthe rate of energy production is Q?