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 which the rate of energy production is Q?

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a

(Q4πR2σ)14

b

Q4πR2σ

c

(Q4πR2σ)

d

(4πR2Qσ)14

answer is A.

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Detailed Solution

If r is the radius of the star and T is temperature, then the energy emitted by the star per second through radiation in accordance with Stefan's law will be given byAσT4 = 4πr2σT4Q = 4πR2σT4    ⇒  T = (Q4πR2σ)14
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