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