First slide

Radiation

Question

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?

Moderate

A

$Q / 4 π R^{2} σ$
B

${(Q / 4 π R^{2} σ)}^{- 1 / 2}$
C

${(4 π R^{2} Q / σ)}^{1 / 4}$
D

${(Q / 4 π R^{2} σ)}^{1 / 4}$

Solution

From Stefan' law, $E = σ T^{4}$
So, the rate of energy production,
$Q = E \times A \Rightarrow Q = σ T^{4} \times 4 π R^{2}$
Temperature of star, $T = {(\frac{Q}{4 π R^{2} σ})}^{1 / 4}$

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