Thermal Properties of Matter - Result Question 21

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21. 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 $Q$ ?

======= ####21. 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 $Q$ ?

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed:content/english/neet-pyq-chapterwise/physics/thermal-properties-of-matter/thermal-properties-of-matter—result-question-21.md (a) $Q / 4 \pi R^{2} \sigma$

(b) $(Q / 4 \pi R^{2} \sigma)^{-1 / 2}$

(c) $(4 \pi R^{2} Q / \sigma)^{1 / 4}$

(d) $(Q / 4 \pi R^{2} \sigma)^{1 / 4}$

[2012]

( $\sigma$ stands for Stefan’S constant)

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Answer:

Correct Answer: 21. (d)

Solution:

  1. (d) Stefan’s law for black body radiation

$ Q=\sigma e A T^{4} $

$T=[\frac{Q}{\sigma(4 \pi R^{2})}]^{1 / 4}$

Here $e=1$

$ A=4 \pi R^{2} $