SATHEE: Thermal Properties of Matter

Thermal Properties of Matter - Result Question 21

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 $Q$ ?

(a) $Q / 4 π R^{2} σ$

(b) $(Q / 4 π R^{2} σ)^{- 1 / 2}$

(d) $(Q / 4 π R^{2} σ)^{1 / 4}$

[2012]

( $σ$ stands for Stefan’S constant)

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Answer:

Correct Answer: 21. (d)

Solution:

(d) Stefan’s law for black body radiation

$Q = σ e A T^{4}$

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

Here $e = 1$

$A = 4 π R^{2}$

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Thermal Properties of Matter - Result Question 21

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 ?

Answer:

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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 $Q$ ?