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BITSAT 2013

Exam: BITSAT
Year: 2013
Subject: Physics
Chapter: Thermal Properties of Matter

BITSAT 2013 · Physics · Thermal Properties of Matter

If the radius of a star is R and it acts as a black body, what...

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

?

Options

A $Q / 4 \pi R^{2} \sigma$
B $\left(\mathrm{Q} / 4 \pi R^{2} \sigma\right)^{-1 / 2}$
C $\left(4 \pi R^{2} Q / \sigma\right)^{1 / 4}$
D $\left(\mathrm{Q} / 4 \pi R^{2} \sigma\right)^{1 / 4}$

Correct answer

D. $\left(\mathrm{Q} / 4 \pi R^{2} \sigma\right)^{1 / 4}$

Step-by-step solution

Stefan's law for black bodyradiation

Q=\sigma e A T^{4}

T=

\left[\frac{Q}{\sigma \left(4 \pi R^{2}\right)}

\right]^{1 / 4}

Here

e=1

A=4

\pi

R^{2}

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