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NEET 2012

Exam: NEET
Year: 2012
Subject: Physics
Chapter: Thermal Properties of Matter

NEET 2012 · 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

? (

\sigma

stands for Stefan's constant.)

Options

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

Correct answer

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

Step-by-step solution

From Stefan' law,

E=\sigma T^4

So, the rate energy production

\begin{aligned} & Q=E \times A \\ & Q=\sigma T^4 \times 4 \pi R^2 \end{aligned}

Temperature of star

T=\left(\frac{Q}{4 \pi R^2 \sigma}\right)^{1 / 4}

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