First slide

Radiation

Question

The radiation emitted by a star A is 1000 times that of the sun. If the surface temperatures of the sun and star A are 6000 K and 2000 K respectively, the ratio of the radii of the star A and the sun is:

Moderate

A

300 : 1
B

600 : 1
C

900 : 1
D

1200 : 1

Solution

According to Stefan-Boltzmann law. the energy radiated per second through the surface of area A is given by
$E = {σAT}^{4}$
$\frac{E_{1}}{E_{2}} = \frac{A_{1}}{A_{2}} {(\frac{T_{1}}{T_{2}})}^{4}$
or $10000 = \frac{{r_{1}}^{2}}{{r_{2}}^{2}} {(\frac{2000}{6000})}^{4}$
or $\frac{{r_{1}}^{2}}{{r_{2}}^{2}} = {(30)}^{4}$
or $r_{1} : r_{2} = 900 : 1$

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