First slide

Heat transfer-Radiation

Question

The radiation emitted by a star A is 10000 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

Easy

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 $E = {σAT}^{4}$
$\begin{array}{l} ∴ \frac{E_{1}}{E_{2}} = \frac{A_{1}}{A_{2}} {(\frac{T_{1}}{T_{2}})}^{4} \\ 10000 = \frac{r_{1}^{2}}{r_{2}^{2}} {(\frac{2000}{6000})}^{4} \\ \frac{r_{1}^{2}}{r_{2}^{2}} = (30)^{4} \\ r_{1} : r_{2} = 900 : 1 \end{array}$

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