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  4. Two spherical black bodies have radii ‘r1’ and 'r2' . Their surface temperatures are 'T1' and 'T2'. If they radiate same power then (r2/r1) is

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Q. Two spherical black bodies have radii $‘r_1’$ and $'r_2'$ . Their surface temperatures are $'T_1'$ and $'T_2'$. If they radiate same power then $\frac{r_2}{r_1}$ is

MHT CETMHT CET 2017

Solution:

$P _{1}= A \sigma T _{1}^{4}=\pi r _{1}^{2} \sigma T _{1}^{4}$
$P _{2}= A \sigma T _{2}^{4}=\pi r _{2}^{2} \sigma T _{2}^{4}$
$P _{1}= P _{2}$
so $\frac{ r _{2}}{ r _{1}}=\frac{ T _{1}^{2}}{ T _{2}^{2}}$