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Two black metallic spheres of radius $4 m$ , at $2000 K$ and $1 m$ at $4000 K$ will have ratio of energy radiation as:

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$1 : 1$

$4 : 1$

$1 : 4$

$2 : 1$

answer is A.

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Detailed Solution

$Q = σ A t T^{4}$

$\frac{Q_{1}}{Q_{2}} = \frac{A_{1}}{A_{2}} {(\frac{T_{1}}{T_{2}})}^{4} = \frac{π r_{1}^{2}}{π r_{2}^{2}} {(\frac{T_{1}}{T_{2}})}^{4}$

$= {(\frac{4}{1})}^{2} \times {(\frac{2000}{4000})}^{4} = 16 \times \frac{1}{16} = 1 : 1$

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