All bodies radiate heat in proportion to the fourth power of temperature T. If a body (coated black) at 400 K surrounded by atmosphere at 300 K has cooling rate $r_{0}$ , the same body at 900 K, surrounded by the same atmosphere, will have cooling rate closest to

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$16 r_{0}$

$4 r_{0}$

$81 r_{0} / 16$

$1296 r_{0} / 35$

answer is A.

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Detailed Solution

According to Stefan's law
$r_{0} = σ (400^{4} - 300^{4})$ and $r = σ (900^{4} - 300^{4})$
$∴ r = [\frac{(900^{4} - 300^{4})}{(400^{4} - 300^{4})}] r_{0} = 1296 r_{0} / 35$

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