Radiation

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Question

A surface at temperature $T_{0}$ Kelvin receives power P by radiation from a small sphere at temperature $T > > T_{0}$ and at a distance d. If both T and d are doubled, the power received by the surface will become approximately

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Solution

$P α \frac{T^{4}}{d^{2}}$
When T and d are doubled, power received by the surface $P^{'} α \frac{{(2 T)}^{4}}{{(2 d)}^{2}} α \frac{4 T^{4}}{d^{2}}$
$\Rightarrow P^{'} = 4 P$

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