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  4. The power received at distance d from a small metallic sphere of radius r(<< d ) and at absolute temperature T is P. If temperature is doubled and distance reduced to half of initial value, then the power received at that point will be

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Q. The power received at distance $d$ from a small metallic sphere of radius $r(<< d$ ) and at absolute temperature $T$ is $P$. If temperature is doubled and distance reduced to half of initial value, then the power received at that point will be

Thermal Properties of Matter

Solution:

Solar constant $\propto \frac{T^{4}}{r^{2}}$
Solar constant equivalent to power received so
$\frac{P_{1}}{P_{2}}=\frac{T_{1}^{4}}{r_{1}^{2}} \times \frac{r_{2}^{2}}{T_{2}^{4}}$
$\frac{P}{P_{2}}=\frac{T^{4}}{r^{2}} \times \frac{(r / 2)^{2}}{(2 T)^{4}}$
$P_{2}=64\, p$