The total radiative power emitted by spherical black body with radius $R$ and temperature $T$ is $P$. If the radius is doubled and the temperature is halved, then the radiative power will be
KVPY 2011, Medium
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(a)
Radiative power of a spherical body is given by
$P=\sigma A T^4$
$=\sigma 4 \pi R^2 T^4$
$\Rightarrow \quad P \propto R^2 T^4$
When temperature is halved and radius is doubled, then power becomes
$P^{\prime} =P \times(2)^2 \times\left(\frac{1}{2}\right)^4$
$=P\left(\frac{4}{16}\right)=\frac{P}{4}$
So, power is reduced to $\frac {1}{4}$ th.
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