A black metal foil is warmed by radiation from a small sphere at temperature $T$ and at a distance $d$. It is found that the power received by the foil is $`P$ '. If both the temperature and the distance are doubled, the power received by the foil will be
Diffcult
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(b) Energy received per second i.e., power $P \propto ({T^4} - T_0^4)$
==> $P \propto {T^4}$
Also energy received per sec (p)$ \propto \frac{1}{{{d^2}}}$
(inverse square law)
==> $P \propto \frac{{{T^4}}}{{{d^2}}}$
==> $\frac{{{P_1}}}{{{P_2}}} = {\left( {\frac{{{T_1}}}{{{T_2}}}} \right)^4} \times {\left( {\frac{{{d_2}}}{{{d_1}}}} \right)^2}$
==> $\frac{P}{{{P_2}}} = {\left( {\frac{T}{{2T}}} \right)^2} \times {\left( {\frac{{2d}}{d}} \right)^2} = \frac{1}{4}$
==>${P_2} = 4P.$
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