Question

A black metal foil is warmed by radiation from a small sphere at temperature $‘T^{\prime }$ and at a distance $‘d^{\prime }$. It is found that the power received by the foil is $P$. If both the temperature and distance are doubled, the power received by the foil will be :

• A. $16P$
• B. $4P$
• C. $2P$
• D. $P$

Answer 1

The correct option is B $4P$

Emissive power of a body is given as : $E=\sigma T^4$
$E\propto \frac{1}{r^2}$
$\frac{T_1^4}{r_1^2}=\frac{T_2^4}{r_2^2}$
$\frac{T_1^4}{r_1^2}=P\Rightarrow \frac{(2T_1{)}^4}{(2r_1{)}^2}=4P$