Question

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 :

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

Answer 1

Answer: (B)

$4P$

As we know that emissive power of body is given as: $E=\sigma T^4$
and they are kept at some known distance so $E\propto \frac{1}{r^2}$
now if the temperature and distances are $T$ and $r$ the power received is $P$ and when both temperature and distance increased twice,we get the mathematical relation
$\frac{T_1^4}{r_1^2}=\frac{T_2^4}{r_2^2}$
So, $\frac{T_1^4}{r_1^2}=P$
Then $\frac{({2T}_1{)}^4}{({2r}_1{)}^2}=4P$