Question

A surface at temperature $T_{0}K$ receives power P by radiation from a small sphere at temperature $T>>T_0$ and at a distance d. If both T and d are doubled, the power received by surface will become approximately

• A. P
• B. 2P
• C. 4P
• D. 16P

Answer 1

The correct option is C 4P

$P\propto \frac{T^4}{d^2}$
When T and d are doubled, then power received by the surface
$P^{\prime }\propto \frac{(2T{)}^4}{(2d{)}^2}\propto \frac{2^4{T}^4}{2^2{d}^2}\propto \frac{4T^4}{d^2}$
Hence, $P^{\prime }=4P$
Hence, the correct answer is option (c).